HMT QUESTON BANK Unit – I Conduction · HMT QUESTON BANK Unit – I Conduction 1. State the laws governing three basic modes of Heat transfer 2. Write the 3-D heat conduction equation

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Department of Mechanical Engineering, University Visvesvaraya College of Engineering, Bangalore-01.

HMT QUESTON BANK

Unit – I Conduction

1. State the laws governing three basic modes of Heat transfer

2. Write the 3-D heat conduction equation in Cartesian co-ordinate system. Explain the terms Involved.

3. What is thermal diffusivity? Explain is importance in heat conduction problems.

4. Describe different types of boundary conditions applied to heat conduction problems.

5. Consider one dimensional steady state heat conduction in a plate with constant thermal conductivity in a

region 0 ≤ x ≤ L. A plate is exposed to uniform heat flux q W/m2 at x=0 and dissipates heat by convection at x

= L with heat transfer coefficient h in the surrounding air at T∞. Write the mathematical formulation of this

problem for the determination of one dimensional steady state temperature distribution within the wall.

6. Explain the modes of heat transfer with corresponding basic governing equations.

7. Derive 3-dimensional heat conduction equation in Cartesian co-ordinates for an isotropic material.

8. Explain briefly the mechanism of conduction, convection and radiation heat transfer

9. With sketches, write down the mathematical representation of three commonly used different types of

boundary conditions for one dimensional heat equation in rectangular Coordinates.

10. A plate of thickness ‘L’ whose one side is insulated and the other side is maintained at a temperature T1 is

exchanging heat by convection to the surrounding area at a temperature T2, with atmospheric air being the

outside medium. Write mathematical formulation for one dimensional, steady state heat transfer, without

heat generation.

11. Write down 3-dimensional conduction equation in Cartesian coordinates. Explain the meaning of each term.

12. What do you mean by initial conditions and boundary conditions of 1st, 2nd & 3rd kind?

13. What are the different types of boundary conditions? Explain them with suitable sketches for one dimensional heal conduction.

14. Consider à solid cylinder of radius r = b in which energy is generated at a constant rate of 15. Go W/m3, While, the boundary surface at r = b is maintained at a constant temperature T2. Develop an

expression for the one-dimensional radial steady state temperature distribution T(r) and the heat flux q(r) 16. Starting from fundamental principles, derive the general, three-dimensional heat conduction Equation in

Cartesian co-ordinates 17. A liquid at 100°C flows through a pipe of 40 mm outer and 30 mm inner diameter. The thermal conductivity

of pipe material is 0.5 W/mK. The pipe is exposed to air at 40°C - The inner and outer convective heat transfer coefficients are 300 W/m2K and 5 W/m2K respectively. Calculate the overall heat transfer coefficient and the heat loss per unit length of pipe

18. What is the technical need have undertaken a detailed study of heat transfer, having studied thermodynamics already?

19. Explain briefly: 1) Thermal conductivity 2) Thermal diffusivity 3) Overall heat transfer co-efficient.

20. Derive the general three dimensional conduction equation in Cartesian co-ordinates and state the assumptions made.

21. A square plate heater of size 20 cm x 20 cm is inserted between two slabs Slab ‘A’ is 3 cm thick (K = 50 W/mK) and slab ‘B’ is 1.5cm (K = 0.2 W/mK), The outside heat transfer co-efficient on both sides of A and B are 200 and 50 W/m2K respectively. Temperature of surrounding air is 25°C, if the rating of the heater is 1 kW, find i) Maximum temperature in the system. ii) Outer surface temperature of two slabs. Draw the equivalent circuit for the system.

22. Derive general 3-dimensional conduction equation in Cartesian co-ordinates. 23. Write the mathematical formulation of one-dimensional, steady-state heat conduction for a hollow sphere

with constant thermal conductivity in the region a ≤ r≤ b, when heat is supplied to the sphere at a rate of ‘qo’

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W/m2 from the boundary surface at r = a and dissipated by convection from the boundary surface at r = b into a medium at zero temperature with a heat transfer coefficient ‘h’.

24. A stream pipe with internal and external diameters 18 cm and 21 cm is covered with two layers of insulation each 30 mm thick with thermal conductivities 0.18 W/m.K and 0.09 W/m.K. The difference in temperature between inside and outside surfaces is 250°C. Calculate the quantity of heat lost per meter length of the pipe if its thermal conductivity is 60 W/m.K. What is the percentage error if the calculation is carried out considering the pipe as a plane wall?

25. Explain briefly: i) Thermal conductivity ii) Thermal diffusivity iii) Thermal contact resistance. 26. The walls of a house in cold region consist of three layers, an outer brick work 15 cm thick, an inner wooden

panel 1.2 cm thick, the intermediate layer is made of an insulating material 7 cm thick. The thermal conductivity of brick and wood are 0.7 W/mk and 0.18 W/mk respectively. The inside and outside temperatures of the composite wall are 2 1 °C and - 1 5 °C respectively. If the layer of insulation offers twice the thermal resistance of the brick wall, calculate, i) Heat loss per unit area of the wall. ii) Thermal conductivity of insulating material

27. An insulated steam pipe having outside diameter of 30 mm is to be covered with two layers of insulation, each having a thickness of 20 mm. The thermal conductivity of one material is 3 times that of the other. Assuming that the inner and outer surface temperatures of composite insulation are fixed, how much heat transfer will be increased when the better insulation material is next to the pipe than when it is at the outer layer?

28. Derive the general form of one dimensional heat transfer conduction differential equation in spherical co-ordinates.

29. Consider a cylindrical wall with inside radius r1 and outside radius r2. The inner surface is heated uniformly at a rate of qi W/m2. The outside surface is in contact with a fluid at a uniform temperature T∞ and a surface heat transfer co-efficient of h∞ W/m2°K. Write the governing differential equation and boundary conditions to determine one dimensional steady state temperature distribution in the radial direction.

30. The hot combustion gases of a furnace are separated from the ambient air at 25°C by a brick wall of 0.15 m thick. The brick has a thermal conductivity of 1.032 W/m°K and a surface emissivity of 0.8 under steady state conditions. The gas-side surface temperature is 800°C. Free convection heat transfer coefficient at the air-side surface and air is 17.2 W/m2°K. What is the surface temperature of the brick wall on the air side? Take σ = 4.876 x 108 W/m2°K4.

31. Derive the general heat conduction equation in Cartesian coordinates. 32. Compare the heat loss from an insulated and an uninsulated copper pipe under the following conditions: The

pipe (k = 400Wm °C) has an internal diameter of 10cm and an external diameter of 12cm. Saturated steam flows inside the pipe at 110°C with heat transfer coefficient 10000 W/m2 °C. The pipe is located in a space at 30°C and the heat transfer coefficient on its outer surface is estimated to be 15W/m2 °C. The insulation available to reduce heat transfer is 5cm thick and its thermal conductivity is 0.2W/m °C.

33. Explain the modes of heat transfer with corresponding basic governing equations. 34. A hollow sphere is made up of steel having thermal conductivity of 45W/m°C. It is heated by means of a coil

of resistance 100Ω which carries a current of 5 amperes. The coil is located inside the hollow space at the centre. The outer surface area of the sphere is 0.2m2 and its mass is 32kg. Assuming the density of the sphere material to be 8 gm/cc, calculate the temperature difference between the inner and outer surfaces.

35. Derive an expression for the temperature distribution and the rate of heat transfer for a hollow cylinder. 36. An electrical resistance of mattress type is inserted in between two slabs of different materials on a panel

heater. On one side, the material has a thermal conductivity of 0.174W/mK and 10mm thick. On the other side of the heater the material has a thermal conductivity of 0.05W/mK and 25mm thick. The convection heat transfer co-efficient from the thinner and thicker slabs are 23.26 and 11.63 W/m2K. The temperature of the surrounding air on both the sides is 15°C. If the energy dissipation for each square meter of the mattress is 5kw, neglecting edge affects, find (i) the surface temperature of the slab. (Ii) The temperature of the mattress assuming it to be the same as the inner surface of the slabs.

37. Two bodies of thermal conductivity K1 and K2 are brought into thermal contact. Neglect the thermal contact resistance. Formulate this as steady— state, one— dimensional, no heat generation problem. (04 Marks)

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38. A wall of a furnace is made up of inside layer of silica brick 120mm thick covered with a layer of magnesite brick 240 mm thick. The temperatures at the inside surface of silica brick wall and outside surface of magnesite brick wall are 725°C and 110°C respectively. The contact thermal resistance between the two walls at the interface is 0.0035°C/w per unit wall area. If thermal conductivities of silica and magriesite bricks are 1 .7w/m°c and 5.8w/m°c, Calculate: j) the rate of heat loss unit area of walls and ii) the temperature drop at the interface.

39. Derive 3-dimensional heat conduction equation in Cartesian co-ordinates for an isotropic material. 40. Explain the three kinds of boundary conditions needed for the analysis of heat conduction problems. 41. Explain: i) Radiation heat transfer coefficient, ii) Three kinds of boundary conditions, iii) Critical thickness of

insulation, 42. Using the method of formulation, obtain an expression for the temperature variation for one dimensional

steady state conduction without heat generation through a plane wall of thickness L, constant thermal conductivity K and whose faces are maintained at temperatures T1 and T2.

43. A hollow sphere of pure iron contains a liquid chemical mixture which releases 8000 watts. Inside diameter of the sphere is 120mm and outside diameter of the sphere is 240 mm. Steady state conditions prevail and outside surface temperature of the sphere is 60C. Determine the temperature at a Location 30 mm from the outside surface of the sphere. Assume material of sphere has a thermal conductivity of 75 W/mK & heat release by the chemical mixture is constant.

44. State the assumptions and derive the most general three dimensional heat conduction equations in Cartesian coordinates.

45. a. Explain 1) Convective heat transfer coefficient 2) Radiation heat transfer coefficient 3) Combined heat transfer mechanism.

46. What do you mean by Boundary conditions of First, Second and Third kind? 47. The inside surface of an insulating layer is at 270°C & the outside surface is dissipating heat by convection

into air at 20C. The insulation is 4Omm thick and has thermal conductivity 1.2 W/mC. What is the minimum value of heat transfer coefficient at the outside surface, if the surface temperature should not exceed 70°C? Also calculate the rate of heat transfer

48. A furnace wall is made up of inside silica brick (K – 1.6W/m K). Outside magneta brick (K — 4.8 W/m k), 10cm thick each. The inside and outside surfaces are exposed to fluid temperatures of 820C and 120°C respectively. Find the heat flow through the wall per m2 per hour. Assume a contact resistance of 0.002m2/W, Draw the temperature profile through the composite wall. The inside and outside heat transfer coefficients are 35W/m K and 12 W/mK respectively.

49. Compare the heat loss form an insulated and an un-insulated copper pipe under the following conditions: The pipe (K 400 W/m°C) has an intimal diameter of 10cm and an external diameter of 12cm. Saturated steam flows inside the, pipe at 110°C with heat transfer co-efficient 10000 W/m2 °C The pipe is located in a space at 30°C and the heat transfer co-efficient on its outer surface is estimated to be 15W/m2 °C. The insulation available to reduce heat transfer is 5cm thick and its thermal conductivity is 0,2W/m°C.

50. By writing an energy balance for a 1-D volume element, derive the one dimensional time dependent heat conduction equation with internal energy generation and variable thermal conductivity iii a rectangular coordinate system for the ‘x’ variable.

51. Calculate the rate of heat flow per m2 through a furnace wall consisting of 200 mm thick inner layer of chrome brick, a centre layer of Kaolin brick of 100 mm thick and an outer layer of masonry brick 100 mm thick. The heat transfer coefficient at the inner surface is 74 W/m2°C and the outer surface temperature is 70°C. The temperature of the gases inside the furnace is 1670°C. What temperatures prevail at the inner and outer surfaces of the centre layer? Take thermal conductivity of chrome brick as 1.25 W/m-°C, thermal conductivity of Kaolin brick as 0.074 W/m-°C and thermal conductivity of masonry brick as 0.555 W/m-°C

52. What do you mean by boundary condition of 1st 2nd and 3rd kind? 53. Compare the heat loss form an insulated and an un insulated copper pipe under the following conditions : flic

pipe ( K — 400 W/mC) has an internal diameter of 10cm and an external diameter of 12cm. Saturated steam flows inside the pipe at 110C with heat transfer co-efficient 10000 W/m2 °C. The pipe is located in a space at

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30C and the heat transfer co-efficient on its outer surface is estimated to be 15W/m2C. The insulation available to reduce heat transfer is 5cm thick and its thermal conductivity is 0.2W/m°C.

54. Derive general heat conduction equation in Cartesian co-ordinates. 55. With sketches, write down the mathematical representation of three commonly used different types of

boundary conditions for one-dimensional heat equations in rectangular co-ordinate, 56. A plate of thickness L, whose one side is insulated and the other side is maintained at a temperature T1 is

exchanging heat by radiation to the surrounding area at a temperature T2, with atmospheric air being the outside medium. Write mathematical formulation for one dimension, steady state heat transfer, without heat generation.

57. What are the three boundary conditions used in the analysis of heat conduction problems?

58. Explain the concept of driving potential as applied to heat transfer problems. 59. What are boundary and initial conditions? Explain in brief 60. Derive the general three dimensional heat conduction equation in Cartesian co-ordinate system and hence

obtain Laplace and Poisson equations (10 Marks) 61. A steel tube (k - 43.26 W/mK) of 5.08 Cm I.D and 7.62 cm CD, is covered with a 2.54 cm layer of asbestos

insulation (k=0.208 w/mk) The inside surface of the tube receives heat by conversion from a hot gas at a temperature of T1 = 316°C with a heat transfer coefficient h=284 w/m2K, while the outer surface of insulation is exposed to the ambient air at Th=38C with a heat transfer coefficients of hb=17 w/m2K Calculate i) The heat loss to ambient air for 3m Length of the tube. ii) The temperature drop across the tube material and insulation layer.

62. A hot metal slab, of thickness L and initial temperature ‘To’ is removed from a heat treating furnace and placed in Quenching oil both at temperature ‘T’. The convective heat transfer co—efficient at each face is h. Write the mathematical formulation of the problem.

63. Briefly explain the three modes of Heat Transfer. 64. What is the thickness required of o masonry wall having thermos conductivity of O.75W/(m—K) if the heat

transfer rate is to be 80% of the heat Transfer rate through a composite structural wall having a thermal conductivity of O.25W/(m K) and a thickness of 100mm. Both walls are subjected to the same surface temperature.

65. A hollow sphere of pure iron contains a liquid chemical mixture which releases 8000 watts. If inside diameter of the sphere is 120mm and 8000W and outside diameter of the sphere is 240mm, steady state conditions prevails and outside surface temperature of the sphere is 60°C. Determine the temperature at a location 30mm from the outside surface of the sphere. Assume material of sphere has 75W/mk thermal conductivity and heat release by the chemical mixture is constant.

66. A plane wall of Thickness L and with constant thermal properties is initially at a uniform temperature T. Suddenly the surface at x = L is subjected to heating by the flow of hot gases at temperature T∞; with the surface heat transfer coefficient h. The other surface at x=0 is kept insulated. Write the mathematical formulation to determine one dimensional transient temperature distribution T(x,t) in the wall.

67. In a semi - infinite cylinder of radius R, the flat surface of the cylinder is insulated and 68. The curved surface is exposed to a medium at 0°C with a surface heat transfer coefficient the cylinder is

generating heat at a uniform rate of qw/m3. Write the governing differential equation and the relevant boundary conditions to determine the two dimensional Steady state temperature distribution T(r, ɵ) the semi- cylinder

69. Write down the three dimensional, heat conduction equations in Cartesian, cylindrical and spherical co-ordinate systems.

70. Calculate the heat loss per square meter area from a composite furnace wall made up of the following materials: 200 mm thick firebrick with K1 = 1.16 W/mK, 15O mm thick insulating brick with K2 =0.1 W/mK. 100mm of red brick K3 = 1.74 W/mK. The outside film coefficient of heat transfer is 20 W/mK. The inside surface temperature of wall is 1200 C and temperature of room air is 50C.

71. Two bodies of thermal conductivities K1 and K2 are brought into thermal contact. Neglect the thermal contact resistance. Draw the sketch and formulate this as steady state, 1D, no heat generation problem.

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72. A 0.8 m high and 1 .5 m wide double plane window consists of two 4 mm thick layers of glass (k = 78 W/m°C), separated by a 10 mm wide stagnant air space (k = 0.026 W/m°C), Determine the rate of heat transfer through this window and the temperature of the inside surface, when the room is maintained at 20 “C and the outside air is at —10 ©C. Take the convention heat transfer co-efficient on the inside and outside surfaces of the window as 10 and 40 W/m°C respectively.

73. A steel tube is covered with a layer of insulation made of asbestos material. This tube is used for the flow of hot gases. The following data is given: ID of steel tube = 75 mm, OD of steel tube 100 mm, Thickness of asbestos layer = 30 mm. Temperature of hot gases = 350°C,Temperature of outside ambient air = 40C, K for steel 50 W/m-K, K of asbestos layer =0. 15 W/m-K, Convective heat transfer coefficients for hot gases and ambient air are 300 and20 W/m2-K respectively. Calculate: i) Overall heat transfer coefficient based on outside surface area ii) Heat loss per metre length of pipe and iii) Temperature drop across the asbestos.

74. A composite wall consists of 10cm layer of building brick (0.7W/m°C) and 3cm plaster(0.5W/m2C). An insulating material of K= 0.08 W/m°C is to be added to reduce the heat transfer through the wall by 70%. Determine the thickness of insulating layer

75. Calculate the rate of heat flow per m2 through a furnace wall consisting of 200 mm thick inner layer of chrome brick, a centre layer of Kaolin brick of 100 mm thick and an outer layer of masonry brick 100 mm thick. The heat transfer coefficient at the inner surface is 74 W/m2°C and the outer surface temperature is 70°C. The temperature of the gases inside the furnace is 1670°C. What temperatures prevail at the inner and outer surfaces of the centre layer? Take thermal conductivity of chrome brick as 1.25 W/m-°C, thermal conductivity of Kaolin brick as 0.074 W/m-°C and thermal conductivity of masonry brick as 0.555 W/m-°C

76. A furnace has a composite wall constructed of a refectory material for the inside layer and an insulating

material on the outside. The total wall thickness is limited to 60 cm. The mean temperature of the gases

within the furnace is 850°C, the external ambient temperature is 30°C and the interface temperature is

500°C. The thermal conductivities of refractory and insulating materials are 2 W/mK and 0.2 W/mK the

combined co-efficient of heat transfer by convection and radiation between gases and the refractory surface

is 200 W/m2K and between outside surface and atmosphere is 40 W/m2K. Find:

i) The required thickness of each material.

ii) The rate of heat loss to atmosphere is kW/ma.

iii) The temperatures of the external and internal surfaces.

77. An industrial freezer is designed to operate with an internal air temperature of -20°C when the external air temperature is 25°C and the internal and external heat transfer coefficients are 12 W/m2°C and 8 W/m2°C, respectively. The wall of the freezer are composite construction, comprising of an inner layer of plastic 3 mm thick with thermal conductivity of 1 W/m°C. An outer layer of stainless steel of thickness 1 mm and thermal conductivity of 16W/m°C. Sandwiched between these layers is a layer of insulation material with thermal conductivity of 0.07W/m°C. Find the width of the insulation required to reduce the convective heat loss to 15 W/m2.

78. Derive an expression for one dimensional, steady state temperature distribution T(x) in a slab of thickness L for the following conditions : heat is generated in the slab at a constant rate of go W/mk. the boundary surface at x = 0 is kept insulated and the boundary surface at x = L is kept at 0 temperatures. Assume constant thermal conductivity. Give the relations for the temperature of the insulated boundary. Calculate the temperature of insulated surface for K = 40 W/mC , go 10 W/m3 and L =0. 1m.

79. The outside dia steam pipe is to be covered with two layers of insulation each having thickness of 25 mm. The average thermal conductivity of one insulating material is five times that of the other; Determine the percentage decrease in heat transfer if better insulating materials is put next to the pipe than when it forms the outer layer. Assume that the outside and inside surface temperatures of the composite insulation are fixed

80. Derive an expression for rate of heat transfer and temperature distribution for a plane wall of non-uniform thermal conductivity undergoing one dimensional steady state heat conduction.

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Unit – convection

1. Derive an expression for critical thickness of insulation for a cylinder. Discuss the design aspects for providing

insulation scheme for cable wires and steam pipes.

2. Find the amount of heat transferred through an iron fin of thickness of 5 mm, height 50 mm and width 100 cm.

Also determine the temperature difference 13’ at the tip of fin assuming atmospheric temperature of 28°C and

base temperature of fin to be 108°C. Take K = 50 W/mK, h = 10 W/m2K.

3. What is critical thickness of insulation on a small diameter wire or pipe? Explain its physical significance and

derive an expression for the same

4. A set of aluminum fins (K = 180 W/mK) that are to be fitted to a small air compressor. The device dissipates 1

KW by converting to the surrounding air which is at 20°C. Each fin is 100 mm long, 30 mm high and 5 mm thick.

The tip of each fin may he assumed to be adiabatic and a heat transfer coefficient of 15 W/m2K acts over the

remaining surfaces. Estimate the number of fins required to ensure the base temperature does not exceed

120°C.

5. Define critical radius of insulation and derive an expression for critical radius of insulation for a cylinder Explain

the physical significance of critical radius of insulation (08 Marks)

6. b. Explain the following:

i) Thermal resistance.

ii) Variable thermal conductivity.

iii) Fin efficiency.

7. A carbon steel rod of thermal conductivity 54 W/m°C with a cross section of an equilateral triangle having each

side 5 mm is 80 mm long. It is attached to a plane wall which is maintained at a temperature of 400°C. The

surrounding environment is at 50°C and the heat transfer coefficient is 90 W/m2-°C. Compute heat dissipated by

the rod.

8. An electric cable of 10mm diameter is to be laid in atmosphere at 20°C. The estimated surface temperature of

the cable due to heat generation is 65°C. Find the maximum percentage increase in heat dissipation, when the

wire is insulated with rubber having K = 0.155 W/mK. Take h = 8.5 W/m2K.

9. Differentiate between the effectiveness and efficiency of fins

10. In order to reduce the thermal resistance at the surface of a vertical plane wall (50 x 5 0cm), 100 pin fins (1 cm

diameter, 10cm long) are attached. If the pin fins are made of copper having a thermal conductivity of 300

W/mK and the value of the surface heat transfer coefficient is 15 W/m2K, calculate the decrease in the thermal

resistance. Also calculate the consequent increase in heat transfer rate from the wall if it is maintained at a

temperature of 200°C and the surroundings are at 30°C.

11. Obtain an expression for heat transfer through a plane wall in which thermal conductivity is given by K= K0( 1+

aT) , where a is constant, K0 thermal conductivity at reference temperature T is the temperature. (06 Marks)

12. Derive an expression for critical thickness of insulation for a cylinder.

13. A wire of 8mm diameter at a temperature of 60°C is to be insulated by a material having K= 0.174W/mC Heat

transfer coefficient ha 8W/m2 K and ambient temperature T= 25°C For max heat loss find the minimum

thickness of insulation. Find increase in heat dissipation due to insulation.

14. What is the critical thickness of insulation? Derive an expression for critical thickness of insulation for a sphere.

15. Obtain an expression fin temperature distribution and heat flow through a rectangular fin. when the end of fin is

insulated.

16. The temperature of the air stream in a tube is measured, with the help of a thermometer placed into a

protective well filled with oil. The Thermometer well is made of a steel tube (K = 55.8 W/m-K), I200 mm long and

1 .5 mm thick. The heat transfer coefficient between the flowing air and the protective well is 23.3 W/m2-K and

the temperature recorded by the thermometer is 84C. Estimate the error in the measurement if the

temperature at the base of the well is 40°C.

17. A tube an outer diameter of 20 mm is covered with insulation, The thermal conductivity of insulating material is

0. 18W/mK. The outer surface losses heat by convection with a heat transfer coefficient of 12 W/m2K

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Determine the critical thickness of insulation. Also calculate the ratio of heat loss from the tube with critical

thickness of insulation to that from the bare tube (without insulation).

18. Derive the one-dimensional fin equation for a fin of uniform cross section. By integrating the fin equation, obtain

the expression for the temperature variation in a long fin.

19. What is physical significance of critical thickness of insulation? Derive an expression for critical thickness of

insulation for a cylinder.

20. Derive an expression for temperature distribution for a pin fin with the tip insulated.

21. A carbon steel (k= 54 W/ m°C) rod with a cross section of an equilateral triangle (each side 5 mm) is 80 mm

long. It is attached to a plane wall which is maintained at a temperature of 400 C. The surrounding environment

is at a 50 C and unit surface conductance is 90 W/ m°C. Compute the heat dissipated by the rod (assuming tip is

insulated).

22. Derive an expression for the temperature distribution for a long pin of uniform cross section without insulated

tip.

23. b. A rod (K = 200 W/mK) 10 mm in diameter and 5 cms long has its one end maintained at 100°C. The surface of

the rod is exposed to ambient air at 30°C with convective heat transfer co-efficient of 100 W/m2K. Assuming

other end insulated, determine i) the temperature of the rod at 25 mm distance from the end at 100°C. ii) Heat

dissipation rate from the surface of the rod and iii) Effectiveness,

24. Clearly define i) Fin efficiency and ii) Fin effectiveness.

25. Derive an expression for rate of heat transfer and temperature distribution for a plane wall with variable

thermal conductivity. (08 Marks)

26. Thin fins of brass whose K =75 W/mK are welded longitudinally on a 5 cm diameter brass cylinder which stands

vertically and is surrounded by air at 20°C. The heat transfer coefficient from metal surface to the air is 17

W/m2K. If 16 uniformly spaced fins are used each 0.8 mm thick and extending 1.25 cm from the cylinder, what is

the rate of heat transfer from the cylinder per meter length to the air when the cylinder surface is maintained at

150°C?

27. Define fin efficiency and fin effectiveness with respect to a fin with insulated tip. (04 Marks)

28. What is the physical significance of critical thickness of insulation? Derive an expression for critical thickness of

insulation for a sphere.

29. The handle of a ladle used for pouring molten metal at 327°C is 30 cm long and is made of 2.5 cm x 1.5 cm mild

steel bar stock (K =43 W/mK). In order to reduce the grip temperature it is proposed to make a hollow handle of

mild steel plate of 0.15 cm thick to the same rectangular shape. if the surface heat transfer coefficient is 14.5

W/m2K and the ambient temperature is at 27°C, estimate the reduction in the temperature of grip. Neglect the

heat transfer from the inner surface of the hollow shape.

30. Derive an expression for the temperature distribution for a pin fin with the tip insulated.

31. A plane wall is a composite of two materials A and B. the wall of material A has a heat generation If qA = 1 .5 x

106 W/m3 with KA = 75 W/m°K and the thickness LA = 50 mm. The wall of material B has no heat generation

with KB = 150 W/m°K and the thickness LB = 20 mm. The inner surface of material A is well insulated, while the

outer surface of material B is cooled by the water stream with T∞= 30°C and h=1000 W/m2°K. Determine the

temperature T0 of the insulated surface and the temperature T2 of the cooled surface.

32. Derive an expression for the inside overall heat transfer co-efficient for composite sphere considering two layers

and convection transfer on the inside and outside. (08 Marks)

33. A saturated refrigerant at -30°C flows through a copper pipe of 12mm inside diameter and 4mm wall thickness.

A layer of 40mm thick thermocole is provided on the outer surface of the pipe to reduce the heat flow.

Determine the heat leakage into the refrigerant per meter length of pipe. The ambient temperature is 35°C.

Assume internal and external heat transfer coefficients to be 450 and 6 W/m2K respectively. k(copper) = 410

W/mk ; k(thermocole) = 0.0295 W/mK. Find the amount of refrigerant vaporized per hour per meter length of

pipe when the pipe is covered and the pipe is bare. (Take latent heat of evaporization at -30° = 267 kJ/kg.

34. Design critical thickness of insulation and derive an expression for critical thickness of insulation for a cylinder. .

(10 Marks)

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35. b. A wire of 6.5 mm diameter at a temperature of 60°C is to be insulated by a material having K = 0.174 w/m°c.

Convection heat transfer coefficient 8.722 w/m2°c. The ambient temperature is 20°C. For maximum heat loss,

what is the minimum thickness of insulation and heat loss per meter length? Also find percentage increase in

heat dissipation.

36. Derive an expression for the temperature distribution for a pin fin, when the tip of the fin is insulated,

37. Derive the differential equation governing the temperature distribution for a fin of uniform cross section by

assuming thermal conductivity, the heat transfer coefficient and the ambient temperature being constant.

Hence obtain the expression (for the heat transfer and temperature distribution for a short fin insulated at the

tip,

38. b. A steel pipe of 220mm OD is carrying steam at 280C. It is insulated with a material with K=0.06[1+0.0018T]

where ‘K’ is in W/m °K. Thickness of insulation is 50mm and the outer surface temperature is 50C. Determine

the heat flow per ‘m’ length of the pipe and the temperature at the mid thickness of the pipe.

39. Define critical thickness of insulation. Derive an expression for critical thickness of insulation for a sphere.

40. An electric motor drives a centrifugal pump which circulates a hot liquid metal at 480°C. The motor is coupled to

the pump impeller by a horizontal steel shaft [K = 32 W/m°C] 25 mm in diameter. If the ambient air temperature

is 20°C, the temperature of the motor is limited to a maximum value of 55°C and heat transfer coefficient

between steel shaft and ambient air is 14,8 W/m2 °C what length of shall should be specified between motet

and pump?

41. Derive expression for temperature distribution and heat transfer rate for a fin of circular cross section with

insulated tip.

42. In a conductivity measurement experiment two identical long rods are used. One rod is made of Aluminum ( K =

200 W/m K). The other rod is the specimen. One end of both rods is fixed to a wall at 100C and they are

suspended in air at 25°C. The steady temperature at same distance along the rods were measured and found to

be 75°C on aluminum rod and 60°C on the specimen rod, Find K of the specimen.

43. Find an expression for steady state heat flow in a plane wall for which thermal conductivity varies according to

� = ��

� . Where Ko is constant and L is the wall thickness. The temperature on the two sides of the wall is T1 & T2. (

44. b. In a cylindrical fuel rod of a nuclear reactor, heat is generated initially according to the equation �� =

�� 1 − ��

��

�� . Where qg is the local rate of heat generation per unit volume at radius r’, R is the outside radius

and q is the rate of heat generation per unit volume at the centre line. Calculate the temperature drop from the centre line to the surface for a 25 mm outer dia fuel rod having thermal conductivity of 25 W/m K, if the rate of heat removal from the surface is 1650 kW /m’.

45. Obtain the expressions for temperature distribution and heat dissipation Iron a fin of circular cross section with

insulated tip.

46. There are longitudinal fins of thickness 5 mm, height 25mm and length 500 mm on a wall. the wall temperature

is 56 C and ambient temperature is 26 C, Determine the heat dissipation from a fin. take h= 25W/m2K and K =

3OW/mK,

47. What is the physical significance of critical thickness of insulation? Derive an expression

48. for critical thickness of insulation put on an electrical cable.

49. The thermal conductivity of a certain material varies according to the relation K = Ko[1+αT], where α is constant

and K0, is thermal conductivity at some reference temperature arid T is the temperature. Derive an expression

for heat loss from a hollow cylinder made up of this material with inner radius “a” and outer radius “b”.

50. Obtain the expressions for temperature distribution and heat dissipation from a fin of circular cross section with

insulated tip.

51. A casing of electric motor is an approximate cylinder of 250 mm dia and 500 mm long. There are 30 equi-spaced

longitudinal fins of thickness 5 mm and height 25 mm on the periphery of the casing. If the casing temperature is

56°C and ambient temperature is 26°C, determine the heat dissipation from the casing body. (Neglect the

circular plane surface on either side). take h =25 W/m2K and kfin= 30 W/m K.

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52. For a material with variable thermal conductivity, show that:

� = −1

�+ ��

1

�� + �1�

�

−2��

��

53. A furnace wall is made up of three layers of thicknesses 250mm, 100mm and 150mm with thermal

conductivities 1.65, K and 9.2 W/m°C respectively. The inside is exposed to gases at 1250°C with a convection

coefficient of 25 W/m2°C and the inside surface is at 1100°C, the outside surface is exposed to air at 25°C with

convection coefficient of 12 W/m2°C, determine:

i) Unknown thermal conductivity K

ii) The overall heat transfer coefficient

iii) All surface temperatures.

54. Obtain an expression for temperature distribution and heat flow through a rectangular Fin, when the end of flu

is insulated (12 Marks)

55. The aluminium square fins (0.5 rum X 0.5 mm). 10 mm long Are provided on the surface of semiconductor

electronic device to carry 1 W of energy generated: The temperature at the surface of the device should not

exceed 80 C, when the surrounding temperature is 40C. K(aluminium) = 200 W/m°C; h = 15 W/m2 C Determine

the number of fins required To carry out the above duty. Neglect the heat loss from the end of the fin,

56. An electric motor drives a centrifugal pump which circulates a hot liquid metal at 480C. the motor is coupled to

the pump impeller by a horizontal steel shaft [K = 32 W/m°C] 25 mm in diameter. if the ambient air temperature

is 2OC, the temperature of the motor is limited to a maximum value of 55°C and heat transfer coefficient

between steel shall and ambient air is 14.8 W/m2 °C. what length of shall should be specified between motor

and pump?

57.

58. What is critical thickness of insulation on a small diameter wire or pipe? Explain its physical significance.

59. A steel tube carries steam at a temperature of 300C. A thermometer pocket of iron [K= 52.3 W/m-k] of inside

diameter of 16 mm and thickness 1mm is used to measure the temperature. The error to be tolerated is 2% of

maximum. Calculate the length of pocket required to measure temperature within this error. How should the

thermometer be located? take the tube wall temperature as 130C and diameter as 90 mm. Assume the

convective heat transfer co-efficient as 95 W/m2-K.

60. Explain the significance of the critical thickness of insulation and derive an expression for the critical thickness of

insulation for a cylinder. (QN Mark5)

61. A cylinder 1m long and 5cm in diameter is placed in an atmosphere at 45°C, it is provided with 10 longitudinal

straight fins of material giving k=120 w/mk. The height of 0.76 mm thick fins is 1.27 Cm from the cylinder

surface. the heat transfer coefficient between cylinder and atmospheric air is 17W/m2K. Calculate the rate of

heat transfer and the temperature at the end of fins if surface temperature of cylinder is 150°C.

62. An electric cable of 10mm diameter is to be laid in atmosphere at 20°C. The estimated surface temperature of

the cable due to heat generation is 65°C. Find the maximum percentage increase in heat dissipation when the

wire is insulated with rubber having k = 0.155 W/mK. Take h= 8.5 w/m2k,

63. Derive an expression for the temperature distribution and rate of heat transfer from a fin of’ uniform cross

section. Neglect the heat transfer from the end of the fin.

64. One end of a long rod 1 cm diameter is maintained at a temperature of 500°C, by placing it in a furnace. The rod

is exposed to air at 30°C with a heat transfer coefficient of 35 W/mK. The temperature measured at a distance of

78.6 mm was 147 C. Determine the thermal conductivity of the material.

65. A composite cylindrical wall is composed of two materials of thermal conductivity KA and KB. A thin electric

resistance heater for which interfacial contact resistances are negligible separates the two materials. Liquid

pumped through the inner tube is at temperature with the inside surface heat transfer coefficient hi. The outer

surface of the composite wall is exposed to an ambient at a uniform temperature to with a surface heat transfer

coefficient ho. Under steady state conditions of uniform heat flux of q is dissipated by the heater.

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66. Sketch the equivalent thermal circuit for the composite wall and express oh thermal resistances in terms of the

relevant variable’s. Obtain on expression that may be used to determine the temperature of the heater.

67. Derive an expression for the inside overall heat transfer co-efficient for composite sphere considering two layers and convection transfer on the inside and outside. (8 Marks)

68. A saturated refrigerant at —30°C flows through a copper pipe of 12mm inside diameter and 4mm wall thickness. A layer of 40mm thick thermocole is provided on the outer surface of the pipe to reduce the heat flow. Determine the heat leakage into the refrigerant per metre length of pipe . If the ambient temperature is 35°C. Assume internal and external heat transfer co-efficient to be 450 and 6 W/m2k respectively. k(copper) = 410 W/mk ; k(thermocole) = 0.0295 W/mK. Find the amount of refrigerant vaporized per hour per metre length of pipe when the pipe covered and the pipe is bare. (Take latent heat of evaporization at -30= 267 kJ/kg.)

69. A 3 meter inside dia spherical tank made of 20 mm thick stainless steel (K 15 W /m K) is used to store iced water at 0C. The tank is located in a room whose temperature is 22° C. The walls of the room are also at 22C. The outer surface of the tank is black and heat transfers between the cooler surface of the tank and the surroundings are by natural convection and radiation. the convection heat transfer coefficient at the inner and outer surfaces of the tank are 80 W/m2 K and 10 W/m2 K respectively. The radiation heat transfer coefficient at the outer surface of the tank is 5.24 W /m2 K. Determine —i) Rate of heat transfer to the iced water in the tank ii) the amount of ice at 0C that melts during 24 hour period. Assume latent heat of ice as 334 kj /kg.

70. Aluminium fins of rectangular profile are attached to a plane wall with 5mm spacing. The fins have thickness of 1mm length 10mm and thermal conductivity of 200W/(m — K). The wall is maintained at a uniform temperature of 200C and the fins dissipate heat by convection into an ambient at 40°C with a surface heat transfer coefficient of 50W/m2K. Determine i) The fin efficiency and. ii) The heat loss from the plane wall per m2 of the wall surface. Neglect The heat loss from the fin tip

71. Derive an equation for temperature distribution and heat flow through a fin of rectangular C.S.

Unit -3

1. Define Biot number and explain its significance. 2. Derive an expression for the instantaneous and total heat flow in terms of the product of Biot number and

Fourier number is one dimensional transient heat conduction. 3. Aluminium rod of 5 cm diameter and 1 metre long at 200°C is suddenly exposed to a convective

environment at 70°C. Calculate the temperature of a radius of 1 cm and heat lost per meter length of the rod 1 minute after the cylinder is exposed to the environment properties of At p = 2700 kg’m3. Cr 900J/KG-K, K - 215 W/m-K, h = 500 W/mK. α = 8.5 x 10-5 m2/S.

4. What are Biot and Fourier numbers? Explain their physical significance. 5. What are Heisler charts? Explain their significance in solving transient convection problems. 6. The temperature of a gas stream is measured with a thermocouple. The junction may be approximated as a

sphere of diameter 1 mm, K = 25 W/m°C, p = 8400 kg/m3 and C = 0.4 kJ/kg°C. The heat transfer coefficient between the junction and the gas stream is h — 560 W/m2°C. How long will it take for the thermocouple to record 99% of the applied temperature difference?

7. What is lumped parameter analysis? Prove that the temperature distribution at time t during Newtonian

heating is given by, ��

��= ��, where T0 is the temperature at t = 0.

8. A 5 cm thick iron plate is initially at temperature of 225°C. It is suddenly exposed to an ambient at 25°C with heat transfer coefficient of 500 W/m2-°C. Determine the centre temperature at t =2 min after the start of the cooling. Calculate the temperature at a depth of 1 cm from the surface at t =2 min after the start of the cooling. Also calculate the energy removed from the plate per square metre during this time. Take properties of iron as K= 60 W/m-°C, Cp= 460 J/kg-K, p= 7850 kg/m3, and α = 1.6x10-5 m2/s.

9. Show that the temperature distribution in a body during Newtonian heating or cooling is given by ��

��=

�

��= ��

��

��

10. The steel ball bearings (K = 50 W/mK, α = 1.3 x 105 m2/sec), 40mm in diameter are heated to a temperature of 650°C. It is then quenched in an oil bath at 50°C, where the heat transfer coefficient is estimated to be

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300 W/m2K. Calculate: j) The time required for bearings to reach 200°C. The total amount of heat removed from a bearing during this time and iii) the instantaneous heat transfer rate from the bearings, when they are first immersed in oil bath and when they reach 200°C.

11. Obtain an expression for instantaneous heat transfer and total heat transfer for lumped heat analysis treatment heat conduction problem

12. Explain physical significance of Biot and Fourier numbers. (06 Marks 13. A household electric iron (p = 2700 kg/m3, Cp= 0.896 kJ/kg K and K = 200W/m°C) and weighs 1.5 kg. The

total area of iron is 0.06m2 and it is heated with 500W heating element. Initially the iron is at 25°C (ambient Temp). How long it takes for the iron to reach 110°C. Take h =15W/m2K.

14. Derive an expression for temperature distribution in a lumped system. Also derive equations for instantaneous rate of heat flow and to energy transfer for the given time.

15. A person is found dead at 5 PM in a room which is at 20°C. The temperature of body is measured to be 25°C when found and the heat transfer coefficient is estimated to be 8 W/m2- K. Modelling the body as a short cylinder of 30 cm dia and 1.7m long, estimate the time of death of that person. Use the lumped system of analysis and assume the following properties: K= 0.617 W/m-K, S=996 kg/m3. C= 4187 J/kg-K, Temperature of the body before died = 37C. (05 Marks)

16. One surface of a thick Nickel steel (K = 19 W/m-K. α= 0.52x 10-5 m2/s) slab which is initially at 30°C, is suddenly raised to a temperature of 530°C. By treating this as a one- dimensional transient conduction problem in a semi—infinite medium, determine the temperature a depth of 50 min after a time of 50 seconds.

17. Consider a solid, with a uniform initial temperature, suddenly immersed in a Liquid. Derive the relevant governing differential equation, considering the system as lumped. By solving the differential equation, obtain the expression for the temperature variation with time.

18. A 50 mm thick iron plate (K=60 W/mK. Cp=460 j/kg K, ρ=7800 kg/m3, α= 1.6x10-5m2/s) is initially at 225°C- Suddenly both surfaces are exposed to a fluid at 25°C, with a heat transfer coefficient of 500 W/m2K Calculate the centre and the surface temperatures 2 minutes after the cooling begins using Heislers charts

19. What are Biot, Fourier numbers and thermal time constant.? Explain their physical significance. 20. Obtain an expression for instantaneous heat transfer and total heat transfer for lumped heat analysis

treatment heat conduction problems. 21. A solid copper sphere of 10 cm dia [density= 8954 kg/m3, specific heat 383 J/kg C, thermal conductivity 386

W/C] initially at a uniform temp t= 250 C is suddenly immersed in a well stirred fluid which is maintained at a uniform temperature ta = 50°C, the heat transfer co-efficient between the sphere and the fluid is 200 W/m2C. Determine the temperature of the copper block at 5 minutes after the immersion

22. Explain physical significance of biot number and Fourier number. 23. Obtain an expression for instantaneous heat transfer and total heat transfer for lumped heat analysis

treatment of heat conduction problem. 24. A 15 mm diameter mild steel sphere K = 42 W/m°C is exposed to cooling air flow at 20°C resulting in the

convective co-efficient h = 120 W/m2°C. Determine the following: i) Time required to cool the sphere from 550C to 90°C. ii) instantaneous heat transfer rate 2 minutes after the start of cooling For mild steel ρ =7850 kg/m3; Cp = 475 J/kg°C; α= 0.045 m2/hr

25. Show that the temperature distribution under lumped analysis is given by��

��= ��, where T0 is the

initial temperature and T is the surrounding temperature. 26. A long cylinder 12 cm in diameter and initially at 20°C is placed into a furnace at 820°C with local heat

transfer coefficient of 140 W/m2.K. Calculate the time required for the axis temperature to reach 800°C. Also calculate the corresponding temperature at a radius of 5.4 cm at that time, Take a — 6.11x10-6 m2/s, K=21 W/m,K.

27. Obtain an expression for instantaneous heat transfer and total heat transfer for lumped heat analysis treatment of heat conduction problems.

28. An aluminum sphere weighing 5.5 kg and initially at a temperature of 290°C is suddenly immersed in a fluid at 15°C. The convective heat transfer coefficient is 58 W/m2K. Estimate the time required to cool the aluminum to 95°C using the lumped capacity method of analysis (For aluminum, ρ = 2700 kg/m3, C =900 J/kgK, K= 205 W/mK)

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29. An average convection heat transfer co-efficient for the flow of air at 90°C over a flat plate is measured by observing temperature time history of a 40 mm thick copper slab with p = 9000 kg/m3, Cp = 0.38 kJ/kg°K, K = 370 W/m°K exposed to the air at 90°C. In one test run the initial temperature of the plate was 200°C and in 4.5 minutes the temperature was decreased by 35°C. Find the convection heat transfer co-efficient for this case, Neglect the intemal thermal resistance

30. A long cylindrical bar with K = 17.4 W/m°K, α = 0.019 m2/hr of radius 80 mm is brought out of an oven at 830°C and is cooled by quenching it in a large bath of 40°C coolant. The surface convection heat transfer co-efficient between the bar surface and the coolant is. 180 W/m °K. Determine : i) The time taken by the shaft centre to reach 120°C, ii) The surface temperature of the shaft when its centre temperature is 120°C. Also calculate the temperature gradient at the outside surface at the same instant of time

31. Show that the temperature history of a cooling body with negligible intemal resistance is given by�

��= �

��

��.

State the assumptions made 32. A metallic sphere of radius 10mm is initially at a uniform temperature of 335°C. It is quenched in water bath

at 20°C with h = 6000 W/m2 °C. Determine the time taken for the centre temperature to reach 50°C. Also determine surface temperature when the centre temperature is 50°C. Take: ρ = 3000kg/m3, C = 1000J/kg °C, k = 20W/m°C, α= 6.66 x 10-6 m2/s.

33. What are Heisler charts? Explain their significance in solving transient conduction problems. A 12cm diameter long bar initially at a uniform temperature of 40°C is placed in a medium . at 65 0°C with a convective coefficient of 22 w/m2k.Cälculate the time required for the bar to reach 255°C. Take K =20 w/mk, p = 580 kg/m3 and e = 1050 J/kgk.

34. A cylinder of length 1m and diameter 5cm is placed in an atmosphere of 40°C, is provided with 12 longitudinal fins (K = 65 W/m°C) 0.75mm thick. The fins protrude 2.5cm from the cylinder surface. The heat transfer coefficient from the cylinder and fins to the ambient air is 20 W/m2°C. Calculate : i) The rate of heat transfer if the surface temperature of the cylinder is 150°C. ii) Temperature at the centre of the fin. iii) Effectiveness of the fin. Assume the heat transfer from the end is negligible.

35. A 10mm diameter, cable is to be laid in an atmosphere of 20°C (h0 =8.5 W/m2°C). The surface temperature of the cable is likely to be 65°C. Discuss the effect of insulating the cable with rubber having thermal conductivity of 0.15 W/m°C.

36. Derive an expression for the instantaneous and total heat flow in terms of the product of Biot Number and Fourier Number in one dimensional transient heat conduction

37. A 5cm thick iron plate with K 60 W/m °K, Cp= 460 j/kg °C, ρ = 7850 kg/m3, α=1.6x10-5m2/sis initially at 225C. Suddenly both the surfaces are exposed to an environmental temperature of 25C with a convective heat transfer co-efficient of 500W/m2 °K. Calculate i) the centre temperature at t= 2 min after start of cooling ii) the temperature at a depth of 1 cm from the surface at t = 2 min after the start of cooling iii)the energy removed from the plate per m2 during this time.

38. A thin metal plate 0.1 m by 0.1m is placed in a large container whose walls are kept at 300K The bottom surface of the plate is insulated and the top surface is maintained at 500k as a result of electric heating. If the emissivity of the surface of plate is 0.8, what is the rate of heat exchange between the plate and the walls of container? Take σ —5.67 x108W/m2

39. Using lumped system analysis, determine the time required for a solid steel ball of diameter 5cm [ρ= 7833 kg/m3, C = 465 J/kg°C and K= 54 W/mC] to cool from 600°C to 200C, if it is exposed to an air stream at 50C having a heat transfer coefficient h = 100 W/m2 °C.

40. A very thick concrete wall (α = 7x 102 m2/s) is initially at a uniform temperature T = 25°C. Suddenly one of its surface is raised to T0 = 125

0C and maintained at that temperatures By treating the well as a semi-infinite solid, calculate the temperature at 5, 10 and 15 cms from the hot surface 30 cm min after raising of the surface temperature.

41. Explain in brief the use of Heisler charts in solving transient conduction heat transfer problems 42. Aluminium rod of 5 cm diameter and 1 metre long at 200C is suddenly exposed to a temperature

(convective atmosphere) of 70°C. Calculate the temperature at a radius of 1 cm and heat lost per metre length of the rod, one minute after the cylinder is exposed to the environment.

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43. State the assumptions made in lumped parameter analysis and derive expression for instantaneous temperature and heat transfer rate for a body subjected to heating or cooling in terms of Biot and Fourier numbers.

44. An Iron sphere [K — 60W/m K, Cp — 460 J/kg°K, p= 7850 kg/m3 and α=1.6x10-5 m2/s] of 5 cm diameter is initially at a uniform temperature Ti= 225°C. Suddenly the surface of the sphere is exposed to an ambient at T∞= 25 C with a heat transfer coefficient h — 500W/m °K. Find I) the centre temperature at time t 2 min after start of cooling. ii) the temperature at a depth of 1 cm from the surface at time t — 2 min after start of cooling. Iii) the energy removed from the sphere during this time period.

45. Obtain a relation for the time required for lumped system to reach the average temperature of ��

� where

Ti = initial temperature and T∞ the temperature of environment. 46. A 12mm dia M.S. sphere at 540C is exposed to cooling air flow at 27°C and heat transfer coefficient of 114 W

/m2 K. Find i) the time required to cool the sphere from 540°C to 95C. ii) Instantaneous heat transfer rate, two minutes after start of cooling. iii) Total heat transferred from the sphere during first two minutes. Properties of M.S, are p =7850 kg/m3, C=475 j/kg K and α — 0.045 m2/hr.

47. A cylinder 1 meter long and 50 mm in dia is placed in an atmosphere at 455C. It is provided with 12 Longitudinal straight fins of material having thermal conductivity 120 W/m K. The height of fins is 12.7 mm from the cylinder and Thickness of fins is 0.76 mm. The heat transfer co efficient between cylinder and atmospheric air is 17 W /mK, Calculate the rate of heat transfer and the temperature at the end of the fins if surface temperature of cylinder is 150 C, Assume the tip of the fin to be insulated. (Neglect the circular plane surface on either side)

48. Explain in brief the use of Heisler charts in solving transient conduction heat transfer problems. 49. Aluminium rod of 5 cm diameter and 1 meter long at 200C is suddenly exposed to a temperature

(convective atmosphere) of 70C. Calculate the temperature at a radius of 1cm and heat lost per meter Length of the rod, one minute after the cylinder is exposed to the environment.

50. What is a semi-infinite medium? Give examples of solid bodies that can be treated as semi-infinite medium for heat transfer purposes.

51. An Iron sphere [k 60 W/mC, Çp=460 j/kg°C, ρ= 7850kg/m3 and α = 1.6x10-5 m2/S] of diameter D= 5cm is initially at a uniform temperature Ti= 225°C. Suddenly the surface of the sphere is exposed to an ambient at T∞ = 25°C with a heat transfer coefficient h = 500 W/m2C i) Calculate the centre temperature at �me t = 2 min after start of the cooling. ii) Calculate the temperature at a depth 1.0cm from the surface at time t =2min after start of the cooling. iii) Calculate the energy removed from the sphere during this time period.

52. Aluminium rod of 5 cm diameter and 1 metre long at 200°C is suddenly exposed to a temperature (convective atmosphere) of 70°C. Calculate the temperature at a radius of 1 cm and heat lost per metre length of the rod, one minute after the cylinder is exposed to the environment.

53. derive an expression for temperature distribution in a lumped system and show the nature of graph of temperature variation Vs dimensionless parameter.

54. A ball of 60 mm diameter at 600Th is suddenly immersed in controlled medium at 100C. Calculate the time required for the ball to obtain a temperature of 150C. Assume K = 40 W/mK, p =800 kg/m3, C= 500j/kg K, h= 20 W/m2K for the ball.

55. An iron sphere [K = 60 W/mC, Çp = 460 J/kg°C. p= 7850 kg/m3, α= 1.6 X10-5] of diameter. D =5 cm is initially at uniform temperature T — 225°C, suddenly the surface of the sphere is exposed to an ambient at Tb = 25°C with a heat transfer coefficient. h =500 W/m2C. Calculate the centre temperature at t= 2 min after the start of the cooling- Calculate the temperature at a depth of 1.0 cm from the surface at t= 2 rain after the start of cooling, Also calculate the energy removed from the sphere during this period of time.

56. Obtain expressions for instantaneous heat transfer and total heat transfer for Lumped heat analysis treatment of heat conduction problems.

57. A slab of aluminium 1O cm thick is originally at a temperature of 500C. It is suddenly immersed in a liquid at 100C resulting in a heat transfer co-efficient of 1200 W/m2-K. Determine the temperature at the centre line and the surface 1 minute after the immersion. Also calculate the total thermal energy removed per unit area of the slab during this period. The properties of aluminium for the given conditions are α=8.4x10-5m2/s, p=2700kg/m3, K=215W/m—K, C =0.9kJ/kg—K

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58. An iron sphere [k=60w/mC, Cp—460 J/kg C, p =7850 kg/m3, α = 1.6x10-5 m2/s.] of dia, D=5 cm is initially at uniform temperature Ti=225°C , suddenly the surface of the sphere is exposed to an ambient at Tb=25C with a heat transfer coefficient, h=500 W/m2K. Calculate the centre temperature at t=2min after the start of the cooling. Calculate the temperature at a depth of 1 .0 cm from the surface at t=2mm after the start of cooling. Also calculate the energy removed from the sphere during this period of time.

59. A solid iron md of diameter 60 mm initially at temperature 800°C, is suddenly dropped into an oil bath at 50°C. The heat transfer coefficient between the fluid and the surface is 400 W/m2K. The properties of iron rod are as follows: u2x lO4m2fs and K=60W/m°C. i) Calculate the centre tine temperature 10 min after immersion in fluid. ii) How long will it take the centre Line temperature to reach 100°C ? iii) Determine the energy removed from the rod during 10 min time.

60. A steel ball 5 cm diameters and initially at a temperature of 500C is suddenly placed in a controlled environment in which the temperature is maintained at 100°C. Neglecting intemal temperature gradient, derive an expression for temperature distribution and calculate the time required for the ball to attain a temperature of 250°C. Assume the following properties. Value for steel. k = 40W/mk; Cp = 0.45kJ/kgk p = 8000kg/m3; convection heat transfer coefficient is 10W/m2 k.

61. What do you mean by lumped system analysis? Explain clearly

Unit 4

1. Using dimensional analysis, derive an expression relating Nusselt number, Prandtl and Grashoff number for natural convection.

2. A plate of length 750 mm and width 250 mm has been placed longitudinally in a stream of crude oil which flows with a velocity of 5 m/s. if the oil has a specific gravity of 0.8 and kinematic viscosity of I0 m2/s, calculate: i) Boundary layer thickness at the middle of plate. ii) Shear stress at the middle of plate and iii) Friction drag on one side of the plate.

3. Two horizontal steam pipes having 100 mm and 300 mm are so laid in a boiler house that the mutual heat transfer may be neglected. The surface temperature of each of the steam pipes is 475°C. If the temperature of the ambient air is 35C. Calculate the ratio of heat transfer co-efficient and heat losses per metre length of the pipes.

4. Establish a relation between Nusselt. Prandtl and Grashoff numbers using dimensional analysis. 5. Explain velocity and thermal boundary layers. 6. a 30 cm long glass plate is hung vertically in the air at 27°C while its temperature is maintained at 77°C. Calculate

the boundary layer thickness at the trailing edge of the plate. Take properties of air at mean temperature K — 28.15 x 10-3 W/m.K, y = 18.41 x 10-6 m2/s, Pr = 0.7, β= 3.07 x 10-3 k

7. Explain the following: j) Velocity boundary layer ii) Thermal boundary layer. iii) Thermal entry length. (06 Marks) 8. Obtain fundamental relationship between Nusselt, Prandtl and Grashoff numbers applied to natural convection

using Buckingham π theorem. (08 Marks) 9. A 30 cm long glass plate is hung vertically in the air at 27°C while its temperature is maintained at 77°C.

Calculate the boundary layer thickness at the trailing edge of the plate. Also calculate the average heat transfer coefficient over the entire length of the plate. 1 (06 Marks)

10. With reference to fluid flow over a flat plate, discuss the concept of velocity boundary and thermal boundary layer, with necessary sketches. (05 Marks)

11. The exact expression for local Nusselt number for the laminar flow along a surface is given by Nu=��

�=

0.332Rex1/2.Pr

1/3 Show that the average heat transfer coefficient from x = O to x = L over the length ‘L’ of the surface is given by 2hL where hL is the local heat transfer coefficient at x = L. (05 Marks)

12. A vertical plate 15cm high and 10cm wide is maintained at 140°C. Calculate the maximum heat dissipation rate from both the sides of the plates to air at 20°C. The radiation heat transfer coefficient is 9.0 W/m2K. For air at 80°C, take r = 21.09 x 10-6 m2/sec, Pr 0.692, kf= 0.03 W/mK. (10 Marks)

13. Define Hydrodynamic and thermal Boundary layer in case of flow over a flat plate 14. An appropriate expression for temperature profile in thermal boundary layer is given by

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15. With sketches, explain the velocity boundary layer and thermal boundary layer thickness for a flow over the flat plate. (04 Marks)

16. An approximate expression for the velocity profile for laminar boundary layer flow along a flat plate is given by, �

��= sin �

�

2

�

��

Where the boundary layer thickness � is given by, �

�= 4.8��

�� i) Develop an expression for the local drag

coefficient. ii) Develop an expression for the average drag coefficient over a distance L from the leading edge of the plate. (08 Marks)

17. Calculate the rate of heat loss from the top and bottom of a flat 1 m square horizontal restaurant grill heated to 227°C and kept in a stagnant ambient air at 27°C. �(�.�)��

��=

��

��(�)−

�

��

�

��(�)�

� where ��(�) = 4.53

�

��/�

��/� develp an expression for local heat transfer

coefficient (06 Marks) 18. A vertical pipe 15cm OD, 1m long has a surface temperature of 90C. If the surrounding air is at 30°C. What is the

rate of heat loss by free convection? (08 Marks)

19. The velocity profile for boundary layer flow over a flat plate is given by, �(�,�)

��=

�

�

�

�(�)−

�

��

�

�(�)�

� Where

boundary laver thickness δ(x)=��

�� . Develop an expression for local drag coefficient. Also develop an

expression for average drag coefficient for a length of L. 20. Consider a square plate of size 0.6 m in a room with stagnant air at 20 C. One side of plate is maintained at 100C.

While the other side is adiabatic. Determine the heat loss if the plate is. I) vertical and ii) horizontal with hot surface facing up.

21. With reference to fluid flow over a flat plate, discuss the concepts of velocity boundary layer and thermal boundary layer, with necessary sketches. (06 Marks)

22. Air at 27 C and at atmospheric pressure flows over a flat plate at a speed of 2 m/sec. If the plate is maintained at 93 C. calculate the heat transfer per unit width of the plate, assuming the length of the plate along the flow of air is 2 metres. (08 Marks)

23. A steam pipe 5 cms diameter is lagged with insulating material of 2.5 cm thick. The surface temperature is 80 C and emissivity of the insulating material surface is 0.93. Find the total heat loss from 10 metre length of pipe considering the heat loss by natural convection and radiation. The temperature of the air surrounding the pipe is 20 C. Also find the overall heat transfer co-efficient and heat transfer co-efficient of radiation. (06 Marks)

24. What do you mean by hydro dynamic and thermal boundary layer? (04 Marks) 25. Explain physical significance of, i) Grashoff number ii) Prandtl number iii) Nusselt number iv) Reynolds number 26. A nuclear reactor with its core constructed of parallel vertical plates 2.2 m high and 1.4 m wide has been

designed on free convection heating of liquid bismuth. the maximum temperature of the plate surface is limited to 960°C while the lowest allowable temperature of bismuth is 340°C. Calculate the maximum possible heat dissipation from both sides of each plate. For the convective co-efficient the appropriate correlation is = 0.13(Gr.Pr)0.333.

27. Using Buckingham π theorem, obtain a relationship between Nu, Pr and Gr for free convection heat transfer. . (08 Marks)

28. Explain the development of hydrodynamic boundary layer for flow over a flat surface. (06 Marks) 29. Considering the body of a man as a vertical cylinder of 300 mm diameter and 170 cm height, calculate the heat

generated by the body in one day. Take the body temperature as 36°C and atmospheric temperature as 14°C. . (06 Marks)

30. What do you mean by hydrodynamic and thermal boundary layer? How does the ratio of vary with prandtl number? (06 Marks)

31. Using Buckingham’s π-theorem, obtain the relationship between various non-dimensional numbers for free convection heat transfer. . (08 Marks)

32. Air at 20°C flows over a thin plate with a velocity of 3 m/sec. The plate is 2 m long and 1 m wide. Estimate the boundary layer thickness at the trailing edge of the plate and the total drag force experienced by the plate. (06 Marks)

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33. 4 Derive expressions for the friction factor and pressure drop for the flow through tubes. 34. Water is heated while flowing through (1.5x3.5) cm2 rectangular cross section tube at a velocity of 1.2 m/s. The

entering temperature of water is 40°C and the tube wall is maintained at 100°C. Determine the length of the tube required in order to raise the temperature of water by 40°C.

35. Show by using Buckingham it theorem that Nusselt number is a function of Reynolds’ number and Prandtl number in case of forced convection heat transfer. (10 Marks)

36. A fine wire having a diameter of 3.94 x 10-5m is placed in a 1 bar air stream at 25°C having a velocity of 50 m/s perpendicular to the wire. An electric current is passed through the wire raising the temperature to 50°C. Calculate the heat loss per unit length. (10 Marks)

37. Briefly explain: i) Hydrodynamic boundary layer ii) Thermal boundary layer. (06 Marks) 38. Define: i) Nusselt number ii) Prandtl number iii) Stanton number iv) Grashoff number. (04 Marks) 39. A square plate (0.5m x 0.5m) with one surface insulated and the other surface maintained at temperature of

385K is placed in ambient air at a temperature of 315K. Calculate the average heat transfer coefficient for free convection for the following orientations of the hot surface: i) The plate is horizontal and hot surface faces up. ii) The plate is horizontal and the hot surface faces down. (10 Marks)

40. Prove that the temperature distribution in a body at time t during a Newtonian heating or cooling is given by where T is the temperature at t = 0. (10 Marks)

41. An aluminium plate [K=160W/m°C; ρ=2790kg/m3; Cp =O.88kj/Kg°C] of thickness L = 3cm and at a uniform temperature of 225°C is suddenly immersed at time t = O in a well stirred fluid maintained at a constant temperature of 25°C, h = 320W/m2°C. Determine the time required for the centre of the plate to reach 50°C. (10 Marks)

42. The exact expression for local Nusselt Number for the laminar flow along a surface is given 43. by N =(hxx)/K = 0.332Pr

1/3 Re1/2. Show that the average heat transfer coefficient from x= 0 to x= L. over the length ‘L’ of the surface is given by 2hL where hL is the local value at x=L. (OS Marks)

44. A tube of 0.036m OD and 40cm length is maintained at a uniform temperature of 100°C. It is exposed to air at a uniform temperature of 20°C. Determine the rate of heat transfer from the Surface of the tube when (i) the tube is vertical (ii) the tube is horizontal, (12 Marks)

45. With a suitable diagram, explain the velocity boundary layer for the flow over flat plate. Clearly indicate the viscous sub layer and buffer layer in the diagram and explain them.

46. (02 Marks) 47. h, An approximate expression for the velocity profile for a laminar boundary -- layer flow

48. along a fiat plate is given by�(�,�)

��=2

�

�(�)− 2 �

�

�(�)�

�+ �

�

�(�)�

� where the boundary layer thickness

�(�)

�=

�.��

��.

i) Develop an expression for local drug coefficient Cx, ii) Develop an expression for the average drag coefficient Cm over a distance x = L from the leading edge of the plate. iii) Determine the drag force F acting on a plate 2m x 2m for the flow of air at atmospheric pressure and at T= 350 K with a velocity of Ux= 4m/s. (12 Marks)

49. Using Buckingham’s π- theorem, obtain the relationship between various non dimensional numbers for forced convection heat transfer

50. A hot square plate 50 cm x 50 cm at 100C is exposed to atmosphere at 20 C. Find the heat loss from both surfaces of the plate if the plate is horizontal.

51. 4 Distinguish between i) Hydrodynamic and thermal boundary layers ii) Laminar and turbulent flow, 52. Air at 20°C and at atmospheric pressure flows over a flat plate at a velocity of 3m/s. the plate it 30cm long and

at 60°C. Calculate i) Velocity and thermal boundary layer thicknesses at 20cms from the leading edge. ii) Average heat transfer coefficient. iii) Total drag force on the plate per unit width.

53. Air at atmosphere pressure and at Temperature of 30°C flows with a velocity of 1.5 m/s along the plate, find : i) Distance from the leading edge of the plate where transition begins from laminar to turbulent flow ii) The drag force acting per meter width of the plate over the distance from the leading edge to the transition starts. Assume the transition Reynolds’s number as 5 x 104.

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54. Air at one atmospheric pressure and temperature 25 C flowing with a velocity of 50 m/s crosses an industrial heater made of long solid rod of dia 20 mm. Thu surface temperature of the heater is to be kept constant at temperature of 475°C. Determine the allowable electrical power density (W/m2) with in the heater per meter length.

55. What do you mean by hydrodynamic and thermal boundary layer? how does the ratio �/�t vary with prandtl number? 106 Marks)

56. Derive an expression for friction factor & pressure drop for hydro dynamically developed Laminar flow through tubes.

57. Atmospheric air at T∞= 400 K flows with a velocity of U∞ = 4m/s along a flat plate L = 1m long maintained at a uniform temperature T = 300K, The average heat transfer coefficient is determined to be hm = 7.75 W/m2 °C. Using Reynolds — Colbum analogy. Estimate the drag force exerted on the plate per 1m width. Take p = 0.998 kg/m3, Cp= 1009 j/kg °C, Pr = 0.697, (08 Marks)

58. Show by using Buckingham it theorem that Nusselt number is a function of Reynolds’s number and Prandlt number in case of forced convection heat transfer,

59. A fine wire having a diameter of 3.94 x10-5 m is placed in a 1 bar air stream at 25°C having a velocity of 50 m/s perpendicular to the wire. An electric current is passed through the wire raising the temperature to 50°C. Calculate the heat loss per unit length.

60. Air at 200°C’ and velocity 5 m/s flows over a plate of 1.5 m long. the plate is maintained at a uniform temperature of 100°C. The average heat transfer coefficient is 7.5 W/m3K. Calculate the drag force exerted on the plate per 0.75 m width by using Reynolds Colbum analogy.

61. What is dimensional analysis? What are its applications? (04 Marks) 62. Atmospheric air at mean temperature of 300 K and a bulk stream velocity of 1O m/s flows through a tube with

2.5 mm inside diameter. Calculate the pressure drop for IO0 m length of the tube for i) A smooth tube ii) Commercial steel tube.

63. Water flows with a velocity of 0.6 m/s though a Tube of inside diameter 60 mm and length 3.5 m Find the heat transfer rate by forced convection, [(s mean water temperature is 50°C and Tube wall surface temperature is 70C, Use the empirical correlation Na = 0.023(Re)0.8(Pr)0.4.

64. Explain the concept of velocity and thermal boundary layers. (06 Marksl 65. Why are the correlations for an entry region different than those of a fully developed zone? (04 Marks) 66. Air at 20C is flowing along a heated flat plate at I34C at a velocity of 3 m/s. The plate is 2 m long and 15 cm wide.

Calculate the thickness of hydrodynamic boundary Layer ‘and the skin friction coefficient at 40 cm from the leading edge of the plate. The kinematic viscosity of the air at 20’C is 15.06 x 10-6 m2/s. Also calculate the local heat transfer co-efficient at x =0.4 m and the heat transferred from the first 40cm of the plate. (10

67. Explain With a neat sketch the development of hydrodynamic boundary Layer and velocity distribution over a flat plate.

68. Define Reynolds’s number and Nusselt number. What are their significances? (04 Marks)

69. Water at 20C with a flow rate of 0.05 kg/s enters a 20mm inside diameter tube which is maintained at a uniform temperature of 90°C. Determine the thermal entry Length. Assuming hydrodynamic ally and thermally fully developed flow, determine the convection heat transfer coefficient and tube length required to heat the water to 70°C, (10 Marks)

70. Distinguish between velocity boundary layer and thermal boundary layer. 71. Distinguish between laminar and turbulent flow. 72. Air at 20°C and at an atmospheric pressure flows over a flat plate at a velocity of 3 m/s. If the plate is 30 cm

length and at a temperature of 60 C, calculate i) Velocity and thermal boundary layer thicknesses at 20 cm. ii) Average heat transfer coefficient, iii) Total drug force on the plate, per unit width. Take the following properties of air: p= 1.18 kg/m3, v = 17 x 10-6 m2/s, K = 0.0272 W/mK, Cp= 1.007kj/kgK, Pr = 0.705.

73. Explain with a neat sketch the development of hydrodynamic boundary layer and velocity distribution over a flat plate. (06 Marks)

74. Define Reynold’s number and Nusselt number. What are their significances? 75. Water at 20°C with a flow rate of 0.015 kg/s enters a 20mm inside diameter tube, which is maintained at a

uniform temperature of 90°C. Determine the thermal entry length. Assuming hydro dynamically and thermally

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fully developed flow, determine the convection heat transfer coefficient and tube length required to heat the water to 70°C. (10 Marks)

76. What is dimensional analysis? What are the applications of dimensional homogeneity?(4 Marks) 77. Atmospheric air at mean temperature of 300k and a bulk stream velocity of 10m/s flows through a tube with

diameter 2.5mm inside diameter. Calculate the pressure drop for 100m length of the tube for i) A smooth tube ii) Commercial steel tube. (8 Marks)

78. Water flows with a velocity of 10m/s through a tube of inside diameter 60mm and length 3.5m. Find the heat transfer rate by forced convection. If mean water temperature is 50°C and tube wall surface temperature is 70°C. Using empirical correlation Nu = 0.023(Re)0.8 (F)0.4

Unit 5

1. define stanton number and explain its physical significance.

2. Prove that ��

��.��=

��

� usual notations.

3. Explain the significance of: i) Reynolds number, ii) Prandtl number. iii) Nusselt number, iv) Stanton number. 4. Atmospheric air at 275 K and free stream velocity 20 m/s flows over a flat plate of length 1.5 m long maintained

at 325 K. Calculate: i) The average heat transfer coefficient over the region where the boundary layer is laminar. ii) Find the average heat transfer over the entire length 1.5 m of the plate. iii) Calculate the total heat transfer rate from the plate to the air over the length of 1.5 m and width 1m. Assume transition occurs at a Reynolds no. 2 x 105. Take air Properties at mean temperature of 300 K. K 0.026 W/ m°C, Pr— 0.708, y = l.8 x 10-6 m2/s, µ = 1.98 x 10-5 kg/m-s.

5. Air at a temperature of 20C, flows over a flat plate at 3 m/s. The plate is 50cm x 25cm. Find the heat lost per hour if air flow is parallel to 50cm side of the plate. If 25 cm side is kept parallel to the air flow, what will be the effect on heat transfer? Temperature of the plate is 100°C.

6. Define and explain the physical significance of the following dimensionless numbers: i) Reynolds number ii) Prandtl number. iii) Nusselt number iv) Stanton number. (08 Marks)

7. Define local and mean heat transfer coefficients. On what factors does the value of mean heat transfer coefficient depend? (04 Marks)

8. Air at 27°C and 1 atm flows across a sphere of 15 mm diameter at a velocity of 5m/s. A small heater inside the sphere maintains the surface temperature at 77°C. Estimate the rate of heat transfer from the sphere. (08 Marks)

9. Explain the physical significance of i) Nusselt number; ii) Groshoff number. (04 Marks) 10. Air at 2 atm and 200°C is heated as it flows at a velocity of 12 m/sec through a tube with a diameter of 3cm. A

constant heat flux condition is maintained at the wall and the wall temperature is 20°C above the air temperature all along the length of the tube. Calculate:.1) The heat transfer per unit length of tube.ii) The increase in bulk temperature of air over a 4m length of the tube. Take the following properties for air Pr = 0.681, µ =2.57 x 10-5 kg/ms, K = 0.0386 W/mK and Cp= 1.025 kJ/kg K. (10 Marks)

11. Obtain a relationship between drag coefficient, Cm and heat transfer coefficient, hm for the flow over a flat plate. . . (06 Marks)

12. Using dimensional analysis, obtain a relation between NJ, RL And P- for forced convection heat transfer, (I O Marks)

13. Air flows over a flat plate at 30°C. 0.4m, 075m long with a velocity of 20m/s. determine the heat transfer from the surface of plate assuming plate is maintained at 90°C. Use NuL = 0.664 Re0.5 Pr0.333 for laminar = (0.036 Re0.8 -836)Pr0.333. (10 Marks)

14. Using Buckingham‘s π—theorem. Obtain the relationship between various non-dimensional numbers for forced convection heat transfer. (10 Marks)

15. A nuclear reactor uses a heat exchanger consisting of 5 cm ID constant heat flux tube, 3.5 kg/s mass flow rate of liquid metal at 200°C is passed through the tube having wall temperature of 230°C. find the length of the tube required for a 10°C rise in temperature of the find. Use the following properties of the fluid: ρ = 7.7 x 103 kg/m3, u =8 x 10-8 m/s. Cp= 130 J/kg-K, K =12W/m-K. Average Nusselt number is given by, Nu=4.82+0.0185(�� )�.��

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16. Air at 0°C and 20 m/s flows over a flat plate of length 1.5 m, that is maintained at 50°?. 17. Calculate the average heat transfer coefficient over the region where flow is laminar. Find the average heat

transfer coefficient and the heat loss for the entire plate per unit width, 18. Air at -20°C and 30 m/s, flows over a sphere of diameter 25 mm, which is maintained at 80°C. Calculate the

heat loss from sphere. (08 Marks) 19. With the help of dimensional analysis, derive expression for the Reynolds number, Prandtl number and Nusselt

number. (10 Marks) 20. A surface condenser consists of two hundred thin walled circular tubes (each tube is 22.5 mm diameter and 5

m long) arranged in parallel, through which water flows. If the mass flow rate of water through the tube bank is 160 kg/sec and its inlet and outlet temp are known to be 21°C and 29°C respectively, calculate the average heat transfer co-efficient associated with flow of water. (10 Marks

21. With the help of dimensional analysis derive expression which relates Reynolds number, Nusselt number and Prandtl number. (11) Marks)

22. Air at standard conditions of 760 mm of Hg at 20°C flows over a flat plate at 3 m/sec. The plate is 50cms x 25 cms Find the heat lost per hour if air flow is parallel to 50 cms side of the plate. 1f 25 cms side is kept parallel to the air flow, what will be the effect on heat transfer? Temperature of the plate is 100°C

23. Define clearly and give expressions for . I) Reynolds number ii) Prandtl number iii) Nusselt number iv) Stanton number.(O8 Marks)

24. 50 kg of water per minute is heated from 30°C to 50°C by passing through a pipe of 2 cm diameter. The pipe is heated by condensing the steam on its surface at 100°C. Find the length of the pipe required. Take for water at 90°C, ρ = 965 kg/m3, K = 0.585 W/m.K, Cp = 4200 J/kg.K and � = 0.33x10-6 m2/s. (06 Marks)

25. Air at a temperature of 20°C flows through a rectangular duct with a velocity of 10 m/s. The duct is 30cm x20cm in size and air leaves at 34°C. Find the heat gain by air when it is passed through 10m long duct, (06 Marks)

26. With the help of dimensional analysis, derive expressions for the Reynolds number, Prandtl number and Nusselt number. (10 Marks)

27. Air at 25°C and atmospheric pressure flows across a heated cylinder of diameter 7.5 cm. if the velocity of air flow is 1.2 m/s and the cylinder surface is maintained at 95°C, compute the rate of heat transfer. (10 Marks)

28. Explain the following: i) Grashoff number ii) Prandtl number iii) Sherwood number iv) Schmidt number (08 Marks)

29. A 500W cylindrical immersion heater (3cm dia 20cm long ) is placed vertically in a stagnant water at 25°C. Calculate the average surface temperature of the plate. (12 Marks)

30. Using dimensional analysis, obtain the dimensionless parameters in forced convection heat transfer. (10 Marks) 31. Water at a velocity of 1.5 m/s enters a 2cm diameter heat exchanger tube at 40°C. The heat exchanger tube

wall is maintained at a temperature of 100°C. If the water is heated to a temperature of 80°C in the heat exchanger tube, find the leng

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HMT QUESTON BANK Unit – I Conduction · HMT QUESTON BANK Unit – I Conduction 1. State the laws governing three basic modes of Heat transfer 2. Write the 3-D heat conduction equation