Expt. HT 307

Finned Tube Heat Exchanger

Objective

To determine the efficiency of given longitudinal/pin fin and compare it with the theoretical value for thegiven fin.

Apparatus

1. Longitudinal fin heat exchanger.

2. Pin fin heat exchanger.

3. Bare pipe without fins.

4. Steam generator to generate steam at constant pressure. The steam generator is also provided withtemperature indicator and a dead weight safety valve.

Procedure

1. IMPORTANT INSTRUCTIONS: Follow instructions 1 and 2 without fail, otherwise electrical heaterwill burn out.

2. Open the drain valve provided at the bottom of steam generator and drain out the water from steamgenerator completely.

3. Close the drain valve and charge 4 lit. of water through charging valve provided at the top of the steamgenerator and close it. Ensure that the dead weight safety valve is free.

4. Start the electrical heater of steam generator. Initially supply full voltage to the electrical heater.Steam will start forming within about 15-20 min. of switching on the heater. During this period,keep open the valve to one of the test sections (either longitudinal fin heat exchanger or pin fin heatexchanger). Also keep the needle valve at the end of test section open. Once the steam generationstarts, the finned tube heat exchanger will start getting heated up and condensate will start coming outof the needle valve provided at the bottom of condensate collector. When the test section (finned tubeheat exchanger) is fully heated up, steam will start coming out of the needle valve. Now regulate theneedle valve in such a way that only condensate comes out of it. At this point of time also regulatethe voltage supplied to the electrical heater so as to keep the pressure in the steam generator constant.The pressure can be regulated between 0-1 atm. gauge as per the requirement.

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5. Once the test section (finned tube heat exchanger along with bare pipe without fins) is fully heated,drain out completely the condensate it any. Close the needle valve on condensate drain line simul-taneously starting the stop-watch. Collect the condensate accumulated at an interval of 15 min. forfinned tube heat exchanger and 30 min. for bare pipe. If the quantity of condensate collected is samefor 2 to 3 consecutive readings (within experimental accuracy), note down the volume of condensatecollected and time interval.

6. Repeat the procedure given in 4 for pin fin heat exchanger as well as bare pipe.

Theory

In a heat exchanger, the two fluids namely; hot and cold, are separated by a metal wall. Under this conditionthe rate of heat transfer will depend on the overall resistance to heat transfer given by the equation:

1UiAi

=1

hiAi+

xKAlm

+1

hoAo(1)

where,

Ui = Overall heat transfer coefficient based on inner area [Kcal/hr m2 ◦C ]

Uo = Overall heat transfer coefficient based on outer area [Kcal/hr m2 ◦C ]

hi ,ho = Inside and outside film heat transfer coefficients [Kcal/hr m2 ◦C ]

Ai ,Ao =Inside and outside surface area [m2]

When viscous liquids are heated in a double pipe heat exchanger or any standard tubular heat exchanger bycondensing steam or hot fluid of low viscosity, the film heat transfer coefficient of the viscous liquid willbe much smaller than that on the hot fluid side and will therefore, become controlling resistance for heattransfer. This condition is also present in case of air or gas heaters where the gas side film heat transfercoefficient will be very low (typically of the order of 0.01 to 0.005 times) compared to that for the liquidor condensing vapour on the other side. Since, the heat transfer coefficient of viscous fluid or gas cannotbe improved much, the only alternative is to increase the area available for heat transfer on that side so thatits resistance to heat transfer can be reduced. To conserve space and to reduce the cost of equipment inthese cases, certain type of heat exchange surfaces, called extended surfaces, have been developed in whichoutside area of tube is increased many fold by fins and other appendages.

Two types of fins, are in common use viz; longitudinal fins and transverse fins. Longitudinal fins are usedwhen the direction of flow of the fluid is parallel to the axis of tube and transverse fins are used when thedirection of the flow of the fluid is across the tube. Spikes, pins, studs or spines are also used for eitherdirection of flow.

The outside are of a finned tube consists of two parts: the area of fins and the area of bare tube not coveredby the bases of fins. A unit area of fin surface is not as efficient as a unit area of bare tube surface becauseof the added resistance to the heat flow by conduction through the fin at its base. The expression for finefficiencies can be derived by solving the general differential equation of heat conduction with suitableboundary conditions. Generally three boundary conditions are used;

1. Fin of infinite length so that there is no heat dissipation from its tip, or in other words temperature atthe tip of fin is same as that of the surrounding fluid.

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2. Insulated tip. This condition even though cannot be realized in practice, but considering that the tiparea is negligible as compared to the total fin area, heat dissipated from tip can be neglected and hence,dt/dx is assumed to be zero at the tip.

3. Finite heat dissipation from the tip. Even though the assumption of insulated tip is invalid, most ofthe fins are treated under this category, and longitudinal fin efficiency for this case is given by theexpression:

η f in =tanh(mL)

mL(2)

where

m =√

(hC/KA)

h = film heat transfer coefficient from the fin surface [Kcal/hrm2◦C ]

C = circumference of the fin [m]

K = thermal conductivity of fin material [Kcal/hr m◦C ]

A = cross-sectional area of fin [m2]

From the above equation, it can be seen that the fin efficiency is a function ofmL, and as the value ofmLincreases, the fin efficiency decreases. A reasonable value of fin efficiency will be around 50 to 75% forwhich mL should have a value between 1 and 2. If the fin heightL should be sufficient (of the order of 5 to8 cm), then it can be seen that the value ofh should be around 10 to 20 which can be given by air in naturalconvection. The value of film heat transfer coefficient for any other liquid in natural convection, or any gasin forced convection will be much higher than 20. Thus, the given set-up is used for heat transfer to air innatural convection region.

Observations

1. Finned Tube:

1. Height of fin (L) : cm.

2. Width of fin (W) : cm.

3. Thickness of fin (b) : cm.

4. Number of fins (N) : 4

5. O.D. of fin tube : cm.

6. Thermal conductivity of fin material (K) : Kcal/hr m◦C

2. Bare Tube:

1. Length of tube (l) : cm.

2. O.D. of tube : cm.

3. Tambient : ◦C

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Calculations

1. Circumference of fin (C):C = 2(w + b) = m. (3)

2. Cross-sectional area of fin (A):A = wxb= m2 (4)

3. Fin area available for heat transfer:

AF = CxLxN= m2 (5)

4. Tube area available for heat transfer in finned tube heat exchanger:

AB = (ΠD − Nb)xw = m2 (6)

5. Total area of finned tube heat exchanger:

At = AF + AB = m2 (7)

6. Heat given out by steam through finned tube heat exchanger (Q1):

Q1 = (m1x)xλ = Kcal/hr (8)

7. Heat given out by steam through bare tube (Q2):

Q2 = (m2x)xλ = Kcal/hr (9)

whereλ = latent heat of vaporization of water at steam pressure (Kcal/Kg)

8. Film heat transfer coefficient from bare tube (h):

h = Q2/(Ax∆T) = Kcal/hrm2◦C;

A = ΠDL = m2;

∆T = (Tsteam− Tambient) =◦C

9. m=√

(hC/KA) =

10. mL=

11. η f in (Theoretical)= tanhmL/mL

12. Amount of heat actually dissipated by fin:

Qf in = Q1 − (AB × h× ∆T) = Kcal/hr (10)

13. Amount of heat that can be dissipated by ideal fin:

Qideal = AF × h× ∆T = Kcal/hr (11)

14. Observed value of fin efficiency:

η(Observed) =Qf in

Qideal= (12)

Conclusion

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