AEA4724 ADVANCED HEAT TRANSFER
QUESTION BANK
PART A
1. Write down the equation for conduction of heat through a plane wall.
2. Define Thermal conductivity.
3. Differentiate laminar and turbulent flow.
4. State transient heat conduction.
5. Define Reynolds Number.
6. Define Grashof Number.
7. Write the different types of heat exchanger.
8. Define the mean film temperature.
9. State Kirchoff’s law of radiation.
10. Differentiate Counter flow and parallel for heat exchanger.
11. Define critical thickness of insulation.
12. Define Thermal conductivity.
13. State transient heat conduction.
14. Define extended surfaces. Give some examples.
15. According to Newton’s law of cooling the amount of heat transfer from a
solid surface of area A at a temperature Tw to a fluid at a temperature T∞
is given by ----16. Define Grashof Number.
17. Define the mean film temperature.
18. State the advantage of NTU method over the LMTD method.
19. Write the different types of heat exchanger.
20. State Kirchoff’s law of radiation.
21. State Newton’s law of cooling.
22. Write down the equation for conduction of heat through a plane wall.
23. What is meant by infinite solid?
PART B
1. Determine the heat transfer through the plane of length 6 m, height 4 m and thickness 0.30m. The
temperature of inner and outer surface is 100°C and 40°C. Thermal conductivity of the wall is 0.55
W/mK .
2. A concrete wall of 1 m thick is poured with concrete. The hydration of concrete generates
150W/m3 heat. If both the surfaces of the wall are maintained at 35°C. Find the maximum
temperature in the wall.
3. An aluminium rod of 7mm thick and 50 mm long whose base is maintained at 120 °C the ambient
temperature is 22 °C, h= 140 W/m2-K, k=55 W/m-K. Find out the heat transferred by fin.
4. A copper rod of outer diameter 20 mm initially at a temperature of 380°C is suddenly immersed
in water at 100°C. Determine the time required for the rod reach 210°C. Take convective heat
transfer co-efficient is 95W/m2 K.
5. A fluorescent tube of 38 mm diameter and 1.2 m long is fitted horizontally and exposed to still air
at 20 °C. Determine the convective heat transfer coefficient, if its surface is maintained at 40°C.
6. Air at 20°C.at atmosphere pressure flows over a flat plate at a velocity of 3.5 m/s. If the plate is
0.5 m wide and at 60°C calculate the following at x=0.400m.
7. Dry saturated steam at a pressure of 2.45bar condenses on the surface of a vertical tube of height
1m. The tube surface temperature is kept at 117°C. Estimate the thickness of the condensate film.
8. Emissivity of two large parallel plates maintained at 800 °C and 300 °C are 0.3 and 0.5 respectively.
Find the net radiant heat exchanged per meter square for these plates.
9. Two concentric cylinders of 300 mm and 400 mm diameter respectively at 500 K and 400 K.
Determine heat exchange by radiation for infinite cylinders. Both cylinders are covered with same
paint of emissivity 0.6.
10. A heat exchanger has 17.5 m2 area available for heat transfer. It is used for cooling oil at 200°C by
using water available at 20°C. The mass flow and specific heat of oil are 10000 kg/hr and 1.9 kJ/kg
K and the mass flow and specific heat of water are 3000kg/hr. and 4.187 kJ/kg K. if the overall heat
transfer coefficient is 300 W/m2-K, estimate the outlet temperatures of oil and water for parallel
flow and counter flow arrangements by using LMTD method.
11. A spherical shaped vessel of 1.2 m diameter is 100 mm thick. Find the rate of heat leakage,
if the temperature difference between the inner and outer surfaces is 200 o C. Thermal
conductivity of material is 0.3 kJ /mhoC.
12. A large vertical plate of 4 m height is maintained at 60 °C and exposed to atmospheric air
at 10 °C. Calculate the heat transfer coefficient.
13. Water flows at the rate of 65 kg/min through a double pipe counter flow heat exchanger.
Water is heated from 50o C to75oC by an oil flowing through the tube. The specific heat of
the oil is 1.780 kj/kg.K. The oil enters at 115oC and leaves at 70oC.the overall heat transfer
co-efficient is 340 W/m2K.calculate the Rate of heat transfer.
14. In a counter flow double pipe heat exchanger, water is heated from 25 oC to 65 oC by oil
with specific heat of 1.45 kJ/Kg K and mass flow rate is 0.9 Kg/S. The oil is cooled from
230 oC to 160 oC. If the overall heat transfer co-efficient is 420W/m2 oC, calculate the rate
of heat transfer.
15. The temperature of a black surface 0.25 m2 of area is 650 oC calculate the total rate of energy
emission and intensity of normal radiation.
16. The amount of radiant energy falling on a 50 cm x 50 cm horizontal thin metal plate
insulated to the bottom is 3600 KJ/ m2 hr. If the emissivity of the plate surface is 0.8 and
the ambient air temperature is 30 oC , find the equilibrium temperature of the plate.
17. A Plane wall 10cm thick generates heat at the rate of 4 x 104 W/m3 when an electric current is
passed through it. The convective heat transfer co-efficient between each face of the wall the
ambient air is 50 W/m2K. Determine the surface temperature.
18. A stainless steel cylindrical rod fin of 1.2cm diameter and 6cm height with thermal conductivity of
25W/mK is exposed to surrounding with a temperature of 60°C. The heat transfer co-efficient is 45
W/m2K and the temperature at the base of the fin is 100°C. Determine Fin efficiency.
19. Air at 30°C flows over a flat plate at a velocity of 4m/s and the plate is maintained at a uniform
temperature of 90°C. If the transition occurs at a critical Reynolds number of 5 x 105, calculate the
thickness at which the boundary layers change from laminar to turbulent. At that location find the
hydrodynamic boundary layer thickness.
20. A copper rod of outer diameter 20 mm initially at a temperature of 380°C is suddenly immersed in
water at 100°C. Determine the time required for the rod reach 210°C. Take convective heat transfer
co-efficient is 95W/m2 K.
21. A thin 80 cm long and 8 cm wide horizontal plate is maintained at temperature of 130 °C in large
tank full of water at 70 °C. Estimate the rate of heat input into the plate necessary to maintain the
temperature of 130°C.
22. Dry saturated steam at a pressure of 2.45bar condenses on the surface of a vertical tube of height
1m. The tube surface temperature is kept at 117°C. Estimate the thickness of the condensate film.
23. Estimate the net radiant heat exchange per square meter from a very large plate at a temperature
of 550°C and 320°C. Assume that emissivity of hot plate is 0.8 and clod plate is 0.6.
24. Two large parallel plates are maintained at a temperature of 900 K and 500 K respectively. Each
plate has an area of 6 square meters. Compare the net heat exchange between the plates for the
following cases. Both plates are black and plates have an emissivity of 0.5.
25. A heat exchanger has 17.5 m2 area available for heat transfer. It is used for cooling oil at 200°C by
using water available at 20°C. The mass flow and specific heat of oil are 10000 kg/hr and 1.9 kJ/kg
K and the mass flow and specific heat of water are 3000kg/hr. and 4.187 kJ/kg K. if the overall heat
transfer coefficient is 300 W/m2-K, estimate the outlet temperatures of oil and water for parallel
flow and counter flow arrangements by using LMTD method.
PART C
1. A furnace walls made up of three layers, one of fire brick, one of insulating brick and one
of red brick. The inner and outer surfaces are at 870o C and 40o C respectively. The
respective co- efficient of thermal conductivity of the layer are 1.0, 0.12 and 0.75 W/mK
and thicknesses are 22 cm, 7.5, and 11 cm. assuming close bonding of the layer at their
interfaces, find the rate of heat loss per sq. Meter per hour.
2. An electrical wire of 10m length and 1mm diameter dissipates 200 W in air at 25 o C. The
convection heat transfer co-efficient between the wire surface and air is 15 W/m2k. The
thermal conductivity of wire is 0.582 W/mk. Calculate the critical radius of insulation and
also determine the temperature of the wire if it is insulated to the critical thickness of
insulation.
3. A 12 cm diameter long bar initially at a uniform temperature of 40oC is placed in a medium
at 650oC with a convective co efficient of 22 W/m2K calculate the time required for the
bar to reach2550oC. Take k = 20W/mK, ρ = 580 kg/m3 and c = 1050 J/kg K.
4. Air at 20oC, flow over a flat plate of 1 m long , 0.5 m wide at a velocity of 100 m/s. The
flow over the whole length of the plate is made turbulent. Calculate the thickness of the
boundary layer and mean value of heat transfer co-efficient.
5. A vertical pipe 80 mm diameter and 2 m height is maintained at a constant temperature of
120 oC. The pipe is surrounded by still atmospheric air at 30 oC. Find heat loss by natural
convection.
6. Water is to be boiled at atmospheric pressure in a polished copper pan by means of an
electric heater. The diameter of the pan is 0.38 m and is kept at 115 oC. Calculate the power
required to boil the water.
7. Heat exchanger is to be designed to condense 8 kg/s of an organic liquid (tsat = 80°C; hfg
= 600 kJ/kg) with cooling water available at 15°C and at a flow rate of 60 kg/s. The overall
heat transfer co-efficient is 400 W/m2 deg. Calculate the number of tubes required. The
tubes are to be of 25mm outer diameter, 2mm thickness and 4.85 m length.
8. Steam condenser is transferring 250 KW of thermal energy at a condensing temperature of
65°C. The cooling water enters the condenser at 20°C with flow rate of 7500 kg/hr.
calculate the long mean temperature difference. If overall heat transfer coefficient for the
condenser surface is 1250 W/m2 – deg, what error would be introduced if the arithmetic
mean temperature difference is used rather than the long mean temperature difference.
9. A black body of the total area 0.045 m2 is completely enclosed in a space bounded by 5cm
thick walls. The walls have a surface area 0.5 m2and thermal conductivity 1.07 W/m deg.
If the inner surface of the enveloping wall is to be maintained at 215°C and the outer wall
surface is at 30°C. Calculate the temperature of the black body. Neglect the difference
between inner and outer surface areas of enveloping material.
10. It has been observed that when the sun is overheated the earth’s surface on a clear day, the
radiation received by the earth’s surface is 1 kW/m2 and an additional 0.3 kW/m2 is
absorbed by earth’s atmosphere; assuming the sun to be a black body, determine the
temperature of the sun.
11. A steel tube (k1 = 43.26 W/mK) of 5.08 cm inner diameter and 7.62 cm outer diameter is
covered with 2.5 cm of asbestos insulation (k2=0.208 W/mK). The inside surface of the
tube receives heat by convection from hot gases at temperature of 316 °C with heat transfer
coefficient 284 W/m2-K, while the outer surface of the insulation is exposed to ambient air
at 38 °C with heat transfer coefficient 17 W/m2-K. Calculate loss of heat to the ambient air
for 3 m length of the tube. Find out the surface and interface temperature.
12. A 30 mm outer diameter steel ball is to be covered with two layer of insulation each having
a thickness of 25 mm. ‘k’ for one insulation is five times that of the other. Which material
s next to the ball to minimize the heat loss and also determine the percentage of heat
decrease in this arrangement? Assume the inside and outside surface temperature of the
insulation is fixed.
13. Aluminium fins of rectangular profile are attached to a plane wall with 5 mm spacing. The
fin thickness is 1 mm, fin extension is 10 mm, base temperature 200 °C, ambient
temperature is 40 °C, k=200 W/m-°C and h=50 W/m2-°C. Determine: a) Number of fins
b) Heat transfer from fin b) Fin effectiveness.
14. A copper slab of 400mm x 400mm x 5mm thick is at uniform temperature of 250 °C. It is
suddenly exposed to a fluid at 30℃ , with h=90 w/m2°C. Determine, the time required for
the slab to reach 90℃ Instantaneous heat transfer rate at 90℃ , Total heat flow until the
slab reaches 90℃.
15. A steam pipe of 240 mm OD and 10 m long is passing through
a
room in which still air is at 30 °C. The temperature of surface of the pipe is 90 °C.
Determine heat loss by convection and radiation when the pipe is kept horizontally.
16. A horizontal plate of 800×200 mm is maintained at 160 °C
and it is exposed to still
air at 20 °C. Calculate the heat loss due to convection.
17. Air at 20°C atmospheric pressure flows over a flat plate at a Velocity of 3 m/s. If the plate
is 1 m wide and at 80°C calculate the following at x = 300 mm.
18. Hot oil with a capacity rate of 2500W/K flows through a double pipe heat exchanger. It
enters at 360 °C and leaves at 300 °C. Cold fluid enters at 30 °C and leaves at 200 °C. If
the overall heat transfer coefficient is 800 W/(m^2 K). Determine the heat exchanger area
required for: a) Parallel flow b) Counter flow and give your comments
19. Two large parallel plates are maintained at 1000 K (ε = 0.6) and 500 K (ε = 0.8). Determine
heat exchange. If another plate of reflectivity 0.9 is introduced exactly in between,
determine percentage reduction in heat transfer
20. A concentric sphere of 300 mm ID, 360 mm OD is used to store liquid oxygen at -183 °C.
It is coated with a paint of ε = 0.5. The outer surface is maintained at 20 °C and coated with
same paint. Determine heat exchange. If another spherical wall is introduced exactly in
between, with same colour then determine percentage reduction in heat transfer.
21. A furnace walls made up of three layers, one of fire brick, one of insulating brick and one
of red brick. The inner and outer surfaces are at 870o C and 40o C respectively. The
respective co- efficient of thermal conduciveness of the layer are 1.0, 0.12 and 0.75 W/mK
and thicknesses are 22 cm, 7.5, and 11 cm. assuming close bonding of the layer at their
interfaces, find the rate of heat loss per sq. Meter per hour.
22. A motor body is 360 mm in diameter (outside) and 240 mm long. Its surface temperature
should not exceed 55oC when dissipating 340W. Longitudinal fins of 15 mm thickness and
40 mm height are proposed. The convection coefficient is 40W/m2 oC. determine the
number of fins required. Atmospheric temperature is 30 oC. Thermal conductivity = 40 W/
m oC.
23. A 12 cm diameter long bar initially at a uniform temperature of 40oC is placed in a medium
at 650oC with a convective co efficient of 22 W/m2K calculate the time required for the
bar to reach2550 oC. Take k = 20W/mK, ρ = 580 kg/m3 and c = 1050 J/kg K.
24. Air at 20 oC, at a Pressure of 1bar is flowing over a flat plate at a velocity of 3 m/s. if the
plate is maintained at 60 oC. Calculate the heat transfer per unit width of the plate.
Assuming the length of the plate along the flow of air is 2m.
25. A vertical pipe 80 mm diameter and 2m height is maintained at a constant temperature of
120 oC. The pipe is surrounded by still atmospheric air at 30 oC. Find heat loss by natural
convection.
26. Water is to be boiled at atmospheric pressure in a polished copper pan by means of an
electric heater. The diameter of the pan is 0.38 m and is kept at 115 oC. Calculate the power
required to boil the water.
27. Saturated steam at tsat = 100 oC condenses on the outer surface of a 1.4m long, 2m outer
diameter vertical tube maintained at a uniform temperature Tw = 60 oC. Assuming film
condensation, find the Local heat transfer co-efficient at the bottom of the tube.
28. The engine oil at 150 oC is cooled to 80 oC in a parallel flow heat exchanger by water
entering at 25oC and leaving at 60oC. Estimate the exchanger effectiveness and the number
of transfer units. If the flow rates and internal conditions remain unchanged work out the
lowest temperature to which the oil may be cooled by increasing length of exchanger.
29. The sun emits maximum radiation at λ = 0.52 μ. Assuming the sun to be a black body,
calculate the surface temperature of the sun. Also calculate the monochromatic emission
power of the sun’s surface.
30. Estimate the net radiant heat exchange per square meter from a very large plate at a
temperature of 550°C and 320°C. Assume that emissivity of hot plate is 0.8 and cold plate
is 0.6.