Enrolment No.

/Seat No_____________

GUJARAT TECHNOLOGICAL UNIVERSITY

BE - SEMESTER–V (NEW) EXAMINATION – SUMMER 2024
Subject Code:3151909 Date:18-05-2024
Subject Name:Heat Transfer
Time:02:30 PM TO 05:00 PM Total Marks:70
Instructions:
1. Attempt all questions.
2. Make suitable assumptions wherever necessary.
3. Figures to the right indicate full marks.
4. Simple and non-programmable scientific calculators are allowed.

Marks
Q.1 (a) Do as directed : 03
1) Define : Thermal diffusivity.
2) Arrange the material in descending order of their thermal
conductivity; i) Water ii) Copper iii) Air and iv) Wood.
3) Define: Anisotropic material.
(b) Give four examples of free convection and four examples of forced 04
convection observed from day to day life.
(c) Explain the following with reference to a heat exchanger: 07
1. Fouling factor,
2. Effectiveness of heat exchanger,
3. Correction factor for multipass arrangement.
Q.2 (a) What do you mean by radiation shiled? Give two examples of use of 03
radiation shield.
(b) With suirable example, explain in brief abour black body, white body, 04
opquae body and transperant body.
(c) An aluminim fin (k = 200W/mK, 2.5cm long,1m width, and 3.5mm 07
thick) protrudes from a wall. The base is at 4200C and surrounding air
temperature is 300C.
Determine the heat dissipated from the fin and fin efficiency for the fin
is of finite length and heat loss from fin tip is negligible. Take h =
11W/m2K.
OR
(c) A furnace wall, 32 cm thick, is made up of an inner layer of brick 07
(k=0.84W/mK) covered with a layer of insulation (k=0.16W/mK). The
furnace operates at a temperature of 13250C and the ambient
temperature is 250C.
i) Determine the thickness of brick and insulation which gives
minimum heat loss,
ii) Calculate the heat loss presuming that the insulating material has a
maximum temperature of 12000C.
If the calculated heat loss is not accepted than state whether addition of
another layer of insulation would provide a satisfactory solution.

Q.3 (a) Explain mean film temperature and bulk mean temperature. 03
(b) Differentiate between boiling and condensation. 04
(c) Discuss the electrical analogy for radiant heat transfer. 07

1
 OR
Q.3 (a) Justify that a good absorber is also a good emitter for radiation heat 03
transfer.
(b) Explain in detail about cross flow heat exchanger with its advantages. 04
Give suitable examples.
(c) Define condensation process. Also explain film condensation and drop- 07
wise condensation.
Q.4 (a) ‘It is desirable to use two thin fins instead of one thick fin for engine 03
cooling’. Give reason.
(b) What is insulation? State its four applications in engineering field. 04
(c) Write the most general equation in Cartesian co-ordinates for heat 07
transfer by conduction. Deduce above equation for the following cases
with suitable assumptions;
(i) Laplace equation, (ii) Poisson equation, and (iii) Fourier equation.
OR
Q.4 (a) Use of aluminum material as a cooking utensils are not desirable. 03
Evaluate.
(b) Write the general differential equation in Cartesian co-ordinates for 3-D 04
unsteady heat conduction by considering an infinitesimal volume
element. Deduce there from the conduction equations for the following
cases;
(i) Steady state 1-D flow with heat generation at uniform rate within
material, (ii) Unsteady 2-D flow without heat generation.
(c) Explain physical significance of critical radius of insulation and derive 07
an expression for the same critical radius in case of sphere.

Q.5 (a) Differentiate natural and forced convection. 03

(b) State the similarities and difference between: 04
1) Nusselt number and Biot number,
2) Grashof Number and Reynold number.
(c) What is the limitation of Rayleigh’s method of dimensional analysis? 07
Which method is preferred in such case and how repeating variables are
selected?
OR
Q.5 (a) Define: Nusselt number, Grashof Number and Reynold number. 03
(b) State the governing law for convection heat transfer. Explain in brief 04
about convection heat transfer coefficient.
(c) Using Buckingham–π theorem show that, Nu = f ( Re, Pr) for forced 07
convection.

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

2
Seat No.: ________ Enrolment No.___________

GUJARAT TECHNOLOGICAL UNIVERSITY

BE – SEMESTER- V EXAMINATION-SUMMER 2023
Subject Code: 3151909 Date: 26/06/2023
Subject Name: Heat Transfer
Time: 02:30 PM TO 05:00 PM Total Marks: 70
Instructions:
1. Attempt all questions.
2. Make suitable assumptions wherever necessary.
3. Figures to the right indicate full marks.
4. Simple and non-programmable scientific calculators are allowed.

Q.1 (a) Give difference between free and forced convection. 03

(b) Explain the terms thermal diffusivity and thermal contact resistance. 04
(c) A mild steel tank of wall thickness 10 mm contains water at 90o C. The thermal 07
conductivity of mild steel is 50 W/moC , and the heat transfer coefficient for
inside and outside of the tank area are 2800 and 11 W/m2 oC, respectively. If the
atmospheric temperature is 20oC , calculate
(i) The rate of heat loss per m2 of the tank surface area.
(ii) The temperature of the outside surface tank.

Q.2 (a) A spherical shaped vessel of 1.2 m diameter is 100 mm thick. Find the rate of 03
heat leakage, if the temperature difference between the inner and outer surfaces
is 200o C. Thermal conductivity of material is 0.3 kJ /mhoC.
(b) Write the general three dimensional heat conduction equation in 04
i) Cylindrical coordinates
ii) Spherical coordinates
(c) A 12 cm diameter long bar initially at a uniform temperature of 40oC is placed in 07
a medium at 650oC with a convective co efficient of 22 W/m2K. Calculate the
time required for the bar to reach 2550C. Take k = 20W/mK, ρ = 580 kg/m3 and
c = 1050 J/kg K.
OR
(c) A motor body is 360 mm in diameter (outside) and 240 mm long. Its surface 07
temperature should not exceed 55 oC when dissipating 340 W. 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 30oC. Take thermal conductivity = 40 W/moC.

Q.3 (a) Explain Displacement thickness, Momentum thickness and Energy thickness. 03
(b) Differentiate between steady state and transient heat conduction and give some 04
examples of unsteady state heat conduction.
(c) For natural convection heat transfer, show that Nu = C (Prn , Grm). 07
OR
Q.3 (a) Define radiation. State the range of wavelengths for ultraviolet, visible and 03
thermal radiations.
(b) Discuss the significance of Prandtl, Nusselt and Stanton numbers in convection. 04
(c) Define and discuss velocity boundary layer and thermal boundary layer over a 07
flat plate. Show the thickness of thee layers for different Prandtl numbers.

1
Q.4 (a) Explain the terms absorptivity, reflectivity and transmissivity of radiant energy. 03
(b) The filament of a 75 W light bulb may be considered as a black body radiating 04
into a black enclosure at 700 C. the filament diameter is 0.10 mm and length is 5
cm. Considering the radiation, determine the filament temperature .
(c) State and prove Kirchhoff’s law. 07
OR
Q.4 (a) Calculate the shape factor for cylindrical cavity shown in Fig. 1 with respect to itself. 03

Fig. 1
(b) Define Heat exchanger. Give classification of heat exchangers. 04
(c) Define intensity of radiation and show that for a unit surface the intensity of 07
normal radiation is 1/π times the total emissive power.

Q.5 (a) What do you understand by fouling factor in case of heat exchanger? List the 03
causes of fouling.
(b) Define and explain types of condensation. 04
(c) What is boiling? Explain different regimes of boiling. 07
OR
Q.5 (a) What do you understand by TEMA charts? How are they useful in the design of 03
multi-pass heat exchangers.
(b) Differentiate between pool boiling and forced convection boiling. 04
(c) Derive LMTD formula for counter flow heat exchanger. 07

________________

2
Seat No.: ________ Enrolment No.___________

GUJARAT TECHNOLOGICAL UNIVERSITY

BE - SEMESTER–V(NEW) EXAMINATION – SUMMER 2022
Subject Code:3151909 Date:04/06/2022
Subject Name:Heat Transfer
Time:02:30 PM TO 05:00 PM Total Marks: 70
Instructions:
1. Attempt all questions.
2. Make suitable assumptions wherever necessary.
3. Figures to the right indicate full marks.
4. Simple and non-programmable scientific calculators are allowed.
MARKS
Q.1 (a) State how density of fluid play an important role in natural 03
convection heat transfer?
(b) Write Fourier rate equation of heat transfer by conduction. Give 04
units of each parameter appearing in this equation.
(c) Derive general heat conduction equation in Cartesian coordinates 07
and prove that the steady state heat transfer equation without heat
generation is
𝜕2 𝑡 𝜕2 𝑡 𝜕2 𝑡
+ + =0
𝜕𝑥 2 𝜕𝑦 2 𝜕𝑧 2

Q.2 (a) As shown in the figure, thickness of plaster is tp, thickness of 03

glass window is tg, thickness of brick wall is tb, and the thermal
conductivity for plaster, brick wall and glass is kp, kb and kg
respectively. Inner temperature is Ti and outer temperature is To.
Draw thermal circuit for the given figure and write equation of
heat transfer.

(b) Give applications with explanation where poor thermal 04

conductivity of air restricts the heat transmission by conduction.
(c) A steel rod of thermal conductivity 30W/m-deg is 1 cm in 07
diameter and 5 cm long protrudes from a wall which is
maintained at 100oC. The rod is insulated at the tip and is exposed
to an environment with convective heat transfer coefficient of
50W/m2-deg and ta=30oC. Calculate the fin efficiency,
temperature at the tip of fin and the rate of heat dissipation.

1
 OR
(c) A thermometric pocket is a hollow tube of thermal conductivity 07
of 82 W/m-deg having outer and inner diameter of 18mm and
12mm respectively. The pocket extends upto 6cm depth from the
wall of a 18cm diameter tube which carries hot fluid. The heat
transfer coefficient between the pocket and fluid is prescribed by
the following relation
Nu=0.175(Re)0.62
Make the calculations for the error in temperature measurement.
Considering following data:
Fluid temperature is 150oC and tube wall temperature 50oC.
Reynolds Number is 25000 and thermal conductivity of fluid is
0.04 W/m-deg.

Q.3 (a) Enlist factors need consideration for the optimum design of fins. 03
(b) Show the temperature variation along the length of heat 04
exchanger when
(1) Steam condenses on the outside of a condenser tube with
water flowing inside the tube as coolant
(2) Hot fluid used for evaporating another liquid
(c) Working in terms of inlet and outlet temperatures of the fluids 07
and overall heat transfer coefficient, develop an expression for
the heat transfer from one fluid to another in a conventional
parallel flow heat exchanger.
OR
Q.3 (a) Explain meaning of following as applied to heat exchangers: 03
(1) Heat capacity ratio,
(2) Effectiveness and
(3) Number of Transfer Units.
(b) In a chemical plant, a chemical solution is heated from -15oC to 04
-8.5oC in tube in tube parallel flow heat exchanger by a fluid
entering at 40oC and leaving at 25.5oC at the rate of 10 kg/min.
Determine the heat exchanger area for an overall heat transfer
coefficient of 850W/m2K. For fluid CP = 4186J/kgK.
(c) In an application of heat exchanger, the exhaust gas is used to 07
heat the compressed air so that capacity ratio is very close to
unity. Under this situation, show that
1
𝜖 = 2 [1 − exp⁡(−2𝑁𝑇𝑈)]⁡for parallel flow heat exchanger

Q.4 (a) List the salient features of a black body radiation. 03

(b) Radiant energy with an intensity of 800W/m2 strikes a flat plate 04
normally. The absorptivity is twice the transmitivity and trice the
reflectivity. Determine the rate of absorption, transmission and
reflection of energy.
(c) Prove that total emissive power of a diffused surface is equal to 07
𝜋 times its intensity of radiation.
OR
Q.4 (a) Give statements of: 03
(a) Kirchoff’s Law
(b) Stefan-Boltzman Law
(c) Wein’s displacement Law

2
 (b) Prove that 𝜀 = 𝐸 where 𝜀 is the emissivity of the body, E is the 04
𝐸𝑏
emissive power of the body and Eb is the emissive power of the
black body.
(c) The temperature of the flame in a furnace is 1900 K. Take 07
C1=0.374x10-15Wm2, C2=14.4x10-3mK.
Find:
1. Monochromatic energy emission at 1μ per m2
2. λmax
3. Monochromatic energy emission at λmax and at 1900 K.
4. Total energy emitted/m2.

Q.5 (a) Using usual notations, write dimensions of 03

(1) Dynamic viscosity
(2) Thermal Conductivity
(3) Specific Heat
(b) A steam pipe 60mm in diameter and 3 meter long has been placed 04
horizontal in still air environment at 20oC. If the pipe wall is
maintained at 300oC, determine the rate of heat loss. At the mean
temperature of 160oC, the thermophysical properties of air are as
follow:
k = 3.64x10-2W/m-deg
𝜈 = 30.09x10-6 m2/sec
Pr = 0.682 and
𝟏
𝜷 = 𝟏𝟔𝟎+𝟐𝟕𝟑 = 𝟐. 𝟑𝟐𝒙𝟏𝟎−𝟑⁡ 𝒑𝒆𝒓⁡𝑲

Use following relation for convective heat transfer coefficient,

Nu=0.53(Gr.Pr)0.25
(c) Prove that the temperature of a body at any time  during 07
Newtonian heating or cooling is given by
𝑡 − 𝑡𝑎
= 𝑒𝑥𝑝[−𝐵𝑖 𝐹𝑜 ]
𝑡𝑖 − 𝑡𝑎
Where Bi is Biot Number, Fo is Fourier Number, 𝑡𝑎 is the
ambient temperature and 𝑡𝑖⁡ is the initial temperature of the body
OR
Q.5 (a) State advantages of dimensional analysis. 03
(b) What assumptions are to be made while deriving differential 04
equation for hydrodynamic boundary layer?
(c) A large vertical flat plate 3 m high and 2 m wide is maintained at 07
75°C and is exposed to atmosphere at 25°C. Calculate the rate of
heat transfer.
The thermophysical properties of air are evaluated at the mean
temperature and are as follow:
 = 1.088 kg/m3; Cp = 1.00 kJ/kg.K;
 = 1.96 × 10-5 Pa-s k = 0.028 W/mK.
Pr = 0.7

Use the following correlation for convective heat transfer

coefficient 𝑵𝒖 = 𝟎. 𝟏(𝑮𝒓. 𝑷𝒓)𝟏/𝟑
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3
Seat No.: ________ Enrolment No.___________

GUJARAT TECHNOLOGICAL UNIVERSITY

BE - SEMESTER–V (NEW) EXAMINATION – SUMMER 2021
Subject Code:3151909 Date:09/09/2021
Subject Name:Heat Transfer
Time:10:30 AM TO 01:00 PM Total Marks:70
Instructions:
1. Attempt all questions.
2. Make suitable assumptions wherever necessary.
3. Figures to the right indicate full marks.
4. Simple and non-programmable scientific calculators are allowed.

MARKS
Q.1 (a) Write any three assumptions of Nusselt theory for film 03
condensation.
(b) Draw boiling curve for water at 1 atm. Pressure and 04
Represent different regimes on that.
(c) Steam enters a counter flow heat exchanger dry saturated at 10 bar 07
and leaves at 350 0C. The mass flow of steam is 800 kg/min. the
gas enters the heat exchanger at 650 0C and mass flow rate is 1350
kg/min. if the tubes are 30mm diameter and 3m long. Determine
the number of tubes required.
Neglect the resistance offered by metallic tubes.
Use following data :
Tsat = 180 0C ( At 10 bar)
Cps =2.71 kJ/kg-K
Cpg =1 kJ/kg-K
Heat transfer co-efficient steam side = 600 W/m2-K
Heat transfer co-efficient gas side = 250 W/m2-K

Q.2 (a) Define : 03

1) Critical thickness of insulation for cylinder
2) Thermal diffusivity
3) Thermal resistance
(b) Determine the overall heat transfer coefficient U0 based on the 04
outer surface of a 2.54 cm O.D 2.286 cm I.D. heat exchanger tube
(K= 102 W/mK).If the heat transfer co-efficient at the inside and
outside of the tube are
hi = 5500 W/m2K and ho = 3800 W/ m2K respectively and the
fouling factors are Rfi = Rfo = 0.0002 m2-K/W
(c) Superheated steam at 3300C is flowing at 20m/s velocity (h = 110 07
W/m2K) through a pipe 120 mm in diameter. The temperature of
steam is to be measured by putting a pocket in the pipe of 15mm
ID and 1mm thickness. Pocket material thermal conductivity is
50W/m2K.
1) Determine length of insertion so that error in the
thermometer is 0.5%.
2) If pipe wall is maintained at temperature of 400C ,find
temperature measured by thermometer.
OR
(c) A cylindrical hot ingot of 50mm diameter and 200mm long is 07
1
 taken out from the furnace at 8000C and dipped into the water till
its temperature becomes 5000C. After that it is exposed to air till its
temperature becomes 1000C. Find the total time required to reduce
its temperature from 8000C to 1000C.
Use following data:
k for ingot = 60 W/m-K.
specific heat for ingot = 200 J/m-K
hair =20 W/m2-K ,hwater = 200 W/m2-K
Density of ingot material = 800kg/m3
Temperature of water and air both = 300C
Q.3 (a) Differentiate fin efficiency and fin effectiveness. 03
(b) Prove that logarithmic mean area of hollow sphere is geometric 04
mean of its inner and outer surface area.
(c) A standard cast iron pipe ID = 50mm and OD =55mm is insulated 07
with 85% Magnesium insulation (k = 0.02W/m-K). Temperature at
the interface between the pipe and insulation is 300oC. The
allowable heat loss through the pipe is 600 W per meter length of
pipe and the safety, The temperature of the outside surface of
insulation must not exceed 1000C.
Determine :
1) Minimum thickness of insulation required
2) The temperature of inside surface of the pipe assuming its
thermal conductivity 20 W/m-K.
OR
Q.3 (a) Define time constant of thermocouple and state parameters which 03
affect time constant of thermocouple.
(b) “Generally fin is provided to increase the heat transfer rate but by 04
providing fin heat transfer may decrease” Justify the statement
analytically.
(c) A 240mm steam main 210 m long is covered with 50mm high 07
temperature insulation ( k = 0.092 W/m-K) and 40 mm of low
temperature insulation ( k = 0.062 W/m-K). The inner and outer
surface temperatures are measured 3900C and 400C respectively.
Calculate
1) Total heat loss per hour
2) The temperate at two insulation interface
3) The heat loss per unit outer surface area.
Q.4 (a) Define thermal boundary layer and hydrodynamic boundary layer. 03
Draw them for very low Prandtl number fluid.
(b) Air at 27OC and 1 atm. flow over a flat plate at a speed of 2m/s. 04
Calculate boundary layer thickness at a distance 40 cm from
leading edge of plate. At 27OC viscosity (air) = 1.85 *10-5 kg/m-s.
(c) Ait at 1 bar and a temperature 300C, dynamic viscosity = 0.06717 07
kg-ms flows at a speed of 1.2m/s over a flat plate. Determine the
boundary layer thickness at of 250mm and 500mm from the
leading edge of the plate. Also calculate the mass entrapment
between these two sections. Assume the parabolic velocity
distribution as:
3
u 3 y  1 y 
    
U 2  2 
OR
Q.4 (a) Write the value of critical Reynolds Number for flow over a flat 03
plate. Differentiate viscous sub layer and buffer layer.
(b) Velocity distribution in the boundary layer is given by 04
2
 u y
 , where u is velocity at distance y from the plate and at y =
U 
δ, u =U. Calculate energy thickness.
(c) Using Buckingham – π theorem show that Nusselt number for free 07
convection is a function of Grashof Number and Prandtl number
Q.5 (a) State Wien’s displacement law and write its significance. 03
(b) With respect to shape factor explain : 04
1) Superposition rule
2) Summation rule
(c) Consider two large parallel plates one at 7270C with the emissivity 07
0.8 and other 2270C with the emissivity 0.4. A plate of emissivity
0.05 on the both the sides is placed between the plates. Calculate
percentage reduction in the heat transfer rate between the two
plates as a result of the shield.
OR
Q.5 (a) Define gray body. Differentiate between surface resistance and 03
space resistance w.r.to radiation heat transfer between two grey
bodies.
(b) Calculate the shape factor of cylinder cavity w.r.to itself. Take 04
depth of cavity h and diameter of cylinder is d. it is enclosed with
flat surface.
(c) Define radiation shield. Prove that if radiation shield of the 07
emissivity same as the emissivity of two parallel plate is inserted
between two parallel plates net heat transfer rate due to radiation is
reduced to half as compared to without shield.

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