UNIT I

FINS(EXTENDED SURFACES)

Fin Applications

2

Fins Applications

3

Fins in Motor Body

4

Fin configurations

5

(a) straight fin of uniform cross-section on plane wall

(b) straight fin of uniform cross-section on circular tube

(c) annular fin

d) straight pin fin

UNIT III

HEAT EXCHANGERS

Concentric Tube Parallel & Counter

7

Concentric Tube : parallel, Counter

8

Cross Flow : Mixed & Unmixed

9

Cross Flow : Mixed & Unmixed

10

Shell & Tube HX.

11

UNIT II

CONVECTION BOUNDARY LAYER CONCEPT

Heat and Mass Transfer: Fundamentals & ApplicationsFourth Edition

Yunus A. Cengel, Afshin J. GhajarMcGraw-Hill, 2011

1313

VELOCITY BOUNDARY LAYERVelocity boundary layer: The region of the flow above the plate bounded by in which the effects of the viscous

shearing forces caused by fluid viscosity are felt.The boundary layer thickness, , is typically defined as the

distance y from the surface at which u = 0.99V.The hypothetical line of u = 0.99V divides the flow over a

plate into two regions: Boundary layer region: The viscous effects and the

velocity changes are significant.Irrotational flow region: The frictional effects are

negligible and the velocity remains essentially constant.

1414

THERMAL BOUNDARY LAYER

Thermal boundary layer on a flat plate (the fluid is hotter than the plate surface).

A thermal boundary layer develops when a fluid at a specified temperature flows over a surface that is at a different temperature.

Thermal boundary layer: The flow region over the surface in which the temperature variation in the direction normal to the surface is significant.The thickness of the thermal boundary layer t at any location along the

surface is defined as the distance from the surface at which the temperature difference T − Ts equals 0.99(T− Ts).

The thickness of the thermal boundary layer increases in the flow direction, since the effects

of heat transfer are felt at greater distances from the

surface further down stream.The shape of the temperature

profile in the thermal boundary layer dictates the convection heat transfer between a solid surface and the fluid flowing

over it.

1515

Development of the velocity profile in a circular pipe• A flow field is best characterized by its velocity distribution.

• A flow is said to be one-, two-, or three-dimensional if the flow velocity varies in one, two, or three dimensions, respectively.

• However, the variation of velocity in certain directions can be small relative to the variation in other directions and can be ignored.

The development of the velocity profile in a circular pipe. V = V(r, z) and thus the flow is two-dimensional in the entrance region, and

becomes one-dimensional downstream when the velocity profile fully develops and remains unchanged in the flow direction, V = V(r).

UNIT III

BOILING AND CONDENSATION

17

BOILING HEAT TRANSFER• Evaporation occurs at the liquid–vapor interface

when the vapor pressure is less than the saturation pressure of the liquid at a given temperature.

• Boiling occurs at the solid–liquid interface when a liquid is brought into contact with a surface maintained at a temperature sufficiently above the saturation temperature of the liquid.

18

Classification of boiling

• Boiling is called pool boiling in the absence of bulk fluid flow.

• Any motion of the fluid is due to natural convection currents and the motion of the bubbles under the influence of buoyancy.

• Boiling is called flow boiling in the presence of bulk fluid flow.

• In flow boiling, the fluid is forced to move in a heated pipe or over a surface by external means such as a pump.

excess temperature

Boiling heat flux from a solid surface to the fluid

19

Subcooled Boiling• When the

temperature of the main body of the liquid is below the saturation temperature.

Saturated Boiling• When the

temperature of the liquid is equal to the saturation temperature.

20

POOL BOILING

Boiling takes different forms, depending on the Texcess = Ts Tsat

In pool boiling, the fluid is not forced to flow by a mover such as a pump.

Any motion of the fluid is due to natural convection currents and the motion of the bubbles under the influence of buoyancy.

Boiling Regimes and the Boiling Curve

21

22

Natural Convection Boiling (to Point A on the Boiling Curve)

• Bubbles do not form on the heating surface until the liquid is heated a few degrees above the saturation temperature (about 2 to 6°C for water)

• The liquid is slightly superheated in this case (metastable state).

• The fluid motion in this mode of boiling is governed by natural convection currents.

• Heat transfer from the heating surface to the fluid

is by natural convection.

• For the conditions of Fig. 10–6, natural convection

boiling ends at an excess temperature of about 5°C.

23

• The bubbles form at an increasing rate at an increasing number of nucleation sites as we move along the boiling curve toward point C.

Nucleate Boiling (between Points A and C)

• Region A–B ─ isolated bubbles.

• Region B–C ─ numerous continuous

columns of vapor in the liquid.

Point A is referred to as the onset of nucleate

boiling (ONB).

24

• In region A–B the stirring and agitation caused by the entrainment of the liquid to the heater surface is primarily responsible for the increased heat transfer coefficient.

• In region A–B the large heat fluxes obtainable in this region are caused by the combined effect of liquid entrainment and evaporation.

• For the entire nucleate boiling range, the heat transfer coefficient ranges from about 2000 to 30,000 W/m2·K.

• After point B the heat flux increases at a

lower rate with increasing Texcess, and reaches a maximum at

point C.

• The heat flux at this point is called the

critical (or maximum) heat flux, and is of prime engineering

importance.

25

Transition Boiling (between Points C and D)

• When Texcess is increased past point C, the heat flux decreases.

• This is because a large fraction of the heater surface is covered by a vapor film, which acts as an insulation.

• In the transition boiling regime, both nucleate and film boiling partially occur.

• Operation in the transition boiling regime, which is also called the unstable

film boiling regime, is avoided in practice.

• For water, transition boiling occurs over the excess temperature range from

about 30°C to about 120°C.

26

Film Boiling (beyond Point D• Beyond point D the heater

surface is completely covered by a continuous stable vapor film.

• Point D, where the heat flux reaches a minimum is called the Leidenfrost point.

• The presence of a vapor film between the heater surface and the liquid is responsible for the low heat transfer rates in the film boiling region.

• The heat transfer rate increases with increasing excess temperature due to radiation to the liquid.

27

Burnout Phenomenon

• A typical boiling process does not follow the boiling curve beyond point C.

• When the power applied to the heated surface exceeded the value at point C even slightly, the surface temperature increased suddenly to point E.

• When the power is reduced gradually starting from point E the cooling curve follows Fig. 10–8 with a sudden drop in excess temperature when point D is reached.

28

Any attempt to increase the heat flux beyond qmax will cause the operation point on the boiling curve to jump suddenly from

point C to point E. However, surface temperature that corresponds to point E is

beyond the melting point of most heater materials, and burnout

occurs. Therefore, point C on the boiling curve is also called the burnout

point, and the heat flux at this point the burnout heat flux.

Most boiling heat transfer equipment in practice operate

slightly below qmax to avoid any disastrous burnout.

29

Heat Transfer Correlations in Pool Boiling• Boiling regimes differ considerably in their character.

• Different heat transfer relations need to be used for different boiling regimes.

• In the natural convection boiling regime heat transfer rates can be accurately determined using natural convection relations.

• No general theoretical relations for heat transfer in the nucleate boiling regime is

available.

• Experimental based correlations are used.

• The rate of heat transfer strongly depends on the nature of nucleation and the type and the condition of the

heated surface.

Nucleate Boiling

30

Film condensation• The condensate wets the surface and

forms a liquid film.• The surface is blanketed by a liquid

film which serves as a resistance to heat transfer.

Dropwise condensation• The condensed vapor forms droplets

on the surface.• The droplets slide down when they

reach a certain size.• No liquid film to resist heat transfer.• As a result, heat transfer rates that

are more than 10 times larger than with film condensation can be achieved.

Condensation occurs when the temperature of a vapor is reduced below its saturation temperature.

CONDENSATION HEAT TRANSFER

31

• Liquid film starts forming at the top of the plate and flows downward under the influence of gravity.

• increases in the flow direction x

• Heat in the amount hfg is released during condensation and is transferred through the film to the plate surface.

• Ts must be below the saturation temperature for condensation.

• The temperature of the condensate is Tsat at the interface and decreases gradually to Ts at the wall.

FILM CONDENSATION

32

DROPWISE CONDENSATIONDropwise condensation, characterized by

countless droplets of varying diameters on the condensing surface instead of a continuous liquid film and extremely large heat transfer

coefficients can be achieved with this mechanism.

The small droplets that form at the nucleation sites on the surface grow as a result of

continued condensation, coalesce into large droplets, and slide down when they reach a

certain size, clearing the surface and exposing it to vapor. There is no liquid film in this case to

resist heat transfer.

As a result, with dropwise condensation, heat transfer coefficients can be achieved that are

more than 10 times larger than those associated with film condensation.

The challenge in dropwise condensation is not to achieve it, but rather, to sustain it for prolonged

periods of time.

Dropwise condensation of steam on copper surfaces:

UNIT V

MASS TRANSFER

34

INTRODUCTIONWhenever there is an imbalance of a commodity in a medium, nature tends to redistribute it until a “balance” or “equality” is established. This tendency is often referred to as the driving force, which is the mechanism behind many naturally occurring transport phenomena.

The commodity simply creeps away during redistribution, and thus the flow is a diffusion process. The rate of flow of the commodity is proportional to the concentration gradient dC/dx, which is the change in the concentration C per unit length in the flow direction x, and the area A normal to flow direction.

kdiff is the diffusion coefficient of the medium, which is a measure of how fast a commodity diffuses in the medium, and the negative sign is to make the flow in the positive direction a positive quantity (note that dC/dx is a negative quantity since concentration decreases in the flow direction).

35

The diffusion coefficients and thus diffusion rates of gases depend strongly on temperature. The diffusion rates are higher at higher temperatures.The larger the molecular spacing, the higher the diffusion rate. Diffusion rate: gases > liquids > solids

36

ANALOGY (SIMILARITY) BETWEEN HEAT AND MASS TRANSFERWe can develop an understanding of mass transfer in a short time with little effort by simply drawing parallels between heat and mass transfer.

TemperatureThe driving force for mass transfer is the concentration difference. Both heat and mass are transferred from the more concentrated regions to the less concentrated ones. If there is no difference between the concentrations of a species at different parts of a medium, there will be no mass transfer.

37

ConductionMass is transferred by conduction (called diffusion) and convection only.

Rate of mass diffusion

Fick’s law of diffusion

DAB is the diffusion coefficient (or mass diffusivity) of the species in the mixture CA is the concentration of the species in the mixture

38

Heat GenerationHeat generation refers to the conversion of some form of energy such as electrical, chemical, or nuclear energy into sensible thermal energy in the medium.

Some mass transfer problems involve chemical reactions that occur within the medium and result in the generation of a species throughout.

Therefore, species generation is a volumetric phenomenon, and the rate of generation may vary from point to point in the medium.

Such reactions that occur within the medium are called homogeneous reactions and are analogous to internal heat generation.

In contrast, some chemical reactions result in the generation of a species at the surface as a result of chemical reactions occurring at the surface due to contact between the medium and the surroundings.

This is a surface phenomenon, and as such it needs to be treated as a boundary condition.

In mass transfer studies, such reactions are called heterogeneous reactions and are analogous to specified surface heat flux.

39

ConvectionMass convection (or convective mass transfer) is the mass transfer mechanism between a surface and a moving fluid that involves both mass diffusion and bulk fluid motion. Fluid motion also enhances mass transfer considerably.

Newton’s law of cooling

Rate of mass convection

In mass convection, we define a concentration boundary layer in an analogous manner to the thermal boundary layer and define new dimensionless numbers that are counterparts of the Nusselt and Prandtl numbers.

hmass the mass transfer coefficientAs the surface area

Cs − C a suitable concentration difference across the concentration boundary layer.

40

MASS DIFFUSIONFick’s law of diffusion states that the rate of diffusion of a chemical species at a location in a gas mixture (or liquid or solid solution) is proportional to the concentration gradient of that species at that location.

1 Mass BasisOn a mass basis, concentration is expressed in terms of density (or mass concentration).

The density of a mixture at a location is equal to the sum of the densities of its constituents at that location.

The mass fraction of a species ranges between 0 and 1, and the sum of the mass fractions of the constituents of a mixture be equal to 1.

41

TYPE I STEADY MASS DIFFUSION THROUGH A WALL

Many practical mass transfer problems involve the diffusion of a species through a plane-parallel medium that does not involve any homogeneous chemical reactions under one-dimensional steady conditions.

diffusion resistance of the wall

42

TYPE I : STEADY ONE-DIMENSIONAL MASS TRANSFER THROUGH NONREACTING CYLINDRICAL AND SPHERICAL LAYERS

On a molar basis

43

TYPE II : Equimolar Counterdiffusion

equimolar counterdiffusion

44

TYPE III: DIFFUSION OF VAPOR THROUGH A STATIONARY GAS : STEFAN FLOW

Many engineering applications such as heat pipes, cooling ponds, and the familiar perspiration involve condensation, evaporation, and transpiration in the presence of a noncondensable gas, and thus the diffusion of a vapor through a stationary (or stagnant) gas. To understand and analyze such processes, consider a liquid layer of species A in a tank surrounded by a gas of species B, such as a layer of liquid water in a tank open to the atmospheric air at constant pressure P and temperature T.

45

This relation is known as Stefan’s law, and the induced convective flowdescribed that enhances mass diffusion is called the Stefan flow.

46

CONVECTIVE MASS TRANSFERNow we consider mass convection (or convective mass transfer), which is the transfer of mass between a surface and a moving fluid due to both mass diffusion and bulk fluid motion. The analogy between heat and mass convection holds for both forced and natural convection, laminar and turbulent flow, and internal and external flow.Mass convection is also complicated because of the complications associated with fluid flow such as the surface geometry, flow regime, flow velocity, and the variation of the fluid properties and composition.Therefore, we have to rely on experimental relations to determine mass transfer.Mass convection is usually analyzed on a mass basis rather than on a molar basis.

Concentration boundary layer: In mass convection, the region of the fluid in which concentration gradients exist.

47

In internal flow, we have a concentration entrance region where the concentration profile develops, in addition to the hydrodynamic and thermal entry regions.

The concentration boundary layer continues to develop in the flow direction until its thickness reaches the tube center and the boundary layers merge.

The distance from the tube inlet to the location where this merging occurs is called the concentration entry length Lc, and the region beyond that point is called the fully developed region.

48

SIMULTANEOUS HEAT AND MASS TRANSFER

Many mass transfer processes encountered in practice occur isothermally, and thus they do not involve any heat transfer.

But some engineering applications involve the vaporization of a liquid and the diffusion of this vapor into the surrounding gas.

Such processes require the transfer of the latent heat of vaporization hfg to the liquid in order to vaporize it, and thus such problems involve simultaneous heat and mass transfer.

To generalize, any mass transfer problem involving phase change (evaporation, sublimation, condensation, melting, etc.) must also involve heat transfer, and the solution of such problems needs to be analyzed by considering simultaneous heat and mass transfer.

UNIT IV

FUNDAMENTALS OF THERMAL RADIATION

50

INTRODUCTION Radiation differs from conduction and convection in that it does not require the

presence of a material medium to take place.Radiation transfer occurs in solids as well as

liquids and gases.

The hot object in vacuum chamber will eventually cool

down and reach thermal equilibrium with its

surroundings by a heat transfer mechanism: radiation.

51

Accelerated charges or changing electric currents give rise to electric and magnetic fields. These rapidly moving fields are called electromagnetic waves or electromagnetic radiation, and they represent the energy emitted by matter as a result of the changes in the electronic configurations of the atoms or molecules.

Electromagnetic waves transport energy just like other waves and they are characterized by their frequency or wavelength . These two properties in a

medium are related by

c = c0 /n c, the speed of propagation of a wave in that medium c0 = 2.9979108 m/s, the speed of light in a vacuum

n, the index of refraction of that mediumn =1 for air and most gases, n = 1.5 for glass, and n = 1.33 for water

It has proven useful to view electromagnetic radiation as the propagationof a collection of discrete packets of energy called photons or quanta.

In this view, each photon of frequency n is considered to have an energy of

The energy of a photon is inversely proportional to its wavelength.

52

THERMAL RADIATION

The electromagnetic wave spectrum.

The type of electromagnetic radiation that is pertinent to heat transfer is the thermal radiation emitted as a result of energy transitions of molecules, atoms, and

electrons of a substance. Temperature is a measure of the strength of these

activities at the microscopic level, and the rate of thermal radiation emission increases with increasing

temperature. Thermal radiation is continuously emitted by all matter

whose temperature is above absolute zero.

Everything around us constantly

emits thermal radiation.

53

In heat transfer studies, we are interested in the energy emitted by bodies because of their

temperature only. Therefore, we limit our consideration to thermal radiation.

The electrons, atoms, and molecules of all solids, liquids, and gases above

absolute zero temperature are constantly in motion, and thus radiation is

constantly emitted, as well as being absorbed or transmitted throughout the

entire volume of matter.

That is, radiation is a volumetric phenomenon.

54

BLACKBODY RADIATION• Different bodies may emit different amounts of radiation per unit surface area.• A blackbody emits the maximum amount of radiation by a surface at a given

temperature. • It is an idealized body to serve as a standard against which the radiative

properties of real surfaces may be compared.• A blackbody is a perfect emitter and absorber of radiation.

• A blackbody absorbs all incident radiation, regardless of wavelength and direction.

Stefan–Boltzmann constant

Blackbody emissive power

The radiation energy emitted by a blackbody:

55

Spectral blackbody emissive Power: The amount of radiation energy emitted

by a blackbody at a thermodynamic temperature T per unit time, per unit

surface area, and per unit wavelength about the wavelength .

Boltzmann’s constant

Planck’s law

56

The wavelength at which the peak occurs for a specified

temperature is given by Wien’s displacement law:

57

Observations from the figure• The emitted radiation is a continuous function of wavelength.

At any specified temperature, it increases with wavelength, reaches a peak, and then decreases with increasing

wavelength.• At any wavelength, the amount of emitted radiation increases

with increasing temperature.• As temperature increases, the curves shift to the left to the shorter wavelength region. Consequently, a larger fraction of

the radiation is emitted at shorter wavelengths at higher temperatures.

• The radiation emitted by the sun, which is considered to be a blackbody at 5780 K (or roughly at 5800 K), reaches its peak in the visible region of the spectrum. Therefore, the sun is in

tune with our eyes. • On the other hand, surfaces at T < 800 K emit almost entirely

in the infrared region and thus are not visible to the eye unless they reflect light coming from other sources.

Intensity of Emitted Radiation

58

59

Incident Radiation

60

Radiosity

61

62

RADIATIVE PROPERTIESMost materials encountered in practice, such as metals, wood, and bricks, are opaque

to thermal radiation, and radiation is considered to be a surface phenomenon for such materials.

Radiation through semitransparent materials such as glass and water cannot be considered to be a surface phenomenon since the entire volume of the material

interacts with radiation.A blackbody can serve as a convenient reference in describing the emission and

absorption characteristics of real surfaces.

Emissivity• Emissivity: The ratio of the radiation emitted by the surface at a given temperature

to the radiation emitted by a blackbody at the same temperature. 0 1.

• Emissivity is a measure of how closely a surface approximates a blackbody ( = 1).

• The emissivity of a real surface varies with the temperature of the surface as well as the wavelength and the direction of the emitted radiation.

• The emissivity of a surface at a specified wavelength is called spectral emissivity . The emissivity in a specified direction is called directional emissivity where

is the angle between the direction of radiation and the normal of the surface.

63

64

Absorptivity, Reflectivity, and

Transmissivity

Irradiation, G: Radiation flux incident on a

surface.

for opaque surfaces

65

Kirchhoff’s Law

The total hemispherical emissivity of a surface at temperature T is equal

to its total hemispherical absorptivity for radiation coming from a

blackbody at the same temperature.

Kirchhoff’s law

spectral form of Kirchhoff’s law

The emissivity of a surface at a specified wavelength, direction, and temperature is always equal to its absorptivity at the same wavelength,

direction, and temperature.

66

The Greenhouse EffectGlass has a transparent window in the wavelength range 0.3 m < < 3 m in which

over 90% of solar radiation is emitted. The entire radiation emitted by surfaces at room temperature falls in the infrared region ( > 3 m).

Glass allows the solar radiation to enter but does not allow the infrared radiation from the interior surfaces to escape. This causes a rise in the interior temperature as a result of

the energy buildup in the car. This heating effect, which is due to the nongray characteristic of glass (or clear plastics),

is known as the greenhouse effect.

ATMOSPHERIC AND SOLAR RADIATIONAtmospheric radiation: The radiation energy emitted or

reflected by the constituents of the atmosphere.

The energy of the sun is due to the continuous fusion reaction during which two hydrogen

atoms fuse to form one atom of helium. Therefore, the sun is essentially a nuclear

reactor, with temperatures as high as 40,000,000 K in its core region.

The temperature drops to about 5800 K in the outer region of the sun, called the convective

zone, as a result of the dissipation of this energy by radiation.

Total solar irradiance Gs: The solar energy reaching the earth’s atmosphere is

called the

Solar constant: The total solar irradiance. It represents the rate at which solar energy is

incident on a surface normal to the sun’s rays at the outer edge of the atmosphere when the

earth is at its mean distance from the sun 67

The value of the total solar irradiance can be used to estimate the effective surface temperature of

the sun from the requirement that

The sun can be treated as a blackbody at a

temperature of 5780 K.

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