HMT

MECHANICAL ENGINEERING (HEAT TRANSFER)

5 HEAT EXCHANGER

Classification
I. Based on contact
a) Direct Contact
b) Indirect Contact
ll. Based on direction of flow of fluid
a) Parallel flow
b) Counter flow
c) Cross flow

MECHANICAL ENGINEERING (HEAT TRANSFER)

Design of Heat exchangers

I. LMTD (Logarithmic mean temperature difference method) - This method is used
when outlet temp. of both fluids are known. With this method the surface area of heat
exchanger can be calculated.

II. Effectiveness NTU method – This method is used when the outlet temperature are
unknown.

Logarithmic mean temperature difference (LMTD)

To begin with, we take U to be a constant value. This is fairly reasonable in compact single-
phase heat exchangers. In larger exchangers, particularly in shell-and-tube configurations and
large condensers, U is apt to vary with position in the exchanger and/or with local
temperature. But in situations in which U is fairly constant, we can deal with the varying
temperatures of the fluid streams by writing the overall heat transfer in terms of a mean
temperature difference between the two fluid streams:

Q = UA Tmean

The determination of ∆Tmean for such arrangements proceeds as follows: the differential
heat transfer within either arrangement is

dQ = U TdA = −(m& cp )n dTn = ±(m& cp )c dTc

where the subscripts h and c denote the hot and cold streams, respectively; the upper and
lower signs are for the parallel and counter flow cases, respectively; and dT denotes a change
from left to right in the exchanger

After lengthy manipulation we get for either parallel or counter flow,

Tmean = LMTD = Ta − Tb

ln  Ta 

 Tb 

MECHANICAL ENGINEERING (HEAT TRANSFER)

Effectiveness-NTU method

Often we begin with information such as is shown in Fig. 5-1. If we sought to calculate Q in
such a case, we would have to do so by guessing an exit temperature

Such problems can be greatly simplified with the help of the so-called effectiveness-NTU
method. This method was first developed in full detail by Kays and London in 1955, in a
book titled Compact Heat Exchangers. We should take particular note of the title. It is with
compact heat exchangers that the present method can reasonably be used, since the overall
heat transfer coefficient is far more likely to remain fairly uniform. The heat exchanger
effectiveness is defined as

ε ≡ Cn (Tnin − Tnout ) = Cc (Tcout − Tcin )
Cmin (Tnin − Tcin ) Cmin (Tnin − Tcin )

whereCmin is the smaller of Cc and Ch. The effectiveness can be interpreted as

It flows that ε = actual heat transferred
maximum heat that could possible be
ransferred from one stream to other

Q = ε Cmin (Tnin − Tcin )

A second definition that we will need was originally made by E.K.W. Nusselt This is the
number of transfer units (NTU):

NTU= UA
Cmin

Effectivenessequation for the parallel single-pass heat exchanger:

MECHANICAL ENGINEERING (HEAT TRANSFER)

ε ≡ 1− exp[−(1+ Cmin / Cmax ) NTU]
1 + Cmin / Cmax

Effectiveness equation for the counter flow single-pass heat exchanger:

ε ≡ 1 − exp[−(−1 − Cmin / Cmax ) NTU]
1 − (Cmin / Cmax ) exp[−(−1 − Cmin / Cmax ) NTU

**********************

MECHANICAL ENGINEERING (HEAT TRANSFER)

HEAT TRANSFER

(OBJECTIVE)

CONTENTS

UNIT CHAPTER PAGE NO.
56 – 65
1 Conduction 66 –69
70 – 74
2 Fins & THC 75 – 80
81 - 87
3 Convection 88

4 Radiation

5 Heat Exchanger

6 Answers

No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in
any form or by any means, electronics, mechanical, photocopying, digital, recording, without
the prior permission of the publishers.

Published at : Ascent Gate Academy
“Shraddha Saburi”, Near Gayatri Vidyapeeth,
Rajnandgaon (Chhattisgarh) Mob : 09993336391

MECHANICAL ENGINEERING (HEAT TRANSFER)

1 CONDUCTION

1. Thermal conductivity is lower for (GATE-ME-1990)

a) wood b) air
c) water at 1000C d) steam at 1 bar

2. Two insulating materials of thermal conductivity K and 2K are available for lagging a
pipe carrying a hot fluid. If the radial thickness of each material is same
(GATE-ME-1994)
a) Material with higher thermal conductivity should be used for inner layer and one with
lower thermal conductivity for the outer.
b) Material with lower thermal conductivity should be used for inner layer and one with
higher thermal conductivity for the outer.
c) It is immaterial in which sequence the insulating material are used
d) It is not possible to judge unless numerical values of dimensions are given.

3. For a given heat flow and for the same thickness, the temp drop across the material will

be maximum for (GATE-ME-1996)

a) Copper b) Steel

c) Glass wool d) Refractory brick

4. In descending order of magnitude, the thermal conductivity of a) Pure iron, b) liquid

water c) Saturated water vapour, d) Pure aluminum can be arranged as

(GATE-ME-2001)

a) a b c d b) b c a d

c) d a b c d) d c b a

5. On dimensional unsteady state heat transfer equation for a sphere with heat generation

at the rage ‘q ’ an be written as (GATE-ME-2004)

g

a) 1 ∂  r ∂T  + q = 1 ∂T 1 ∂  r 2 ∂T  + q = 1 ∂T
∂r  ∂r  k α ∂t ∂r  ∂r  k α ∂t
r b) r2

c) ∂2T +q = 1 ∂T d) ∂2 (rT ) + q = 1 ∂T
∂r 2 k α ∂t ∂r 2 k α ∂t

6. In case of one dimensional heat conduction in a medium with constant properties. T is the

∂T (GATE-ME-2005)
temperature at position x, at time t. Then ∂t is proportional to

T ∂T
a) x b) ∂x

∂2T ∂2T
b) ∂x∂t d) ∂x2

MECHANICAL ENGINEERING (HEAT TRANSFER)

7. A well machined steel plate of thickness L is kept such that the wall temperatures are Th
and Tc as seen in the figure below. A smooth copper plate of same thickness L is now
attached to the steel plate without any gap as indicated in the figure below. The

temperature at the interface is Ti. The temperatures of the outer walls are still the same

at Th and Tc. The heat transfer rates are q and q per unit area in the two cases

1 2

respectively in the direction shown. Which of the following statements is correct ?

(GATE-ME-2005)

a) Th > Ti > Tc and q1 < q2 b) Th < Ti < Tc and q1 = q2

c) Th = (T > T) / 2 and q > q d) T < (T + T ) and q > q
i hc 12
i c 1 2

8. In a composite slab, the temperature at the interface (T ) between two materials is

inter

equal to average of the temperature at the two ends. Assuming steady one dimensional

heat conduction, which of the following statements is true about the respective thermal

conductivities. (GATE-ME-2006)

a) 2K1 = K2 b) K1 = K2 c) 2K1 = 3K2 d) K1 = 2K2

9. A pipe of 25 mm outer diameter carries steam. The heat transfer coefficient between the
cylinder and surrounding is 5 W/m2K. It is proposed to reduce the heat loss from the

pipe by adding insulation having a thermal conductivity of 0.05 W/mk. Which one of

the following statements is TRUE ? (GATE-ME-2011)

a) The outer radius of the pipe is equal to the critical radius.

b) The outer radius of the pipe is less than the critical radius.

c) Adding the insulation will reduce the heat loss.

d) Adding the insulation will increase the heat loss.

MECHANICAL ENGINEERING (HEAT TRANSFER)

10. Match the property with their units (GATE-ME-1991)
PROPERTY
A. Bulk modulus UNITS
B. Thermal conductivity
C. Heat transfer coefficient 1. W/s
D. Heat flow rate
2

2. Nm

3

3. N/m

4. W

5. W/mK

2

6. W/m K

2

11. For a current carrying wire of 20 mm dia exposed to air ( h = 20W/m K), maximum

heat dissipation occurs when thickness of insulation (0.5 W/mK) is

(GATE-ME-1993)

a) 30 mm b) 25 mm c) 20 mm d) 15 mm

12. For a current carrying wire of 20mm dia exposed to air (h = 20W/m2K), maximum heat

dissipation occurs when thickness of insulation (0.5 W/mk) is

(GATE-ME-1996)

a) 30 mm b) 25 mm c) 20 mm d) 15 mm

13. The temp variation under steady heat conduction across a composite slab of two
materials with thermal conductivities K and K in fig. is shown in fig. then, which one

12

of the following statements hold ?

a) K1 > K2 b) K1 = K2 c) K1 = 0 d) K1 < K2

14. It is proposed to coat a 1 mm dia wire with enamel paint ( k = 0.1 w/mk) to increase

2

heat transfer with air. If the air side heat transfer co-efficient is 100W/m K, the

optimum thickness of enamel paint should be (GATE-ME-1999)

a) 0.25 mm b) 0.5 mm c) 1 mm d) 2 mm

Common data for questions Q15 & Q16

0

Heat is being transferred by convection from water at 48 C to a glass plate whose surface that

0

is exposed to the water is at 40 C, the thermal conductivity of water is 0.6 W/mk and the

thermal conductivity of glass is 1.2 W/mk. The spatial gradient of temp in the water at the

4

water-glass interface is Dt/dy = 1 x 10 K/m.

MECHANICAL ENGINEERING (HEAT TRANSFER)

15. The value of the temperature gradient in the glass at the water-glass interface in K/m is

4 b) 0.00 4 (GATE-ME-1999)

a) -2 x 10 c) 0.5 x 10 4

d) 2 x 10

2

16. The heat transfer coefficient h in W/m K is

a) 0.0 b) 4.8 c) 6 d) 750

Statement for Linked Answer Question (Q17 & Q18)

Consider steady one-dimensional heat flow in a plate of 20mm thickness with a uniform heat

30

generation of 80 MW/m . The left and right faces are kept at constant temperatures of 160 C

0

and 120 C respectively. The plate has a constant thermal conductivity of 200 W/mK.

17. The location of maximum temp within the plate from left face is (GATE-ME-2007)

a) 15 mm b) 10 mm c) 5 mm d) 0 mm

18. The maximum temp within the plate in degree C is (GATE-ME-2007)

a) 160 b) 165 c) 175 d) 250

19. A stainless steel tube (Ks = 19 W/mK) of a 2 cm ID and 5 cm OD is insulated with 3cm

thick asbestos (Ka = 0.2 W/mK). If the temperature difference between the innermost

and outermost surface is 600C, the heat transfer rate per unit length is

(GATE-ME-2004)

a) 0.94 W/m b) 9.44 W/m c) 944.72 W/m d) 9447.21 W/m

20. Heat flows through a composite slab, as shown below. The depth of the slab is 1 m. The

k value are in W/m.k. The overall thermal resistance in K/W is (GATE-ME-2005)

a) 17.2 b) 21.9 c) 28.6 d) 39.2

21. A 100W electric bulb was switched on in 2.5 x 3 x 3m size thermally insulated room

0

having temperature of 20 C. Room temp at the end of 24 hours will be

(GATE-ME-2006)

a) 321 C b) 341 C c) 450 C d) 470 C

MECHANICAL ENGINEERING (HEAT TRANSFER)

22. With an increase in the thickness of insulation around a circular pipe, heat loss to

surroundings due to (GATE-ME-2006)

a) Convection increases, while that due to conduction decreases

b) Convection decreases, while that due to conduction increases

c) Convection and conduction decreases

d) Convection and conduction increases

23. A long glass cylinder of inner diameter = 0.03 m and outer diameter = 0.05m carries hot

fluid inside. If the thermal conductivity of glass = 1.05 W/mK, the thermal resistance

(K/W) per unit length of the cylinder is (GATE-ME-2007)

a) 0.031 b) 0.077 c) 0.17 d) 0.34

00

24. Building has to be maintained at 21 C (dry bulb) and 14.5 C (web bulb). The dew point

00

temp under these conditions is 10.17 C, the outside temp is -23 C (dry bulb) and

22

internal and external surface heat transfer coefficients are 8W/m K and 23W/m K

respectively. If the building wall has a thermal conductivity of 1.2 W/mK, the minimum

thickness (m) of wall required to prevent condensation is (GATE-ME-2007)

a) 0.471 b) 0.407 c) 0.321 d) 0.125

25. For the three dimensional object shown in the fig below. Five faces are insulated. The

six face (PQRS), which is not insulated, interacts thermally with the ambient, with a

20

convective heat transfer coefficient of 10W/m K, the ambient temperature is 30 C, heat

3

is uniformly generated inside the object at the rate of 100Wm . assuming the face PQRS

to be at uniform temperature, its steady state temp is (GATE-ME-2008)

a) 10C b) 20C c) 30C d) 40C

26. Steady two dimensional heat conduction takes place in the body shown in the fig below.

The normal temperature gradients over surface P and Q can be considered to be
uniform. The temperature gradient ∂t/∂x = at surface Q is equal to 10K/m. surfaces P

and Q are maintained at constant temperatures as shown in the fig. While the remaining

part of the boundary is insulated. The body has a constant thermal conductivity of 0.1

W/mK, the value of ∂t/∂x and ∂t/∂y at surface P are (GATE-ME-2008)

MECHANICAL ENGINEERING (HEAT TRANSFER)

a) ∂t/∂x = 20K/m, ∂t/∂y = 0 K/m
b) ∂t/∂x = 0K/m, ∂t/∂y = 10 K/m
c) ∂t/∂x = 10K/m, ∂t/∂y = 10 K/m
d) ∂t/∂x = 0K/m, ∂t/∂y = 20 K/m
27. Consider the steady state heat conduction across the thickness in a plane composite wall
as shown in fig exposed to convection condition on both sides

Given hi = 30 W/m22 C ; K =
K ; h = 50 W/m K; Tα,i = 20 C; Tα,i = -2 20W/mK;
1
0

K2 = 50W/mK ; L1 = 0.3m ; L2 = 0.15 m; Assuming negligible contact resistance

between the wall surfaces, the interface temp T(C) of the two walls will be

(GATE-ME-2009)

a) -0.50 b) 2.75 c) .75 d) 4.5

28. Heat is being transferred convectively from a cylindrical nuclear reactor fuel rod of

0

50 mm diameter to water at 75 C, under steady state condition, the rate of heat

63

generation within the fuel element is 10 W/m and the connectivity heat transfer

2

coefficient is 1 KW/m K, the outer surface temperature of the fuel element would be

a) 7000C b) 6250 C) 5500C (GATE-PI)
d) 4000C

MECHANICAL ENGINEERING (HEAT TRANSFER)

PRACTICE QUESTIONS :

1. In a composite slab, the temperature at the interface (T ) between two materials is

inter

equal to average of the temperatures at the two ends. Assuming steady one dimensional
heat conduction, which of the following statements is true about the respective thermal
conductivities.

a) 2K = K b) K = K c) 2K = 3K d) K = 2K

12 12 12 12

2. The Poisson’s equation the general conduction heat transfer applies to the case

a) Steady state heat conduction with heat generation

b) Steady state heat conduction without heat generation

c) Unsteady state heat conduction without heat generation

d) Unsteady state that conduction with heat generation

3. Uniform heat generation takes place in a symmetric slab so that heat flows towards both

sides in contact with fluid. The zero-gradient boundary condition ∂T
∂x

a) Left wall of slab b) Right wall of slab

c) Centerline of slab d) Now here in slab

4. Which of the following expressions gives the thermal resistance for heat conduction

through a hollow sphere or radii r and r ? ( r1 − r2 ) ln r2
r1
12 b)
4π k
4π kr1r2
a) r2 − r1 4π k (r2 − r1 )

r2 − r1 d) r1r2
c) 4π kr1r2

5. In MLTθ system ( θ being time and T temperature), what is the dimension of thermal

conductivity ? b) MLT-1θ−3 c) MLθ−1T-3 d) MLθ−1T-2
a) ML-1T-1θ−3

6. A composite wall of a furnace has 3 layer of equal thickness having thermal

conductivities in the ratio of 1 : 2 : 4. What will be the temperature drop ratio across the

three respective layers ?

a) 1 : 2 : 4 b) 4 : 2 : 1

c) 1 : 1: 1 d) log 4 : log 2 : log 1

7. A large concrete slab 1 m thick has one dimensional temperature distribution :

MECHANICAL ENGINEERING (HEAT TRANSFER)

23

T = 4 - 10x + 20x + 10x , where T is temperature and x is distance from one face

-3 2

towards other face of wall. If the slab material has thermal diffusivity of 2 x 10 m /hr,

what is the rate of change of temperature at the other face of the wall ?

0 0 0 0

a) 0.1 C/h b) 0.2 C/h c) 0.3 C/h d) 0.4b C/h

8. The one-dimensional unsteady state heat conduction equation in a hollow cylinder with

a constant heat source q is

∂T = 1 . ∂  r∂T  + q
∂x r ∂r  ∂r 

If A and B state solution to the above equation is

a) T (r) = −qr2 + A + B b) T (r) = −qr 2 + Aln r + B
2
2r

c) T(r) = A 1n r + B d) T (r) = +qr 2 + Aln r(00)B
2k

9. The interrelationship between thermal conductivity, dynamic viscosity and temperature

of gas can be described as

a) Dynamic viscosity and thermal conductivity decrease as temperature increases

b) Dynamic viscosity decreases and thermal conductivity increases as temperature

increase

c) Dynamic viscosity and thermal conductivity decrease as temperature decreases

d) Dynamic viscosity and thermal conductivity increase as temperature decreases

10. Steam is flowing through an insulated steel pipe shown in the fig, is losing heat to the

surroundings. The details are as follows (GATE-ME-1988) (5M)

Inner radius of steel pipe = 50 mm, Outer radius of the steel pipe = 57 mm,

Outer radius of insulation = 157 mm, Thermal conductivity of steel = 43 Wmk

Thermal conductivity of insulating materials = 0.1 W/mK

2

Heat transfer coefficient on steam side = 570 W/m K

20

Heat transfer coefficient on air side = 12 W/m K, Temp of steam = 500 C

0

Temp of surroundings = 30 C

1- Insulation, K = 0.1 W/m K

2- Steel pipe, K = 43 W/m K

02

3- Steam, 500 C, h = 570 W/m K

02

4- Air, 30 C, h = 12 W/m K

MECHANICAL ENGINEERING (HEAT TRANSFER)

Calculate the heat loss per meter length of pipe and temp of the outer surface of the
insulation.

0

11. An electric hot plate is maintained at a temperature of 350 C, and is used to keep a

0

solution boiling at 95 C, the solution is contained in cast iron vessel of wall thickness

25 mm, which is enameled inside to a thickness of 0.8 mm, the heat transfer coefficient

2

for the boiling solution is 5.5 kW/m K and the thermal conductivities of cast iron and

enamel are 50 and 1.05 W/mK, respectively. Calculate the OHTC and the rate of heat

transfer per unit area. (GATE-ME-1993)

12. A gas filled tube has 2 mm inside diameter and 25 cm length. The gas ia heated by an

electrical wire of diameter 50 microns located along the axis of the tube. Current and

voltage drop across the heating element are 0.5A and 4 volts, respectively. If the

00

measured wire and inside tube wall temps are 175 C and 150 C respectively, find the

thermal conductivity of the gas filling the tube. (GATE-ME-98) (5M)

13. A composite wall, having unit length normal to the plane of paper, is insulated at the top

and bottom as shown in fig. it is comprised of four different materials A, B, C and D

MECHANICAL ENGINEERING (HEAT TRANSFER)

Dimensions are

HA = HD = 3 cm, HB = HC = 1.5 cm, L1 = L3 = 0.05 m, L2 = 0.1 m

Thermal conductivity of the materials are

K = K = 50 W/mK, K = 10W/mK, KC = 1 W/mK

A D B 02

The fluid temps and HTC (see fig) are T = 200 C, h = 50W/m K, T = 25C,
11 2
2
h = 10 W/m K,
2

Assuming one dimensional heat transfer condition

Determine the rate of the heat transfer through the wall (GATE-ME-2001) (5M)

14. A copper tube of 20mm outer diameter, 1mm thickness and 20m long (thermal

0

conductivity = 400W/mK) is carrying saturated steam at 150 C (Convective HTC = 150

20

W/m K). The tube is exposed to ambient air temperature of 27 C, the convective HTC

2

of air is 5 W/m K. Glass wool is used for insulation (Thermal conductivity = 0.075

W/mK). If the thickness of the insulation used is 5mm higher than the critical thickness

of insulation, calculate the rate of heat lost by the steam and the rate of steam

condensation in Kg/hr (The enthalpy of condensation of steam = 2230 KJ/kg)

(GATE-ME-2002) (5M)

**************************

“It takes 20 years to make an overnight success”

MECHANICAL ENGINEERING (HEAT TRANSFER)

2 FINS & THC

1. The heat transfer process between a body and its ambient is governed by an internal

conductive resistance (ICR) and an external convective resistance (ECR). The body can

be considered to be a lumped heat capacity system if (GATE-ME-1989)

a) ICR > ECR b) ICR is marginally smaller than ECR

c) ICR = ECR d) ICR is negligible

2. Boit number signifies (GATE-ME-1991)

a) The ratio of heat conducted to heat convected

b) The ratio of heat convected to heat conducted

c) The ratio of external convective resistance to internal conductive resistance

d) The ratio of internal conductive resistance to external convective resistance

3. When the fluid velocity is doubled the thermal time constant of a thermometer used for

measuring the fluid temperature reduces by a factor of 2 (T/F) (GATE-ME-1994)

4. Lumped heat transfer analysis of a solid object suddenly exposed to a fluid medium at a

deferent temp is valid when. (GATE-ME-2001)

a) Biot number < 0.1 b) Biot number > 0.1

c) Fourier number < 0.1 d) Fourier number > 0.1

5. The value of Biot number is very small (less than 0.01), when (GATE-ME-2002)

a) The convective resistance of fluid is negligible

b) The conductive resistance of fluid is negligible

c) The conductive resistance of solid is negligible

d) None of the above

6. Which one of the following configurations has the highest fin effectiveness ?

(GATE-ME&PI-2012)

a) Thin, closely spaced fins b) Thin, widely spaced fins

c) Thick, widely spaced fins d) Thick, closely spaced fins

7. Two rods, one of length L and the other of length 2L are made of the same material and

0

have the same diameter. The two ends of the longer rod are maintained at 100 C. One

0

end of the shorter rod is maintained at 100 C while the other ends is insulated. Both the

rods are exposed to the same environment at 400C. The temp at the insulated end of the

shorter rod is measured to be 550C. The temp at the mid point of the longer rod would

0 0 0 (GATE-ME&PI-1992)

a) 40 C b) 50 C c) 55 C 0

d) 100 C

8. A spherical thermocouple junction of diameter 0.706 mm is to be used for the

measurement of temperature of a gas stream. The convective heat transfer coefficient on

2

the bead surface is 400W/m \K. Thermo-physical properties of thermocouple material

are K = 20W/mK, C = 400 J/kgK and ρ = 8500 Kg/m3. If the thermocouple initially at
00 0
30 C is placed in a hot stream of 300 C, the time taken by the bead to reach 298 C is

(GATE-ME-2005)

a) 2.35s b) 4.9s c) 14.7s d) 29.4s

MECHANICAL ENGINEERING (HEAT TRANSFER)

9. A smaller copper ball of 5 mm diameter at 500 K is dropped into an oil bath whose

temperature is 300 K. The thermal conductivity of copper is 400 W/m. K, its density

3

9000 kg/m .K and its specific heat 385 J/kg, K. If the heat transfer coefficient is 250

2

W/m .K and lumped analysis is assumed to be valid, the rate of fall of the temperature

of the ball at the beginning of cooling will be, in K/s.(G-ME-2005)

a) 8.7 b) 13.9 c) 17.3 d) 27.7

10. A Fin has 5 mm diameter and 100 mm long. The thermal conductivity of fin material is

0

400W/mK. One end of the fin is maintained at 130 C and its remaining surface is

2

exposed to ambient air at 30C. If the convective heat transfer coefficient is 40W/m K,

the heat loss (in W) from the fin is (GATE-ME-2010)

a) 0.08 b) 5.0 c) 7.0 d) 7.8

11. A spherical steel ball of 12mm diameter is initially at 100 K. It is slowly cooled in a

surrounding of 300K. The heat transfer coefficient between the steel ball and the

2

surrounding is 5W/m K. The thermal conductivity of steel is 20 W/mK. The

temperature difference between the centre and the surface of the steel ball is

(GATE-ME-2011)

a) large because conduction resistance is far high than the convective resistance

b) large because conduction resistance is far less than the convective resistance

c) small because conduction resistance is far high than the convective resistance

d) small because conduction resistance is far less than the convective resistance

PRACTICE QUESTIONS :
1. When is a transient heat transfer problem considered as a lump capacity problem ?

a) The internal resistance of the object is negative
b) The internal resistance of the object is zero
c) The internal resistance of the object is infinite
d) The internal resistance of the object is negligible
2. The time constant of a thermocouple is
a) The time taken to attain 100% of initial temperature difference
b) The time taken to attain 63.2% of initial temperature difference
c) The time taken to attain 50% of initial temperature difference
d) The minimum time taken to record a temperature reading
3. For quick response of a thermocouple to observe varying temperatures of fluids
a) Wire diameter must be large
b) Wire material density must be large
c) Wire material specific heat must be large
d) Wire surface heat transfer coefficients must be large
4. On heat transfer surface, fins are provided
a) To increase temperature gradient so as to enhance heat transfer
b) To increase turbulence in flow for enhancing heat transfer
c) To increase surface area to promote the rate of heat transfer
d) To decrease the pressure drop of the fluid

MECHANICAL ENGINEERING (HEAT TRANSFER)

5. Fins are made as thin as possible to

a) Reduce the total weight

b) Accommodate more number of fins

c) Increase the width for the same profile area

d) Improve flow of coolant around the fin

6. Which one of the following is correct ? The effectiveness of a fin will be maximum in

an environment with

a) Free convection b) Forced convection

c) Radiation d) Convection and radiation

7. Three fins of equal length and diameter but made of aluminum, brass and cast iron are

00

heated to 200 C at one end. If the fins dissipate heat to the surrounding air at 25 C, the
temperature at the free end will be least in case of
a) Aluminum fin
b) Brass fin
c) Cast iron fin
d) Each fin will have the same temperature at the free end
8. Which one of the following statement is correct ?
a) Fins should be attached on the side where heat transfer coefficients are high
b) Effectiveness of fins depends on thermal conductivity only
c) Fins must have small thickness for better heat dissipation
d) In boiling heat transfer appliances, fins will be very effective
9. A fin will be necessary and effective only when
a) k is small and h is large
b) k is large and h is also large
c) k is small and h is also small
d) k is large and h is small
where k = thermal conductivity of fin material, h = convective heat transfer coefficient
between the fin surface and environment temperature.

10. A fin of length l protrudes from a surface held at temperature T ; it is being higher than

0

the ambient temperature, T The heat dissipation from the free end of the fin is stated to

a

be negligibly small.

 ∂T 
What is temperature gradient  ∂x x=l at the tip of the fin ?

a) Zero b) T0 − T1
l

c) h (T0 - Ta) d) T1 − Ta
T0 − Ta

MECHANICAL ENGINEERING (HEAT TRANSFER)

11. Which one of the following configurations has the highest fin effectiveness ?

a) Thin, closely spaced fins

b) Thin, widely sped fins

c) Thin, widely spaced fins

d) Thick, closely spaced fins
12. The total efficiency, η for a finned surface may be defined as the ratio of the total heat

t

transferred by the combined area of the fins, A , and the exposed surface to that by the

r

total area, A, if it were maintained at the base temp, T . Assuming uniform heat transfer

0

coefficient over the entire surface, derive an expression for the relationship between

efficiency and effectiveness of the fin. (GATE-ME-1989)

13. An iron rod ( K = 41.5 W/mK) of 15 mm dia. And 160 mm long extends out of a hot

00

surface of temp 150 C into environment at 36 C, the free end of the rod is insulated. If

2

the film heat transfer coefficient is 25W/m K, calculate the rate of heat flowing out of

the hot surface through the rod and the temp at the insulated end of the rod.

(GATE-ME-1990)(5M)

Statement for linked answer questions : Q. 14 & 15

A wall is heated uniformly at a volumetric heat generation rate of 1kw/m3, the

temperature distribution across the 1 m thick wall at a certain instant of time is given by

2 (GATE-PI)(4M)

T (X) = A + BX + CX

02

Where A = 900 C, B = -200 C/m and C = -50 C/m

The wall has an area of 10m2 (as show in the fig) and a thermal conductivity of

40 W/mk.

14. The rate of heat transfer (in KW) into the wall (at x = 0)

a) 900 b) 450 c) 120 d) 80

15. The rate of change of energy storage (in KW) in the wall is

a) 130 b) 120 c) -10 d) -30

*****************

“Success is getting what you want, and happiness is wanting
what you get”

MECHANICAL ENGINEERING (HEAT TRANSFER)

3 CONVECTION

1. For the fluid flowing over a flat plate with prandtle number greater than unity, the

thermal boundary layer for laminar forced convection. (GATE-ME-1988)

a) is thinner than the hydrodynamic boundary layer

b) Has thickness equal to zero

c) is of same thickness as hydrodynamic boundary layer

d) is thicker than the hydrodynamic boundary layer

2. In pool boiling the highest HTC occurs in (GATE-ME-1990)

a) Sub-cooled boiling zone b) Nucleate boiling zone

c) Partial film boiling zone d) Film boiling zone

3. For air near atmospheric condition flowing over a flat plate the laminar thermal

boundary layer is thick than hydrodynamic boundary layer (T/F).

(GATE-ME-1994)

4. Heat transfer coefficient for free convection in gasses, forced convection in gases and

vapors, and for boiling water lie, respectively, in the range of (GATE-ME-1998)

2

a) 5 - 15, 20 - 200 and 3000 - 50000 W/m K

2

b) 20 - 50, 200 - 500 and 50000 - 100000 W/m K

2

c) 50 - 100, 500 - 1000 and 100000 - 1000000 W/m K

2

d) 20 - 100, 200 - 1000 and a constant 1000000 W/m K

5. For flow of fluid over a heated plate, the following fluid properties are known :

Viscosity = 0.001Pa.s; Specific heat at constant pressure = 1 KJ/KgK; Thermal

conductivity = 1 W/mK; The hydrodynamic boundary layer thickness at a specified

location on the plate is 1 mm, thermal boundary layer thickness at the same location is

(GATE-ME-2008)

a) 0.001 mm b) 0.01 mm c) 1 mm d) 1000 mm

0

6. A coolant fluid at 30 C flows over a heated flat plate maintained at a constant

0

temperature of 100 C. The boundary layer temp distribution at a given location on the

plate may be approximated as T = 30 + 70 exp(-y), where y (in m) is the distance

0

normal to the plate and T is in C. If thermal conductivity of the fluid is 1.0 W/mk, the

local convective heat transfer (in W/m2k) at the location will be

(GATE-ME-2009)

a) 0.2 b) 1 c) 5 d) 10

7. A fluid flowing over a flat plate has the following properties; dynamic viscosity =

-6

25 x 1 kg/ms, specific heat = 2.0 kj/kgK, thermal conductivity 0.05 W/mK. The

hydrodynamic boundary layer thickness is measured to be 0.5 mm. The thickness of the

thermal boundary layer would be

(GATE-ME-1992)

a) 0.1 mm b) 0.5 mm c) 1.0 mm d) none

MECHANICAL ENGINEERING (HEAT TRANSFER)

8. Match List - I with List - II and select the correct answer using the code given below the
lists (GATE-ME-2009)

List - I List - II

A. Grashof number 1. Mass diffusion

B. Schmid number 2. Transient conduction

C. Weber number 3. Free convection

D. Fourier number 4. Forced convection

5. Surface tension

6. Radiation

9. Water (Prandtl number = 6) flow over a flat plate which is heated over the entire length.

Which one of the following relationship between the hydrodynamic boundary layer

thickness (δ) and thermal boundary layer thickness (δt) is true (GATE-ME-2001)

a) δ = δ b) δ < δ

t t

c) δ > δ d) can not be predicted

t 3

10. The properties of mercury at 300K are : density = 13529kg/m , Cp = 0.1393 kJ/kgK,

-2
dynamic viscosity = 0.1523 x 10 N-s/m and thermal Conductivity = 8.540 W/m-K.

2

The Prandtl number of the mercury at 300 K is . (GATE-ME-2002)

a) 0.0248 b) 2.48 c) 24.8 d) 248

11. Consider a laminar boundary layer over a heated flat plate. The free stream velocity is

U∞. At some distance x from the leading edge the velocity boundary layer thickness is
δv and the thermal boundary layer is δt, if the Prandtl number is greater than 1, then

(GATE-ME-2003)

a) δ > δ b) δ > δ
rv
vr δr~x-1/2

c) δ = δr~(U∞) d) δ =

v v

STATEMENT FOR LINKED ANSWER QUESTOIN (Q12 & A13)

An un-insulated air conditioning duct of rectangular cross section 1 m x 0.5 m, carrying air at

00

20 C with a velocity of 10 m/s, is exposed to an ambient of 30 C. Neglect the effect of duct

0

construction material. For air in the range of 20-30 C, data are as follows : thermal

conductivity = 0.025 W/m. K; viscotiy = 18µPa.; Prandtl number = 0.73; density = 1.2

kg/m3. The laminar flow Nusselt number is 3.4 for constant wall temperature conditions and,

0.8 0.33 (GATE-ME-2005)
for turbulent flow, Nu = 0.023 Re Pr .

12. The Reynolds number for the flow is

a) 444 b) 890 5 5

c) 4.44 x 10 d) 5.33 x 10
d) 769
13. The heat transfer per meter length of the duct, in watts, is

a) 3.8 b) 5.3 c) 89

MECHANICAL ENGINEERING (HEAT TRANSFER)

14. The temp distribution within the Laminar thermal boundary layer over a heated

isothermal flat plate is given by (T - T) / (Tα - T) = ( 3/2 ) (y/δ ) - ( 1 /2 ) (y/δ t 3 where

w w t )

Tw and Tα are the temp of plate and free stream respectively, and ‘y’ is the normal

distance measured from the plate. The ratio of Average to the local Nussult number

based on the thermal boundary layer thickness δ is given by (GATE-ME-2007)

t

a) 1.33 b) 1.5 c) 1.5 d) 4.64

15. The average heat transfer coefficient on a thin hot vertical plate suspended in still air

can be determined from observations of the change in plate temperature with time as it

cools. Assume the plate temp to be uniform at any instant of time and radiation heat
exchange with the surroundings is negligible. the ambient temperature is 250C, the plate
has a total surface area of 1.0 m2 and a mass of 4 kg. The specific heat of the plate
material is 2.5 KH/KgK. The convective heat transfer coefficient in W/m2K, at instant
when the plate temp is 2250C and the change in plate temp with time dT/dt = -0.02K/s,

is (GATE-ME-2007)

a) 200 b) 20 c) 15 d) 10

16. Match the following (GATE-ME-2010)

P. Compressible flow U. Renolds number

Q. Free surface flow V. Nussult number

R. Boundary layer flow W. Froude number

S. Pipe flow Y. Mach number

Z. Skin friction coefficient

a) P-U, Q-X, R-V, S-Z, T-W b) P-W, Q-X, R-Z, S0U, T-U

c) P-Y, Q-W, R-Z, S-U, T-X d) P-Y, Q-W, R-Z, S-U, T-V

17. The ratios of the laminar hydrodynamic boundary layer thickness to thermal boundary

layer thickness of flows of two fluids P and Q on a flat are 1/2 and 2 respectively. The

4

Reynolds number based on the plate length for both the flow is 10 . The Prandtl and

Nusselt numbers for P are 1/8 and 35 respectively. The Prandtl and Nusselt number for

Q are respectively. (GATE-ME-2011)

a) 8 and 140 b) 8 and 70 c) 4 and 70 d) 4 and 35

*****************

MECHANICAL ENGINEERING (HEAT TRANSFER)

PRACTICE QUETIONS :

1. The Prandtl member of a fluid is the ratio of

a) Thermal diffusivity to momentum diffusivity

b) Momentum diffusivity to thermal diffusivity

c) conductive resistance to convective resistance

d) Thermal diffusivity to kinematic viscosity

2. The non-dimensional temperature gradient in a liquid as the wall of a pipe is

a) The heat flux b) The Nusslet number

c) The Prandtl number d) The Schmidt number

3. In forced convection the Nusslet number Nu is a function of

a) Re and Pr b) Re and Gr c) Pr and Gr d) Re and Sc

4. The laminar boundary layer occurs when a cold fluid flows over a hot plate. In which of

the following positions, the temperature gradient assumes zero value?

a) At bottom boundary layer

b) In mid free streams of fluid

c) At top of boundary layer

d) At junction of laminar and turbulent boundary layer
5. Hot air at 1500C flows over a flat plate maintained at 500C. If the forced convection heat

transfer is 75 W/m2K, the heat gain rate by the plate through an area of 2m2 will be

a) 15 kW b) 22.5 kJ/s

c) 7.5 kJ/s d) None of the above

6. The hydrodynamic and thermal boundary layers will merge when

a) Prandtl number is one

b) Schmidt number tends to infinity

c) Nusslet number tends to infinity

d) Archimedes number is greater than 10,000

7. The Nusslet number (Nu) for heat transfer in a pipe varies with Reynolds number (Re)
as Nu α Re0.8, then for constant average velocity in the pipe, the heat transfer coefficient

varies with the pipe diameter D as

a) D-1.8 b) D-0.2 c) D0.2 d) D1.8

8. For a fluid flowing over a flat plate, the Nusslet number at a point 0.5m from the

leading edge is 100. If the thermal conductivity of the fluid is 0.025 W/mK, the

coefficient of convective heat transfer is b) 5 W/m2K
a) 2000 W/m2K d) 1.25 x 10-4 W/m2K
c) 5 x 10-4 W/m2K

9. The ratio of Nusslet number to Biot number is

a) Conductive resistance of fluid / Conductive resistance of solid

b) Conductive resistance of fluid / Convective resistance of fluid

c) Conductive resistance of solid / Conductive resistance of fluid

d) Unity

10. The thermal boundary layer is significantly thicker than the hydrodynamic layer for

a) Newtonian liquids b) Polymeric liquids c) Liquid metals d) Gases

MECHANICAL ENGINEERING (HEAT TRANSFER)

11. In pipe flow, heat is transferred from hot wall to liquid by

a) Conduction only b) forced convection only

c) Forced convection and conduction d) free and forced convection

12. When a liquid flows through a tube with sub-cooled or saturated boiling, what is the

process known ?

a) Pool b) Bulk boiling

c) Convection boiling d) Forced convection boiling

13. Heat transfer occurs by natural convection because change in temperature causes

differences in

a) Viscosity b) Density

c) Thermal conductivity d) heat capacity

14. In film type condensation of liquid along a vertical tube, the thickness of the

condensable layer increases towards the bottom. This implies that the local heat transfer

coefficient

a) Increases from top to bottom

b) Decreases from top to bottom

c) Remains constant from top to bottom

d) First increases and then decreases from top to bottom

15. Let dh be the hydrodynamic entrance length for mercury in laminar flow in a pipe under
isothermal conditions. Let d1 be its thermal entrance length under fully developed

hydrodynamic conditions. Which ONE of the following is TRUE ?

a) dh>d1 b) dh<d1

c) dh=d1 d) dh>d1 only be greater or smaller than hd

16. As the difference between the wall temperature and the bulk temperature increases, the

boiling heat transfer coefficient

a) Continues to increase b) Continues to decrease

c) Goes through a minimum d) Goes through a maximum

17. The Grashof number is defined as the ratio of

a) Buoyancy to inertial forces b) Buoyancy to viscous forces

c) Interial to viscous forces d) Buoyancy to surface tension forces

18. For condensation of pure vapours if the heat transfer coefficients in filmwise and drop

wise condensation are respectively hf and hd then

a) δ increases, h increases b) Both δ and h increases

c) δ increases, h decreases d) Both δ and ha decreases

19. In a pool boiling experiment, the following phenomena were observed.

(P) Natural convection (Q) Film boiling

(R) Transition boiling (S) Nucleate boiling

What was the correct sequence of their occurrence ?

a) P, Q, R, S b) S, R, Q, P c) Q, R, P, S d) P, S, R, Q

******************

“Don’t give up at half time. Concentrate on wining
the second half”

MECHANICAL ENGINEERING (HEAT TRANSFER)

4 RADIATION

1. For a glass plate transivity and reflectivity are specified as 0.86 and 0.08 respectively,

the absorptivity of the glass plate is (ME-GATE-2008)

a) 0.86 b) 0.08

c) 1.00 d) 0.06

2. A diffuse radiation surface has (ME-GATE-1991

a) Radiation intensity independent of angle

b) Emissive power independent of angle

c) Emissive power independent of wave length

d) Radiation intensity independent of both angle and wavelength

3. The shape factors with themselves of two infinitely long black body concentric

cylinders with a dia ratio of 3 are ..................... For the inner and ..................... for the

outer. (ME-GATE-2004)

4. A plate having 10 cm2 area each side is hanging in the middle of a room of 100 m2 total

surface area. The plate temperature and emissivity are respectively 800 K and 0.6, the

temperature and emissivity values for the surfaces of room are 300 K and 0.3
respectively. Boltzmann constant σ = 5.67 x 10-8 / m2K4 , the total heat loss from the

two surface of the plate is (ME-GATE-2003)

a) 13.66 W b) 27.32 W c) 27.87 W d) 13.66 MW

5. The following figure was generated from experimental data relating spectral black body

emissive power to wave length at three temperatures T1, T2 and T3 (T1>T2>T3),

(ME-GATE-2005)

The conclusion is that the measurements are
a) correct because the maxima in Ebλ show are the correct trend

b) correct because Planck’s la is satisfied

c) wrong because the Stephen Boltzmann law is not satisfied

d) wrong because Wien’s displacement law is not satisfied
6. For an opaque surface, the absorptivity (α) , transmissivity (τ) and reflectivity (ρ) are

related by the equation :

a) α + ρ = τ b) ρ + α + τ = 0 c) α + ρ = 1 d) α + ρ = 0

7. The radiative heat transfer rate per unit area (W/m2) between two plane parallel gray

surfaces (emissivity = 0.9) maintained at 400K and 300K is (σb= Stephen Boltzmann

constant 5.67 x 10-8 W/m2K4) (ME-GATE-1993)

a) 992 b) 812 c) 464 d) 567

MECHANICAL ENGINEERING (HEAT TRANSFER)

8. For the circular tube of equal length and diameter shown in fig below, the view factor

F13 is 0.17, the view factor F12 in this case will be (ME-GATE-2001)

a) 0.17 b) 0.21 c) 0.79 d) 0.83

9. What is the value of the view factor for two inclined flat plates having common edge of

equal width, and with an angle of 20 degrees ? (ME-GATE-2002)

a) 0.83 b) 1.17 c) 0.66 d) 1.34

10. A solid cylinder (surface 2) is located at the centre of a hollow sphere (surface 1). The

diameter of the sphere is 1 m, while the cylinder has a diameter and length of 0.5 m

each. The radiation configuration factor F11 is (ME-GATE-2005)
d) 1
a) 0.375 b) 0.625 c) 0.75

11. A hollow enclosure is formed between two infinitely concentric cylinders of radii 1 m

and 2m respectively. Radiative heat exchange takes place between the inner surface of

the large cylinder (surface - 2) and the outer surface of the smaller cylinder (surface - 1)

the radiating surfaces are diffuse and the medium in the enclosure is no-participating.

The fraction of the thermal radiation leaving the larger surface and striking itself is

(ME-GATE-2008)

a) 0.25 b) 0.5 c) 0.75 d) 1

12. Consider two infinitely long thin concentric tubes of circular cross section as shown in

the figure. If D1 and D2 are the diameter of the inner and outer tubes respectively, then

the view factor F22 is given by (ME-GATE-2012)

a)  D2  −1 b) Zero c)  D1  d) 1−  D1 
     
 D1   D2   D2 

MECHANICAL ENGINEERING (HEAT TRANSFER)

PRACTICE QUESTIONS :

1. Ice is very close to a

a) Gray body b) Black body c) White body d) Specular body

2. In thermal radiation, for a black body

a) a = 1, ∉ ≠ 1 b) a ≠ 1, ∉ = 1 c) a ≠ 1, ∉ = 1 d) a = 1, ∉ = 1

3. A large spherical enclosure has a small opening. The rate of emission of radiative flux

through this opening is 7.35kW/m2. The temperature at the inner surface of the sphere

will be about (assume Stefan Boltzmann constant σ = 5.67x10-8 W/m2k4)

a) 6000C b) 3300C c) 600 K d) 1000K

4. To construct the best possible solar collector one should select a collector materials with

emissivity ε and absorptivity α such that

a) α ε is maximum b) α ε is minimum

c) α /ε is maximum d) ε / α is maximum

5. The spectra emissive power Eλ for a diffusely emitting surface is

Eλ = 0 for λ < 3µm ;

Eλ = 300 2 µm for = 12 <λ2

W/m

Eλ = 0 for λ > 25µm

The total emissive power of the surface over the entire spectrum is

a) 1250 W/m2 b) 2500 W/m2

c) 4000 W/m2 d) 3900 W/m2

6. A black body at a higher temperature, TH transfers energy by radiation to a back body at
a lower temperature TL Initially, TH = 18500C, TL = 5000C and the net rate of energy
transfer is 25W. After some time when TH = 15000C and TL = 7500C, what is the net

rate of energy transfer?

a) 8.73 W b) 9.60 W c) 13.89 W d) 11.01 W

7. Which of the following statements are correct for a blackbody?

1. A blackbody continues to emit radiation even when it is in thermal equilibrium with

its surroundings.

2. A blackbody is a perfect emitter.
3. Absorptivity, α = 1 represent a black surface

a) 1 and 2 only b) 1 and 3 only c) 1,2 and 3 d) 2 and 3 only

8. In radiative heat transfer, a gray surface is one

a) Which appears gray to the eye

b) Whose emissivity is independent of wavelength

c) Which was reflectivity equal to zero

d) Which appears equally bright from all directions

9. Gases have poor

a) Absorptivity b) Reflectivity

c) Transmissivity d) Absorptivity as well as transmissivity

10. Cloudy nights are warmer than clear nights because

MECHANICAL ENGINEERING (HEAT TRANSFER)

a) The water molecules forming the clouds have higher kinetic energy which is

transferred to the arrounding environment.

b) The interaction between negatively charged cloud ions and positively charged ground

ions warms the air

c) The clouds shield the ground, therefore radiation loss is reduced.

d) Chemical reactions between pollutants and water molecules heat up the clouds which

in turn warm the surroundings.

11. A radiation shield should

a) Have high transmissivity

b) Absorb all the radiations

c) Have high reflective power

d) Partly absorb and partly transmit the incident ratiation
12. Sun’s surface at 5800 K emits radiation at a wavelength of 0.5µ. A furnace at 3000C

will emit through a small opening, radiation at a wavelength of nearly

a) 10 µ b) 5 µ c) 15 µ d) 20 µ

13. A man sits on the floor by a fire burning at some distance at same level. The mole of

heat transfer mainly responsible for the man receiving heat is

a) Conduction b) Convection c) Radiation d) Advection

14. A satellite floats in deep space with very high velocity. It will continuously lose heat by

a) Convection b) Conduction and convection

c) Radiation d) Radiation and convection

15. Two radiating surface A1 = 6m2 and A2 = 4m2 have the sphere factor F1-2 = 0.1; the

shape F2-1 will be

a) 0.18 b) 0.15 c) 0.12 d) 0.10

16. Two large parallel grey plates with a small gap, exchange radiation at the rate of
1000W/m2 when their emissivities are 0.5 each. By coating one plate, its emissivity is

reduced to 0.25. Temperatures remain unchanged. The new rate of heat exchange shall

becomes b) 600 W/ m2 c) 700 W/ m2 d) 800 W/ m2
a) 500 W/ m2

17. For the two long concentric cylinders with surface areas, A1 and A2, the view factor F22
is given by

a) 0 b) 1 c) 1 – A1/A2 d) A1/A2

18. For the enclosure formed between two concentric spheres as shown below (R2 = 2R1),
the fraction of radiation leaving the surface area A2, that strikes itself is

MECHANICAL ENGINEERING (HEAT TRANSFER)

1 1 1 3
a) 4 b) 2 c) 2 d) 4

19. Two black plates, each one meter square, are placed parallel to each other in such a way
that the radiation shape factor for the system is 0.4. If the plates are maintained at 8000
C and 4000C respectively, determine the net radiant heat transfer between the plates.

Also calculate the net heat exchange if the plates were infinite in size. Stephen

Boltzmann constant = 5.67 x 10-8 W/m2K4. (ME-GATE-1889)

20. An object has the shape of cubical box of side 10 cm, with no top cover. The box is

placed inside a room whose dimension are much larger than those of the box. All the
five surfaces of box are at a temp of 5000C and have an emissivity of 0.6. The walls of
the room are at 250C and have an emissivity of 0.4. All these surfaces can be assumed to

be difuse-gray. Find the net ratiative heat loss from the inner surface of the box to the
walls of the room. Stephen Boltzmann constant 5.67 x 10-8 W/m2K4. View factor

between two parallel square plates placed directly opposite to each other is 0.2.

(ME-GATE-1991)

21. Consider two large parallel plates, one at T1 = 7270C with emissivity ε = 0.8 and the

1

other at T2 = 2270C with emissivity ε = 0.4. An aluminum radiation shield with an

2

emissity, ε = 0.05 on both sides is placed between the plates. Calculate the percentage

s

reduction is heat transfer rate between the two plates as a result of the shield. Use σ =

5.67 x 10-8 W/(m2K4). (ME-GATE-1995)

22 A thin metal plate is exposed to solar radiation. The air and the surrounding are at 300C.

The heat transfer coefficient by free convection from t he upper surface of the plate is
17.4 W/m2K. The plate has an absorptivity of 0.9 at solar wavelength and an emissivity

of 0.1 at the long wavelength. Neglecting any heat loss from the lower surface,
determine the incident solar radiation intensity in kW/m2, if the measured equilibrium
temperature of the plate is 500C. Stephen Bolizman constant is 5.67 x 10-8 W/m2K4.

(ME-GATE-2000)

MECHANICAL ENGINEERING (HEAT TRANSFER)

COMMON DATA FOR QUESTOIN (Q23 & Q24)

Radiative heat transfer is intended between the inner surface of two very large isothermal

parallel metal plates. While the upper plate (designated as plate 1) is a blck surface and is the
warmer one being maintained at 7270C, the lower plate (plate 2) is a diffuse and gray surface
with an emissivity of 0.7 and is kept at 2270C, assume that the surfaces are sufficiently large

to form a two surface enclosure and steady state condition to exist. Stephen Boltzmann

constant at 5.67 x 10-8 W/m2K4. (ME-GATE-2009)

23. The irradiation (in KW/m2) for the upper plate (plate) is

a) 2.5 b) 3.6 c) 17.0 d) 19.5

24. If plate is also a diffuse gray surface with an emissivity value of 0.8, the net radiant heat
exchange (in KW/m2) between plate 1 and plate 2.

a) 17.0 b) 19.5 c) 23.0 d) 31.7

**************************

“There is no elevator to success. You have to take the stairs”

MECHANICAL ENGINEERING (HEAT TRANSFER)

5 HEAT EXCHANGERS

1. In shell and tube heat exchanger, baffles are mainly used to [ME-GATE-91]

a) Increase the mixing of fluid

b) Increase the heat transfer area

c) Deflect the flow in desired direction

d) Reduce fouling of the tube surface

2. The practice to use steam on the shell side and water on the tube side in condensers of

steam power plant is because [ME-GATE-94]

a) To increase overall HT coefficient, water side velocity can be increased if water is on

the tube side

b) Condenser can act as a storage unit for condensed steam

c) Rate of condensation of steam is invariably smaller than the mass flow rate of cooling

water

d) It is easier to maintain vacuum on the shell side than on the tube side

3. For the same inlet and exit temps of the hot and cold fluids, the Log mean temperature

difference (LMTD) is [ME-GATE-02]

a) Greater for parallel flow heat exchanger than the counter flow heat exchanger

b) Greater for counter flow heat exchanger than the parallel flow heat exchanger

c) Same for both parallel and counter flow heat exchanger

d) Depending on the properties of fluid
4. In a condenser of a power plant, the steam condenses at a temperature of 600C. The

cooling water enters at 300C and leaves at 450C. The logarithmic mean temperature

difference (LMTD) of the condenser is [ME-GATE-11]
d) 37.50C
a) 16.20C b) 21.60C c) 300C

5. In certain HE, both the fluids have identical mass flow rate-specific heat product. The

hot fluid enters at 760C and leaves at 470C , and the cold fluid entering at 280C leave at

550C. the effectiveness of the HE is [ME-GATE-97]

a) 0.16 b) 0.58 c) 0.72 d) 1.0

6. Air enters a counter flow HE at 700C and leaves at 400C. Water enters at 300C and

leaves at 500C, the LMTD in deg C is [ME-GATE-00]

a) 5.65 b) 14.43 c) 19.52 d) 20.17

7. In a counter flow heat exchanger, for the hot fluid the heat capacity = 2 kJ / kg K, mass
flow rate = 5 kg/s, inlet temperature = 1500C, outlet temperature 1000C. For the cold
fluid heat capacity = 4 kJkg K, mass flow rate are = 10 Kg/s, inlet temperature 200C.
neglecting heat transfer to surroundings, the outlet temperature of the cold fluid 0C is

[ME-GATE-03]

a) 7.5 b) 32.5 c) 45.5 d) 70.0

MECHANICAL ENGINEERING (HEAT TRANSFER)

8. In a condenser, water enters at 300C and flows at the rate 1500 Kg/hr. The condensing
steam is at a temperature of 1200C and cooling water leaves the condenser at 800C.

Specific heat of water is 4.187 KJ/KgK. If the overall heat transfer coefficient is 2000
W/m2K, the, the heat transfer area is

[ME-GATE-04]

a) 0.707m2 b) 7.07 m2 c) 70.7 m2 d) 141.4 m2

9. Hot oil cooled from 800C to 500C in an oil cooler which uses air as the coolant. The air

temperature rises from 300 to 400C. The designer uses a LMTD value of 260C. The type

of heat exchanger is [ME-GATE-05]

a) parallel flow b) double pipe c) counter flow d) cross flow

10. In a counter flow heat exchanger, hot fluid enters at 650C and cold fluid leaves at 300C

mass flow rate of the hot fluid is 1 kg/s and that of cold fluid is 2 kg/s. specific heat of

the hot fluid is 10 kJ/kgK and that of cold fluid is 5 kJ/kgK. The LMTD for the heat

exchangers is [ME-GATE-07]

a) 15 b) 30 c) 35 d) 45

11. The LMTD of a counter flow heat exchanger is 200C, the cold fluid enters at 200C and

the hot fluid enters at 1000C. mass flow rate of the cold fluid is twice that of the hot

fluid, specific heat at constant pressure of the fluid is twice that of the cold fluid. The

exit temperature of the cold fluid is [ME-GATE-08]

a) 400C 0
c) 800C
b) 60 C

d) can not be determined

12. In a parallel flow heat exchanger operating under steady state, the heat capacity rates of

the hot and cold fluid are equal. The hot fluid flowing at 1Kg/sec with sp. heat
4KJ/Kgk, enters the heat exchanger at 1020C while the cold fluid has an inlet temp of
150C, the OHTC of the heat exchanger is estimated to be 1 KW/m2K and the
corresponding heat transfer surface area is 5m2, neglecting heat transfer between the

heat exchanger and the ambient. The heat exchanger is characterized by the following

relation. [ME-GATE-09]
2ε = 1 - Exp (-2NTU)

The exit temp (in C) for the cold fluid is

a) 45 b) 55 c) 65 d) 75

13. Cold industrial gas ( Cp = 1 KJ/KgK) enters a parallel flow heat exchanger at 2500C

with a flow area of 2 Kg/s to heat a water stream. The water stream ( Cp = 4 KJ/KgK )
enters the heat exchanger at 500C with a flow rate of 1 Kg/s, the heat exchanger has an

effectiveness of 0.75, the gas stream exit temperature will be [PI-GATE-10]

a) 750C b) 1000C c) 1250C d) 1500C

14. Cold water flowing at 0.1 Kg/s is heated from 200C to 700C in a counter - flow type heat

exchanger by a hot water stream flowing at 0.1 Kg/s and entering at 900C. The specific

heat of water is 4200 J/(kg K) and density is 1000 Kg/m3. If the overall heat transfer

coefficient U for the heat exchanger is 2000 W/ (m2K), the required heat exchange area

(in m2) is [PI-GATE-11]

a) 0.052 b) 0.525 c) 0.151 d) 0.202

MECHANICAL ENGINEERING (HEAT TRANSFER)

15. Water (Cp = 4.18 kJ/kg. K) at 800 C enters a counter flow heat exchanger with a mass
flow rate of 0.5 kg/s. Air (Cp = 1 kJ/kg . K) enters at 300C with a mass flow rate 2.09
kg/s. If the effectiveness of the heat exchanger is 0.8, the LMTD (in 0C) is

[ME&PI-GATE-12]

a) 40 b) 20 c) 10 d) 5

MECHANICAL ENGINEERING (HEAT TRANSFER)

PRACTICE QUESTION :

1. In double-pipe counter flow heat exchanger if mh Ch = mcCc, the temperature profiles of
the two fluids along the length of the heat exchanger will be
a) Converging
b) Diverging
c) Parallel
d) None of the above

2. What does NTU indicate ?
a) Effectiveness of heat exchanger
b) Efficiency of heat exchanger
c) Size of heat exchanger
d) Temperature drop in heat exchanger

3. In a parallel flow heat exchanger operating under steady state, hot liquid enters at a
temperature Th.in and leaves at a temperature Th.out. Cold liquid enters at a temperature
Tc.in and leaves at a temperature Tc.out. Neglect any heat loss from the heat exchanger to
the surrounding. If Th.in >> Tc/in then for a give time interval, which ONE of the
following statements is true ?
a) Entropy gained by the cold stream is GREATER than entropy lost by the hot stream
b) Entropy gained by the cold stream is EQUAL to the entropy lost by the hot stream
c) Entropy gained by the cold stream is LESS than the entropy lost by the hot stream
d) Entropy gained by the cold steam is ZERO

4. Which one of the following statements about baffles in a shell and tube heat exchanger
is false ? Baffles
a) Act as support to the tube bundle
b) Reduce the pressure drop on the shellside
c) Alter the shell - side flow pattern
d) Help in increasing the shell - side heat transfer coefficient

5. For a counter-current heat exchanger with Th1 = 80C, Tc2 = 60C, Th2 = 50C and Tc1 =
30C, and the temperature difference between the two streams being the same
everywhere along z, the direction of flow of the hot fluid, the temperature profile should
satisfy

a) d 2T >0 b) d 2T =0 c) d 2T <0 d) dT = 0
dz 2 dz 2 dz 2
dz

6. The equation of effectiveness ε = 1 – e-NTU of a heat exchanger is valid (NTU is number
of transfer unit) in the case of
a) Boiler and condenser for parallel flow
b) Boiler and condenser for counter flow
c) Boiler and condenser for both parallel flow and counter flow
d) Gas turbine for both parallel flow and counter flow

MECHANICAL ENGINEERING (HEAT TRANSFER)

7. Effectiveness of countercurrent heat exchanger is given by

  − Cmin 
1− exp −NTU 1 
  Cmax 

1− Cmin   − Cmin 
exp −NTU 1 
Cmax   Cmax 

If same liquid at the same flow rate is used as heating and cooling media through a

countercurrent double tube heat exchanger then effectiveness is given by

NTU −1 NTU NTU −1 NTU −1
c) NTU +1 d) NTU + 2
a) b) NTU +1

NTU

8. The overall heat transfer coefficient based on the outside surface area of a turbular heat
exchanger decreased due to fouling during operation from 1000 W/m2K to 800 W m-2K-
1. The fouling film coefficient of the heat exchanger in W m-2 K-1 is ________

9. Hot water (0.01 m3/min) enters the tube side of a countercurrent shell and tube heat
exchanger t 800C and leaves at 500C. Cold oil (0.05 m3/min) of density 800 kg/m3 and
specific heat of 2 kJ/kg K enters at 200C. The log mean temperature difference in 0C is

approximately

a) 32 b) 37

c) 45 d) 50

10. Fruit juice flowing at the rate of 600kg h-1 is to be heated using same flow rate of hot

fruit juice in a countercurrent regenerator. The specific heat capacity of the fruit juice is
3.9 kJkg-1K-1. The overall heat transfer coefficient of the regenerator is 512 Wm-1K-1

and the area of the regenerator is 3.5m2. The effectiveness of the regenerator is

a) 0.547 b) 0.734

c) 0.837 d) 0.943

11. Which of the following diagram represents correctly the gas-gas counter flow heat

exchange ?

a) b)

c) d)

MECHANICAL ENGINEERING (HEAT TRANSFER)

12. Assertion (A) : It is not possible to determine LMTD in a counter flow heat exchanger
with equal heat capacity rates of hot and cold fluids.
Reason (R) : Because the temperature difference is invariant along the length of the
heat exchanger.
a) Both A and R are individually true and R is the correct explanation of A
b) Both A and R are true but R is not the correct explanation of A
c) A is true but R is false
d) A is false but R is true.

13. A shell and tube heat exchanger is to be designed for heating pressurized water by

means of hot gasses which get cooled, the data are as follows [ME-GATE-88]

Temp of water at the inlet = 800C Temp of the water at the outlet = 1400C

Temp of hot gasses at the inlet = 3400C Temp of hot gasses at the outlet = 1800C

Mass flow rate of water = 12 Kg/s, Specific heat of water = 4.2 KJ/kgK
OHTC = 30 W/m2K,

Correction factor for LMTD based on counter flow conditions = 0.9

Calculate the tube surface area required in the heat exchanger and the effectiveness of

the heat exchanger.

14. A double pipe counter flow heat exchanger is to be designed to cool 12000 kg/hr of an
oil of specific heat 1.95 KJ/kgK from 850C to 550C by water entering the heat
exchanger at 300C and leaving at 450C. If the OHTC of heat exchangers is 400W/m2K.

Calculate the LMTD and the surface area of the heat exchanger. [ME-GATE-90]

15. A one shell pass, one tube-pass heat exchanger, has counter flow configuration between

the shell side and tube side fluids. The total number of tubes within the heat exchanger

is 10 and the tube dimensions are ID = 10 m, OD = 12mm and length = 1m, saturated
dry steam enters the shell side at a flow rate of 1kg/s and the temp of 1000C, in the tube
side, cold water enters at a flow rate of 10 kg/s with an inlet temp of 250C, the OHTC
based on the outer surface area of the tubes is 50 W/m2K, the specific heat of water is

4.18 KJ/kgK and the latent heat of steam is 2500 KJ/kg. What is the condition of the

steam at the exit. [ME-GATE-91]

16. Two streams of fluids of unit constant specific heats and unit mass flow are rate

exchange thermal energy in an adiabatic heat exchanger. The inlet temps of hot and cold
streams are 3000C and 300C respectively. Calculate the LMTD and effectiveness of the

heat exchanger if the hot fluid is cooled to zero entropy condition. [ME-GATE-94]
17. A counter flow heat exchanger is to heat air entering at 4000C with a flow rate of 6 kg/s

by the exhaust gas entering at 8000C with a flow rate of 4 kg/s, the overall heat transfer
coefficient is 100 W/(m2K) and the outlet temperature of the air is 5510C. Specific heat

at constant pressure for both air and the exhaust gas can be taken as 1100 J/(kgK).

Calculate the heat transfer area needed and the number of transfer units.

[ME-GATE-95]

MECHANICAL ENGINEERING (HEAT TRANSFER)

18. In a certain double pipe heat exchanger hot water flows at a rate of 50,000 kg/h and gets
cooled from 950 to 650. At the same time 50,000 kg/h of cooling water at 300C enters

the heat exchanger. The flow conditions are such that the overall heat transfer
coefficient remains constant at 2270 W/m2K. Calculate the heat transfer area required,

assuming the tow streams are in parallel flow and for both the streams CP = 4.2 kJ/kgK.

[ME-GATE-97]
19. A hot fluid at 200C enters a heat exchanger at a mass flow rate of 104 kg/hr. Its specific

heat is 2000 J/kgK. It is to be cooled by another fluid entering at 250C with a mass flow

rate 2500 kg/hr and specific heat 400 J/kg K. the overall heat transfer coefficient based
on outside area of 20m2 is 250 W/m2K. Find the exit temperature of the hot fluid when

the fluids are in parallel flow. [ME-GATE-98]

20. Heat water flow with a velocity of 0.1 m/s in a 100 mm long, 0.1m diameter pipe. Heat
lost from the pipe outer wall is uniform and equal to 420 W/m2. If the inlet water
temperature is 800C, calculate the water temp at the exit. Neglect effect of pipe wall
thickness. CP (water) = 4.2 KJ/kgK and density of water = 1000 Kg/m3.

[ME-GATE-98]

21. Two fluids, A and B exchange heat in a counter-current heat exchanger. Fluid a enters
at 4200C and has mass flow rate of 1 kg/s. Fluid B enters at 200C and also has a mass

flow rate of 1 kg/s. Effectiveness of heat exchanger is 75%. Determine the heat transfer

rate and exit temperature of fluid B. (Specific heat of fluid A is 1 kJ/kg K and that of

fluid B is 4 kJ/kgK). [ME-GATE-99]

*******************

MECHANICAL ENGINEERING (HEAT TRANSFER)

HMT OBJECTIVE ANSWERS :

CHAPTER - 1
1-b, 2-b, 3-d, 4-c, 5-b, 6-d, 7-d, 8-d, 9-c, 10-sol, 11-d, 12-d, 13-a, 14-b, 15-c, 16-d, 17-c, 18-c,
19-c, 20-c, 21-c, 22-a, 23-b, 24-b, 25-d, 26-d, 27-c, 28-c
Practice Ques. Ans. :
1-d, 2-a, 3-c, 4-c, 5-c, 6-c, 7-b,8-d, 9-c, 10-53.310C, 11-176.62 kW/m2, 12-0.1878 W/mk, 13-
37.4 W, 14- 1.667 kg/hr

CHAPTER - 2
1-d, 2-d, 3-F, 4-a, 5-b, 6-b,7-c, 8-b, 9-c, 10-b, 11-d
Practice Ques. Ans. :
1-d, 2-b, 3-d, 4-c, 5-b, 6-a, 7-c, 8-c, 9-d, 10a, 11-a, 12 , 13 65.180, 14-d, 15-d

CHAPTER - 3
1-a, 2-c, 3-F, 4-a, 5-c, 6-b,7-b, 8-sol, 9-b, 10-a, 11-a, 12-c, 13-d, 14-c, 15-d, 16-d, 17-a
Practice Ques. Ans. :
1-b, 2-b, 3-a, 4-c, 5-a, 6-a, 7-b, 8-b, 9-a, 10-c, 11-c, 12-d, 13-b, 14-b, 15-a, 16-d, 17-b, 18-c,
19-d

CHAPTER - 4
1-d, 2-a, 3-sol, 4-b, 5-d, 6-c, 7-b, 8-d, 9-a, 10-b, 11-b, 12-d
Practice Ques. Ans. :
1-b, 2-d, 3-c, 4-c, 5-d, 6-d, 7-c, 8-b, 9-b, 10-c, 11-c, 12-b, 13-c, 14-c, 15-b, 16-b, 17-c, 18-d,
19-63.53kW, 20-34.936W, 21-93.4%, 22-0.455kW/m2

CHAPTER - 5
1-b, 2-d, 3-b, 4-b,5-b, 6-b, 7-b, 8-a, 9-d, 10-c, 11-a, 12-b, 13-b, 14-b, 15-c.
Practice Ques. Ans. :
1-c, 2-c, 3-a, 4-c, 5-d, 6-c, 7-b, 8-4000W/m2k, 9-b, 10-b, 11-b, 12-d, 13-0.554, 14-15.28m2,
15-complete condensation takes place, 16-1.11, 17-1.09, 18-32.96 m2, 19-1920C, 20-
80.0040C, 21-300kW.

***************

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Rather become a man of value”