Heat Transfer

Question Bank

Short answer type question

1) What are the three modes of heat transfer? Explain their differences.
2) Determine the critical radius of an insulated sphere with radius r, thermal conductivity k and
heat transfer co-efficient ha.
3) Show that the thermal resistance offered by a spherical surface wall of uniform k is given by
 r0  ri  /  4 kri r0 
4) What is natural convective heat transfer? What is Nusselt number in heat transfer?
5) (i)What is Biot number?

(ii) What is the physical significance of Biot number?

6) Explain the concept of correlations in forced convection heat transfer. Provide an example of
a forced convection heat transfer correlation and its significance.
7) Derive Wien’s displacement law from Planck’s equation
8) What is Shape factor?

(ii) State and explain the reciprocity theorem.

9) What is space resistance and surface resistance?

10) Proof that Where Eb the emissive power and I is intensity.
11) What is Emissivity? How a Black Body does differ from Gray body?
12) What are the primary classifications of heat exchangers based on their construction?
13) (i)What is Heat Exchanger

(ii) Explain the concept of Log Mean Temperature Difference (LMTD) in heat exchangers.

14) What is the NTU method in heat exchanger analysis, and how is it used?
15) What do you mean by Fouling factor ?

(ii) What are the causes of fouling?

16) Explain the concept of "parallel flow" in the context of heat exchangers.

(ii) What type of heat exchanger is most suitable for applications where maintaining a close
temperature approach between hot and cold fluids is essential?

17) Why is there a negative sign in the Fourier’s law of heat conduction?
(ii) Define thermal conductivity and explain its significance in heat transfer.

18) Derive the expression for heat conduction

19) A wire 0.5 mm in diameter is stretched along the axis of a cylinder 50 mm in dia and 250
mm long. The temperature of the wire is 750 K while the cylinder is at 25 K and the gas in it
has a k = 0.0251 W/mK. To find: The rate of heat transfer through the gas by conduction and
by radiation if the wire is black.
20) Deduce the expression rate of heat transfer through conduction mode for the given physical
system shown in Figure, also draw the equivalent electrical circuit

21) Explain thermal resistance and contact resistance in heat transfer with proper diagram.

(i) What is boundary layer thickness?

(ii) What do you mean by laminar and turbulent boundary layers?

22) Show that the Reynolds number (Re) for flow in a circular tube of diameter D can be
expressed as Re = 4m´/πDµ.
23) Consider the flow of oil in a tube. How will the hydrodynamic and thermal entry lengths
compare if the flow is laminar?

(ii) How would they compare if the flow were turbulent?

24) Show by similarity principle that the three dimensionless parameters relevant to free
convection heat transfer are Nusselt number, Grashof number and Prandtl number.
25) State the scope and application of dimensional analysis in heat transfer processes.

(ii) What are the two methods of determining dimensionless groups to correlate experimental
data?

26) Prove that for radiation heat transfer ρ + α + τ = 1 with proper diagram.
27) What is Kirchhoff’s law in radiation heat transfer? Prove that α = ε. Where α is absorptivity
and ε is the emissivity.
28) Derive the expression for Stefan–Boltzmann law. Also find the value of Stefan–Boltzmann
constant.
29) Explain radiosity and irradiation. Also prove that

30) Find the shape factor F22 of the given system

31) Explain about various types of recuperative heat exchangers.

32) With proper diagram explain working of a shell-and-tube heat Exchanger.
33) Derive the expression for heat transfer for counter-flow heat exchanger with proper diagram.
34) Compare the working of parallel flow and counter flow heat exchangers with temperature-
length/area diagram.
35) Prove that for parallel flow heat exchanger
36) A stone slab of thickness 0.6 m has width with normal area 1.5 m2 and is made up of
material of thermal conductivity 0.4 W/mK. The temperatures on the two sides are 800 oC.
What is the thermal resistance of the slab?
37) Determine the critical radius of an insulated pipe with radius r, thermal conductivity k and
heat transfer co-efficient ha.
38) Show that the thermal resistance offered by a spherical surface wall of uniform k is given by
 r0  ri  /  4 kri r0 
39) Consider a slab of thickness L=0.25 m. One Surface is kept at 100 oC and the other surface at
0 oC. Determine the net flux across the slab if the slab is made from pure copper. Thermal
conductivity of copper is 387.6 W/mK.
40) Determine the critical radius of insulation of the asbestors with k=0.125 W/mK surrounding a
pipe exposed to room air with ha =2.5 W/m2K.
41) How does transient heat conduction differ from steady conduction?
42) What is Biot number?

(ii) What is the physical significance of Biot number?

43) What is lumped system analysis? When is it applicable?

44) Derive Wien’s displacement law mK from Planck’s equation
45) Define intensity of radiation. What is solid angle?

(ii) What is Emissivity? How a Black Body does differ from Gray body?

46) What is Shape factor?

(ii) State and explain the reciprocity theorem.

47) What do you mean by radiosity and irradiation

(ii) Proof that the emissive power is π times of its intensity.

48) The filament of a 75 W light bulb may be considered as a black body radiating into a black
enclosure at 700 oC. the filament diameter is 0.10 mm and length is 5 cm. considering the
radiation, determine the filament temperature.
49) (i)Define effectiveness and NTU of a heat exchanger.
50) (i)What is Heat Exchanger

(ii) What are its applications.

51) Explain storage type or Regenerator Heat Exchanger.

52) What do you mean by Fouling factor ?

(ii) What are the causes of fouling?

53) Water flows at the rate of 65 kg/min through a double pipe counter flow heat exchanger.
Water is heated from 50 oC to75 oC by an oil flowing through the tube. The specific heat of
the oil is 1.780 KJ/Kg.K. The oil enters at 115 oC and leaves at 70 oC. The overall heat
transfer co-efficient is 340 W/m2K. Calculate the rate of heat transfer.

Long answer type question

a. What is fin? Write some usages of fines

(ii) If a fin is thin and long and tip loss is negligible, show that the heat transfer from the fin is
given by

Q0  hpka0 tanh ml

Where
m  hp / ka 

2) Define thermal conductivity and how it measures?

(ii)A 0.8 m high and 1.5 m wide double-pane window consists of two 4 mm thick layers of glass
(k= 78 W/m K) separated by a 10 mm wide stagnant air space (k= 0.026 W/m K). Determine the
rate of heat transfer through this window and the temperature of the inside surface, when the
room is maintained at 200 C and the outside air is at -100 C. Take the convection heat transfer
coefficient on the inside and the outside surfaces of the window as 10 and 40 W/m2 K
respectively

3) What is an isotropic solid?

(ii)Show that the temperature variation for heat conduction through a cylindrical wall having
uniform k is logarithmic.

(iii) Why is there a negative sign in the Fourier’s law of heat conduction?

4) (i)Using lumped capacitance method for bodies of infinite thermal conductivity, proof that
Where, T is the average temperature of Billet, is the surrounding fluid temperature and the
other terms have their usual meanings.
5) Calculate the junction diameter of a copper thermocouple, initially at 250 C , which when
placed in a gas stream at 2000 C measures a temperature of 1980 C in 5 seconds. For copper,
ρ=8940 kg/m3, C= 384 J/kgK, k=390 W/mK and the convective heat transfer coefficient
=400 W/m2K.
6) Shaw that the shape factor for two surfaces 1 and 2 connected by a refractory surface is given
by
A2  A1F122
F12 
A1  A2  2 A1F12
7) For two infinite parallel gray planes exchanging radiant energy, show
1
F12 
1 1
 1
1  2

(ii) What is Solid angle? What do you mean by 1 Steragon?

8) ) Explain how the shape factor with respect to itself if the surface is concave, convex and flat

(ii) Show that ,

1
 Q12 With   Q12 Without
N
shied N 1 shied

9) State and explain the reciprocity theorem

(ii) Define emissivity of a surface. Explain Kirchhoff’s Law

10) Two parallel gray planes have emissivities of 0.8 and 0.7 and are maintained at 8000C and
15000C. What is the net radiant energy exchange? What would be the reduction in heat
transfer if a radiation shield of polished aluminum ( ε =0.04 ) is placed between them?

(ii) Show that

1 cos 1 cos 2
A1 F12    dA1dA2
 A1 A2 r2

11) Show that for parallel flow heat exchanger

1  exp[ NTU (1  R )]
 pf 
1 R

(ii) Show that for Counter flow heat exchanger

1  exp[ NTU (1  R)]
 cf 
1  R exp[ NTU (1  R)]

12) Water (cp=4.187 kJ/kg K) is heated at the rate of 1.4 kg/s from 4000 C to 7000 C by an oil (
cp=1.9 kJ/kg K) entering at 1100 C and leaving at 600 C in a counter flow heat exchanger. If
U0 =350 W/m2K, calculate surface area required.
13) Using the same entering fluid temperatures and the same oil flow rate, calculate the exit
temperatures of oil and water and the rate of heat transfer, when the water flow rate is halved.

14) A steam pipe made of steel (k = 58 W/mK) has i.d. of 160 mm and o.d. of 170 mm. The
saturated steam flowing through it is at 300°C, while the ambient air is at 50°C. It has two
layers of insulation, the inner layer (k = 0.17 W/mK) is 30 mm thick and the outer layer (k =
 0.023 W/mK) is 50 mm thick, the heat transfer coefficients on the inside and outside walls
are 30 and 5.8 W/m2K respectively. To find: The rate of heat loss per unit length of the pipe.
15) (i) 2. A 0.8 m high, 1.5 m wide double pane window consists of two 4 mm thick layers
of glass (k = 78 W/mK) and is separated by a 10 mm wide stagnant air space (k = 0.026
W/mK). The room is at 20°C and the outside air is at –10°C. The heat transfer coefficients
are hi = 10 and ho = 40 W/m2K. To find: (i) The rate of heat transfer through the window,
(ii) the inside surface temperature.
16) 9. A plastic pipe (k = 0.5 W/mK) of i.d. 3 cm and o.d. 4 cm carries a fluid of average
temperature 100°C and h = 300 W/m2K. The rate of heat transfer per unit length is 500 W/m.
To find: (i) The outside surface temperature of pipe, (ii) the overall heat transfer coefficient
based on outside area.
17) A furnace wall has the inside surface temperature of 1100°C, while the ambient air
temperature is 25°C. The wall consists of 125 mm thick refractory bricks (k = 1.6 W/mK),
125 mm thick firebricks (k = 0.3 W/mK) and 12 mm thick plaster (k = 0.14 W/mK). There is
an air gap which offers a thermal resistance of 0.16 K/W. The heat transfer coefficient on the
outside wall to the air is 17 W/m2K. To find: (a) The rate of heat loss per unit area of wall
surface, (b) the interface temperatures throughout the wall, and (c) the temperature of the
outside surface of the wall.
18) The roof of an electrically heated home is 6 m long, 8 m wide, and 0.25 m thick, and is made
of a flat layer of concrete whose thermal conductivity is k 0.8 W/m • °C (Fig.). The
temperatures of the inner and the outer surfaces of the roof one night are measured to be
15°C and 4°C, respectively, for a period of 10 hours. Determine (a) the rate of heat loss
through the roof that night and (b) the cost of that heat loss to the home owner if the cost of
electricity is $0.08/kWh.

19) Two large aluminium (k = 240 W/mK), each 2 cm thick, with 10 mm surface roughness are
placed in contact at 105 N/m2 pressure (Fig.) with the outside surface temperatures of 390 °C
and 406°C. The thermal contact resistance is 2.75 × 10–4 m2K/W. To find: (i) The heat flux,
(ii) the temperature drop due to contact resistance, and (iii) the contact temperatures.
20) A steam pipe (o.d. = 10 cm, Ts = 500 K, ε = 0.8) passing through a large room at 300 K. The
pipe loses heat by natural convection (h = 15 W/m2K) and radiation. To find: (i) The surface
emissive power of the pipe, (ii) the total radiation falling upon the pipe, and (iii) the total rate
of heat loss from the pipe.
21) Steam at 350°C flowing in a pipe (k = 80 W/mK) 5 cm i.d., 5.6 cm o.d. is covered with 3 cm
thick insulation (k = 0.05 W/mK). Heat is lost to the surroundings at 5°C by natural
convection and radiation with combined h = 20 W/m2K and hi = 60 W/m2K. To find: (i) The
rate of heat loss from the pipe per unit length, (ii) the temperature drops across the pipe and
the insulation.
22) Water is heated while flowing through a 1.5 cm × 3.5 cm rectangular cross-section tube at a
velocity of 1.2 m/s. The entering temperature of the water is 40°C, and the 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 the mean bulk temperature of 55°C are: ρ = 985.5
kg/m3; cp = 4.18 kJ/kg K, ν = 0.517 × 10–6 m2/s, k = 0.654 W/m K and Pr = 3.26.
23) Nitrogen gas at 0°C is flowing over a 1.2 m long, 2 m wide plate maintained at 80°C with a
velocity of 2.5 m/s. For nitrogen, ρ = 1.142 kg/m3, cp = 1.04 kJ/kgK, ν = 15.63 × 10–6 m2/s
and k = 0.0262 W/mK.

To find: (a) The average heat transfer coefficient and (b) the total heat transfer from the plate.

24) Water at 10°C flows over a flat plate (at 90°C) measuring 1 m × 1 m, with a velocity of 2
m/s. Properties of water at 50°C are ρ = 988.1°C, ν = 0.556 × 10–6 m2/s, Pr = 3.54 and k =
0.648 W/mK. To find: (a) The length of plate over which the flow is laminar, (b) the rate of
heat transfer from the entire plate.
25) What is monochromatic emissive power?

(ii) Derive the expression for Radiant heat exchange between two black bodies separated by a
non-absorbing medium as
26) What is reciprocity theorem?

(ii) Prove that F12A1=F21A2

(i) Derive Rayleigh–Jeans’ Law and Wien’s Law from Planck’s law of thermal radiation

(ii) What is surface resistance and space resistance in thermal radiation.

27) A long steel rod 20 mm in diameter is to be heated from 427OC to 538OC. It is placed
concentrically is a long cylindrical furnace which has an inside diameter of 160 mm. The
inner surface of the furnace is at a temperature of 1093OC and has an emissivity of 0.85. If
the surface of the rod has an emissivity of 0.6, estimate the time required for the heating
operation. Take the density of steel as 7800kg/m3 and its specific heat 0.67kj/kgK.
28) An enclosure measures 1.5 m × 1.7 m with a height of 2 m. The walls and ceiling are
maintained at 250°C and the floor at 130°C. The walls and ceiling have an emissivity of 0.82
and the floor 0.7. Determine the net radiation to the floor.
29) Two very large parallel planes with emissivities 0.3 and 0.8 exchange radiative energy.
Determine the percentage reduction in radiative energy transfer when a polished aluminium
radiation shield (e = 0.04) is placed between them.
30) In an open heart surgery under hypothermic conditions, the patient’s blood is cooled before
the surgery and rewarmed after wards. It is proposed that a concentric tube counterflow heat
exchanger of length 0.5 m is to be used for this purpose, with a thin-walled inner tube having
a diameter of 55 mm. If water at 60OC and 0.1 kg/s is used to heat blood entering the
exchanger at 18OC and 0.05 kg/s, what is the temperature of the blood leaving the exchanger
and the heat flow rate. Take U0 = 500 W/m2 K, cp of blood = 3.5 kJ/kg K and cp of water =
4.183 kJ/kg K.
31) A 4 kg/s product stream from a distillation column is to be cooled by a 3 kg/s water stream in
a counterflow heat exchanger. The hot and cold stream inlet temperatures are 400K and
300K respectively, and the area of the exchanger is 30 m2. If the overall heat transfer
coefficient is estimated to be 820 W/m2K, determine the product stream outlet temperature,
if its specific heat is 2500 J/kgK and the coolant outlet temperature.
32) After a long time in service, a counterflow oil cooler is checked to ascertain if its
performance has deteriorated due to fouling. In the test a standard oil flowing at 2.0 kg/s is
cooled from 420 K to 380 K by a water supply of 1.0 kg/s at 300 K. If the heat transfer
surface is 3.33 m2 and the design value of the overall heat transfer coefficient is 930 W/m2
K, how much has it been reduced by fouling? Take cp of oil as 2330 J/kgK and cp of water
as 4174 J/kgK.
33) A counterflow heat exchanger is employed to cool 0.55 kg/s (cp = 2.45 kJ/kg°C) of oil from
115°C to 40°C by the use of water. The inlet and outlet temperatures of cooling water are
15°C and 75°C, respectively. The overall heat transfer coefficient is expected to be 1450
W/m2 K. Using the NTU method, calculate the following:

The mass flow rate of water, (b) the effectiveness of the heat exchanger and (c) the surface area
required.

34) Derive the expression for heat transfer in parallel flow heat exchanger with proper diagram.

(ii) What is overall heat transfer coefficient and fouling factor?

35) What is fin? Define fin effectiveness.

(ii) If a fin is thin and long and tip loss is negligible, show that the heat transfer from the fin is
Q  mkA0 tanh ml
given by 0

Where
m  hp / ka 
36) Define thermal conductivity and explain its significance in heat transfer

(ii) Explain why an insulated small diameter wire has a higher current carrying capacity than an
uninsulated one.

37) What is an isotropic solid?

(ii)Why is there a negative sign in the Fourier’s law of heat conduction?

(iii) Define thermal diffusivity. What is its dimension? How does it differs from thermal
conductivity?

38) Calculate the rate of heat loss through the vertical walls of a boiler furnace of size 4 m by 3
m by 3 m high. The walls are constructed from an inner fire brick wall 25 cm thick of
thermal conductivity 0.4 W/mK, a layer of ceramic blanket insulation of thermal conductivity
0.2 W/mK and 8 cm thick, and a steel protective layer of thermal conductivity 55 W/mK and
2 mm thick. The inside temperature of the fire brick layer was measured at 600oC and the
temperature of the outside of the insulation 600 oC. Also find the temperature of the junction
of brick and ceramic layers.
39) A 15 cm outer diameter steam pipe is covered with 5 cm high temperature insulation (k=0.85
W/moC) and 4 cm low temperature insulation (k = 0.72 W/moC). The steam is at 500 oC and
ambient air is at 40 oC. Neglecting thermal resistance of steam and air sides and metal wall
calculate the heat loss from 100 m length of the pipe. Also find temperature drop across the
insulation.
40) A long carbon steel rod of length 40 cm and diameter 10 mm (k = 40 w/mK) is placed in
such that one of its end is 400 oC and the ambient temperature is 30 oC. The flim co-efficient
is 10 w/m2K. Determine:

(i) Temperature at the mid length of the fin

(ii) Fin efficiency

(iii) Heat transfer rate from the fin

(iv) Fin effectiveness

41) A motor body is 360 mm in diameter (outside) and 240 mm long. Its surface temperature
should not exceed 55 oC. 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
42) Using lumped capacitance method for bodies of infinite thermal conductivity, proof that
Where, T is the average temperature of Billet, is the surrounding fluid temperature and the
other terms have their usual meanings.
43) An aluminum plate (k=160 W/mK, ρ=2790 kg/m3, cp =0.88 kJ/kg K) of thickness 30 mm
and at a uniform temperature of 225 oC is suddenly immersed at time t=0 in a well-stirred
fluid at a constant temperature of 25 oC. The heat transfer coefficient between the plate and
the fluid is 320 W/m2K. Determine the time required for the centre of the plate to reach 50
oC.
44) A vertical cylinder 1.5 m high and 180 mm in diameter is maintained at 100 oC in an
atmospheric environment of 20 oC. Calculate the heat loss by free convection from the
surface of the cylinder. Assume the properties of air at mean temperature ρ=1.06 Kg/m^3,
ν=18.97×〖10〗^(-6) m^2/s, c_p=1.004 kJ/Kg°C, k=0.1042 kJ/mh°C
45) Show that the shape factor for two surfaces 1 and 2 connected by a refractory surface is given
by

(i) For two infinite parallel gray planes exchanging radiant energy, show
1
F12 
1 1
 1
1  2

(ii) What are space resistance and Surface resistance?

46) What do you mean by radiation shield? Where is it used?

(ii) Show that,
1
 Q12 With   Q12 Without
N
shied N 1 shied

47) Two large plates are maintained at a temperature of 900 K and 500 K respectively. Each
plate has an area of 6 m2. Compute the net heat exchange between the plates for the
following cases.

(i) Both plates are black

(ii) Plates have an emissivity of 0.5

48) A 70 mm thick metal plate with a circular hole of 35 mm diameter along the thickness is
maintained at a uniform temperature of 250 oC. Find the loss of energy to the surroundings at
27 oC, assuming the two ends of the hole to be parallel discs and the metallic surfaces and
surroundings have black body characteristics.
49) Two large parallel planes with emissivities of 0.3 and 0.5 are maintained at temperatures of
527 oC and 127 oC respectively. A radiation shield having emissivities of 0.05 on both sides
is placed between them. Calculate

(i) Heat transfer rate between them without shield.

(ii) Heat transfer rate between them with shield.

50) (i)Show that for parallel flow heat exchanger

1  exp[ NTU (1  R)]
 pf 
1 R

(ii) Show that for Counter flow heat exchanger

1  exp[ NTU (1  R)]
 cf 
1  R exp[ NTU (1  R)]

51) A counterflow heat exchanger is employed to cool 0.55 kg/s (cp=2.45 kJ/kg0 C) of oil from
115 oC to 40 oC using water. The inlet and outlet temperature of cooling water are 15 oC and
75 oC respectively. The overall heat transfer coefficient is expected to be 1450 W/m2K.
Using the NTU method, calculate the following: (a) The mass flow rate of water, (b) the
effectiveness of the heat exchanger and (c) The surface area required
52) When one of the two fluids undergoes phase change, show that the effectiveness value for
both parallel flow and counter flow heat exchangers are equal and given by
  1  exp( NTU )

(ii) What are the different flow arrangements in recuperative heat exchangers?
53) Hot chemical products (Cph = 2.5 kJ/kg.K) at 600 oC and at a flow rate of 30 kg/s are used to
heat cold chemical products (Cp = 4.2 kJ/kg K) at 200 oC and at a flow rate 20 kg/s in a
parallel flow heat exchanger. The total heat transfer is 50 m2 and the overall heat transfer
coefficient may be taken as 1500 W/m2.K. calculate the outlet temperatures of the hot and
cold chemical products.
54) A parallel flow heat exchanger is used to cool 4.2 kg/min of hot liquid of specific heat 3.5
kJ/kg K at 130 oC. A cooling water of specific heat 4.18 kJ/kg K is used for cooling purpose
of a temperature of 15 oC. The mass flow rate of cooling water is 17 kg/min. calculate the
following.

(i) Outlet temperature of liquid

(ii) Outlet temperature of water

(iii) Effectiveness of heat exchanger

55) A counter flow double pipe heat exchanger using super-heated steam is used to heat water at
the rate of 10500 kg/hr. The steam enters the heat exchanger at 180 oC and leaves at 130 oC.
The inlet and exit temperature of water are 30 oC and 80 oC respectively. If the overall heat
transfer coefficient from steam to water is 814 W/m2.K, calculate the heat transfer area.
What would be the increase in area if the fluid flow were parallel?