HEAT TRANSFER

UNIT – IV
(THEORY)
_____________________________________________________________________________________

1. Sketch temperature and velocity profiles in free convection a vertical wall. [S-2003]
2. Discuss the pool boiling curve and regimes of pool boiling. [W-2003]
3. Write short notes on: Pool boiling and condensation. [S-2004]
4. Write short notes on: Free convection from rotating bodies. [S-2004]
5. Write short notes on: Film and Drop wise condensation. [S-2003, W-2004]
6. Discuss various regimes of flow moving with the free stream velocity (U ) over the flat surface.
[W-2005]
7. State the effect of non-condensable gases on condensation. [W-2005, S-2011]
8. Explain with neat sketch development of velocity boundary layer on hot and cold vertical plate
subjected to Natural Convection. [W-2005]
9. Distinguish between filmwise and dropwise condensation process. Also discuss the effect of non-
condensible gases on condensate rate. [S-2006]
10. Explain pool boiling curve. [S-2006]
11. Explain Hydrodynamic and thermal boundary layer with reference to flow over flat heated plate.
[W-2006]
12. Explain Regimes of pool boiling. [W-2006]
13. What do you mean by hydrodynamic and Thermal boundary layers? Explain with reference to
flow over a flat heated plate. [S-2007]
14. Difference between the Mechanism of filmwise and dropwise condensation with sketch. [S-2007]
15. Write short notes on: Hydrodynamic and Thermal boundary layer. [W-2007, W-2008, S-2009]
16. Explain with neat sketch the pool boiling curve and regimes of pool boiling. [W-2007]
17. Write short note on: Filmwise and Dropwise Condensation. [W-2007, S-2010]
18. Differentiate between filmwise and dropwise condensation. [W-2008]
19. Differentiate between Natural and Forced Convection. [W-2008]
20. Distinguish between Dropwise and Filmwise condensation. [S-2009]
21. Write short note on Boundary layer thickness. [S-2010]
22. Explain boundary layer concept and define clearly hydrodynamic and thermal boundary layer
thickness when fluid is flowing over a flat plate. [W-2010]
23. What do you mean by thermal boundary layer? Explain how does the ratio /t vary with Prandtl
number. [S-2011]
24. Explain Nukiyam Boiling Curve. [S-2011]
25. Write short note on: Significance of Reynolds number and Prandtl number. [S-2012]
26. Distinguish between:
(i) Nucleate and Film Boiling
 (ii) Filmwise and Dropwise condensation [S-2012]
27. Explain the following:
(i) Coefficient of volumetric expansion
(ii) Grashoff number. [S-2012]
NUMERICAL
1. A rectangular duct 30cm  20cm in cross –section carries cold air. The temperature of the outer
surface of the duct is 5C and surrounding air temperature is 25C. Find the heat gain by the duct
assuming one meter duct is exposed to the air in vertical position.
The properties of air at mean temperature is given below:
 = 1.2 kg/m3,  = 18.17  10-6 kg/m-s,  = 14.61  10-6 m2/sec, Cp = 1006 J/kg-K,
K = 0.0256 W/mK
Use the following correlation:
Nua = 0.13(GrPr)1/3 [S-2003]
2. 0.5kg of water per minute is heated from 20C to 40C when passed through a tube of 2.5cm
diameter steel pipe. The pipe surface temperature is maintained at 110C by condensing steam on
its surface. Find out the length of the pipe required.
The properties of water at mean temperature is:  = 978 kg/m3, Cp = 4200 J/kg-K, K = 0.575
W/mK,  = 0.415  10-6 m2/sec
The correlating are
Nu = 3.65 for Laminar flow.
Nu = 0.023 Re0.8 Pr0.33 for turbulent flow [S-2003]
3. A thin metal plate 1m  1m. is placed on a rooftop. It receives radiant heat from the sun directly at
a rate of 170 w/m2. If heat transfer from the plate to the ambient occurs purely by free convection,
calculate the steady state temperature of the plate. Assume that there is no heat loss from the
bottom of the plate. The ambient temperature is 25C. [W-2003]
4. Consider a 0.6  0.6m thin square plate in room at 30C. one side of the plate is maintained at a
temperature of 74C, while the other side is insulated. Determine the rate of heat transfer from the
plate by natural convection if the plate is
1. Vertical
2. Horizontal with hot surface facing up.
3. Horizontal with hot surface facing down. [W-2003]
5. Air free saturated steam at Tv = 90C and P = 70.14 Kpa. Condenses on the outer surface of a L =
1.5m log and D = 2.5 m. outside diameter vertical tube maintained at a uniform temperature T w =
70C. assuming filmwise condensation, calculate the average heat transfer coefficient over the
entire length of the tube. Also calculate the total mass flow rate of condensation m, the total heat
transfer rate Q over the entire surface, and the Reynolds number Re at the bottom of the surface.
[hfg = 2309 KJ/kg]. [W-2003]
6. Air flow through a long rectangular (30cm heigh  65cm width) air conditioning duct maintains
the outer duct surface temperature at 15C. If the duct is uninsulated and exposed to air at 25C,
 calculate the heat gained by the duct per meter length assuming it to be horizontal. Use the
following correlation:
Vertical surface = NuL = 0.59 (ReL)1/4
Upper surface heated lower surface cooled  NuL = 0.54 (ReL)1/4
Lower surface heated or upper surface cooled  NuL = 0.27 (ReL)1/4
Take the following properties of air:
 = 1.205 kg/m3, Cp = 1005 J/kgK,  = 15  10-6 m2/sec, K = 0.02593 W/mK [S-2004]
7. Saturated F-12 vapour at 12.3/bar condenses on the outside of a bank of 25 horizontal tubes 1cm
OD arranged in 55 square array. Calculate the rate of condensation per meter length of the array
if the tube surface is maintained at 40C.
F-12 has following properties:
Liquid density = 1218 kg/m3
Latent heat = 128.12 kJ/kg
Liquid K = 0.0686 W/mK
Liquid  = 2.84  10-6 kg/m-s
Saturation temperature at 12.3/bar = 48.9C [S-2004]
8. A vertical plate is heated from one side and is maintained at 96C. On the other side is air at 30C.
Calculate:
(i) Local value of convective heat transfer coefficients at distance of 20cm from the lower
edge.
(ii) Average value of convective heat transfer coeffiecient over the whole 20cm length of plate.
[W-2004]
9. A steel plate 20cm2 and 0.5 cm thick is heated uniformly to 430C and is kept vertically in still air
at a temperature of 20C. Neglecting radiation of making suitable assumption. Calculate time
required for the plate to cool at 330C. [W-2004]
10. The outer surface of a vertical tube which of length 1.25m and outer diameter 50mm is exposed to
saturated steam at atmospheric pressure. The tube surface is maintained at 80C by the flow of
cooling water through it. Determine the rate of heat transfer to the coolent and the rate at which the
steam is condensed at the tube surface. If the tube is held in horizontal position, will there be any
change in the mass of condensate? [W-2004]
11. Air at velocity of 3 m/sec. and at 20C flows over a flat plate along its length. The length , width
and thickness of plate is 100cm, 50cm and 2cm respectively. The top surface of the plate is
maintained at 100C. Calculate the heat lost by the plate and temperature of the bottom surface of
the plate for steady state condition. The thermal conductivity of the plate may be taken as 23
W/mk. Take properties of air as r = 1.06 Kg/m3,  = 18.97  10-6 m2/s, Kair = 0.02894 W/mk, Pr =
0.696, Cp = 1.005 KJ/Kg K. Use relations:
NuL = 0.664 (Re)1/2(Pr)1/3 – For Laminar flow
NuL = 0.036 (Re)4/5(Pr)1/3 – For Turbulent flow [W-2005]
12. Water is heated while flowing through 1.5cm  3.5cm rectangular cross-section tube at a velocity
of 1.2m/s. The entering temperature of water is 40C and tube wall is maintained at 85C.
 Determine the length of the tube required to raise the temperature of water to 70C. Properties of
water at bulk mean temperature are:
r = 985.5 Kg/m3, Cp = 4.18 KJ/Kg K,  = 0.517  10-6 m2/sK = 0.654 W/mk
Use relation,
Nud = 0.023 (Red)0.8 Pr0.4 [W-2005]
13. A horizontal fluorescent tube which is 3.8cm in diameter and 120cm long stands in still air at
1atm. And 20C. If the surface temperature of the tube is 40C and radiation is neglected, what
percentage of power is being air as  = 16.19  10-6 m2/sec. Kair = 0.02652 W/mk, Pr = 0.706.
Use relation NuD = 0.53 (ReD)1/4 [W-2005]
14. A 12cm outside diameter and 2m long tube is used in a big condenser to condense the steam at 0.4
bar. Find the amount of condensate formed in vertical and horizontal position of tube
Given,
1 /4
❑2 g hfgk 3
hav=0.93
[
L ( T s −T w ) ]
1/4
hav D
hah
=1.3
L[ ]
The saturation temperature of steam Ts = 74.5C
Average wall temperature = 50C
r = 982.2 Kg/m3, k = 0.65 W/mk, hfg = 2480 KJ/Kg,  = 0.47  10-3 kg/m-s. [W-2005]
15. Estimate the heat transfer from a 40W incandescent bulb at 127C to 27C quiescent air.
Approximate the bulb as a 50mm diameter sphere. What percentage of the power is lost by free
convection? [S-2006]
16. A horizontal plate 1m  0.8m is kept in a water tank with the top surface at 60C providing heat to
warm stagnant water at 20C. Determine the value of convection coefficient. [S-2006]
17. A wide vertical cooling fin, approximating a flat plate 0.3m high, is exposed to steam at
atmospheric pressure. The fin is maintained at 90C by cooling water. Determine the heat transfer
and also the condensate mass flow rate per unit width. [S-2006]
18. In a certain process, castor oil at 30C flows past a flat plate. The velocity of oil is 0.08 m/sec. the
length of the plate is 5m. The plate is heated uniformly and maintained at 90C. calculate the
following:
(i) Hydrodynamic and thermal boundary layer thickness at the trailing edge of plate.
(ii) Total drag force per unit width on one side of the plate. Use the following correlation:
Nu = 0.332 (ReL)1/2.(Pr)1/3
Take properties as,
 = 956.8 kg/m3, K = 0.213 w/mk,  = 7.2  10-8 m2/s,  = 0.65  10-4 m2/s [W-2006]
19. Saturated vapor at 50C condenses on the outside of a bank of 16 horizontal tubes, 1.2cm diameter,
arranged in 4  4 array. Calculate the rate of condensation per meter length of the array if the tube
surface is maintained at 40C. condensate of vapor has the following properties:
 = 1174 kg/m3, k = 6.9  10-2 w/m – k,  = 2.49  10-4 N-S/m2 [W-2006]
20. A rectangular plate 0.2m  0.4m is maintained at a uniform temperature of 80C. It is placed in
atmospheric air at 24C. Compare the heat transfer rates from the plate for the cases when the
vertical height is,
(a) 0.2m
(b) 0.4m [W-2006, W-2007]
21. A horizontal steam pipe of diameter 20cm runs through a large room and exposed to air at
temperature of 20C. The pipe surface temperature is 180C. find the flow of heat per meter length
of the pipe by convection. Use the correlation
Nu = 0.53 [Gr.Pr]1/4
Take properties of air as,
 = 0.946 kg/m3, Cp = 1.009 kJ/kgk,
K=3.208  10-2 w/mk,  = 23.13  10-6 m2/s [W-2006]
22. Air at 16C and pressure of 1 bar is flowing over a plate at a velocity of 3 m/s. If the plate is 30cm
wide and at 60C, using exact method at x = 30cm at the distance corresponding to the transition
point. Find the following:
(i) Boundary layer thickness
(ii) Average friction coefficient
(iii) Shearing stress due to friction
(iv) Average convective heat transfer coefficient
(v) Total drag force on the plate
Take properties at bulk mean temperature as,
 = 1.1374 Kg/m3, K = 2.732  10-2 w/mK
Cp = 1.005 kJ/KgK,  = 16.7  10-6 m2/sec
Use correlation as,
Nu = 0.332 (Rex)1/2.(Pr)1/3 [S-2007]
23. Water is to be boiled at atmospheric pressure in a polished copper pan by means of electric heater.
The bottom of the copper pan is 0.4m in diameter and is kept at 120C. Calculate:
(i) Power required to boil water in this pan.
(ii) The rate at which water will evaporate from the pan due to the boiling process.
(iii) Critical heat flux these conditions. [S-2007]
24. Saturated steam at 80C condenses on the outside of a horizontal tube of 10cm diameter and
Length ‘L’ maintained at a temperature of 70C. Latent neat at steam = 2300 KJ/kg when the tube
was kept vertical it was observed that, the rate of condensation was same as before. Find the length
of tube ‘L’ and rate of condensation per hour. Take properties of condensate at 75C as,
 = 974.8 kg/m3,  = 380.5  10-6 N.s/m2, K = 0.8715 w/mK [S-2007]
25. Air at a velocity of 3 m/s and at 20C flows over a flat plate along its length. The length, width and
thickness of the plate are 100cm, 50cm and 2cm respectively. The top surface of the plate is
maintained at 100C. Calculate the heat lost by the plate and temperature of bottom surface of the
 plate for the steady state conditions. The thermal conductivity of the plate may be taken as 23
W/mK. [W-2007]
26. A condenser is designed to condense 500 kg/h of dry and saturated steam at 0.1 bar. A square array
of 400 tubes, 6mm in diameter is used. The tube surface is maintained at 24C by flowing water.
Calculate the heat transfer coefficient and length of each tube. [W-2007]
27. A steam condenser consisting of a square array of 625 horizontal tubes, each 6mm in diameter, is
installed at the exhaust of a steam turbine. The tubes are exposed to saturated steam at a pressur of
15 kPa. If the tube surface temperature is maintained at 25C, Calculate:
(i) The heat transfer coefficient and
(ii) The rate at which steam is condensed per unit length of the tubes.
Assume film condensation on the tubes and absence of non-condensable gases.
Properties of saturated water at film temperature are  = 992 kg/m3,  = 663  10-6 Ns/m2, k
= 0631 W/mC [W-2008]
28. A 2-stroke motor cycle petrol engine cylinder consists of 16 fins. If the surface temperature is
475C and atmospheric air temperature is 25C, calculate the heat transfer rate from the fins for
the following cases:
(a) When the motor cycle is stationary
(b) When the motor cycle is running at a speed of 60 km/h.
The fin may be idealized as single horizontal flat plate of the same area.
Properties of air at 250C
K =4.266  10-2 W/mC,  = 40.61  10-6 m2/s, Pr = 0.677
Use correlations:
Nu = 0.54 [Gr.Pr]0.25 for laminar flow
Nu = 0.036 [Re]0.8 [Pr]0.33 for turbulent flow. [W-2008]
29. Air flow through a long rectangular air conditioning duct (50cm  30cm) in size maintains the duct
outer surface at 15C. If the duct is uninsulated and exposed to air at 25C, calculate heat gain by
duct per meter length.
Use:
(i) NuL = 0.15 Ra1/3 for upper surface heated or lower cooled.
(ii) NuL = 0.27 Ra1/4 for lower surface heated or upper cooled.
(iii) Nu = 0.59 Ra1/4 for vertical surfaces
Use:
 = 1.205 kg/m3, K = 0.0259 w/mK,  = 15.06  10-6 m/s, Cp = 1006 J/kg-K
As per of air at MFT [S-2009]
30. A sheet metal air duct carries air-conditioned air at an average temperature of 10C. The duct size
is 320mm  200mm and length of the duct exposed to the surrounding air at 30C is 15m. Find the
heat gained by the air in the duct. Assume 200mm side is vertical and top surface of the duct is
insulated. Use the following properties:
Nu = 0.6 (Gr.Pr)0.25 for vertical surface
 Nu = 0.27 (Gr.Pr)0.25 for horizontal surface.
Take the properties of the air at mean temperature of (30 + 10)/2 = 20C as given below:
Cp = 100 J/kg K,  = 1.204 kg/m3, Pr = 0.71,  = 18.2  10-6 N-s/m2,  = 15.1  10-6 m2/s, K =
0.256 W/mK [S-2010]
31. An electric bulb of 100W has its surface temperature of 70C. it is exposed to the stagnant
atmospheric air at 20C. The bulb can be approximated as a sphere of 4cm diameter. Calculate the
percentage of heat loss by the natural convection from the bulb to the air. [S-2010]
32. A vertical tube of 60mm outside diameter and 1.2m long is exposed to steam at atmospheric
pressure. The outer surface of the tube is maintained at a temperature of 50C by circulating cold
water through the tube. Calculate the following:
(i) The rate of heat transfer to the coolant
(ii) The rate of condensation of steam
The thermo-physical properties of water at 75C are:
 = 975 kg/m3,  = 375  10-6 N-s/m2, K = 0.67 W/mC.
The properties of saturated vapour at 100C are:
 = 0.596 kg/m3, hfg = 2257 kJ/kg [S-2010]
33. Air at atmospheric pressure and 60C flows parallel to and on both sides of a flat plate (20cm
square plate) with a velocity of 15m/s. If the plate is maintained at a temperature of 20C, calculate
the rate of heat transfer to the plate and drag. Take the properties of air at mean film temperature
are:
 = 16.96  10-6 m2/s
 = 1.128 kg/m3
K = 0.0276 w/m-K
Pr = 0.699 [W-2010]
34. A steel plate, 20cm square and 0.5cm thick, is heated uniformly to 430C. Afterwards it is kept
vertically in still air at a temperature of 20C. Neglecting radiation and making suitable
assumptions, Calculate the time required for the plate to cool to 130C. Take the density of steel to
be 7900 kg/m3 and its specific heat to be 0.46 kJ/kgK. [W-2010]
35. A circular plate type heater (300mm) is insulated at one surface and maintained at 200C. It is
exposed to the stagnant surrounding air which is at 20C. Calculate the heat transfer rate from the
plate by natural convection when it is held horizontal with hot surface facing up. [S-2011]
36. Saturated steam at 80C condenses on the outside of a horizontal tube of 10cm diameter and
Length ‘L’ maintained at a temperature of 70C. Latent neat at steam = 2300 KJ/kg when the tube
was kept vertical it was observed that, the rate of condensation was same as before. Find the length
of tube ‘L’ and rate of condensation per hour. [S-2011]
37. In a quenching process a copper plate of 3mm thick is heated up to 350C and then suddenly it is
dipped into a water bath and cooled to 25C. Calculate the time required for the plate to reach the
temperature of 50C. The heat transfer coefficient on the surface of the plate is 94 W/m 2K. The
plate dimension may be taken as length 40cm and width 30cm. Take Cp = 380.9 J/kgK,  = 8800
kg/m3, k = 385 W/mK. [S-2011]
38. Saturated steam at 100°C condenses on the outside of a horizontal tube 25mm in outer diameter
whose surface is maintained at 80°C. Calculate average heat transfer coefficient. Find the length
which would yield the same value of average heat transfer coefficient, if the tube is held vertically.
[S-2012]
39. Beer cars (diameter 65mm, length 150mm) are to be cooled from an initial temperature of 20°C by
placing them in a bottle cooler with an ambient air temperature of 1°C. compare the initial cooling
rates when the cars are laid horizontally, to when they are laid vertically. [S-2012]