Enrolment No.

/Seat No_______________

GUJARAT TECHNOLOGICAL UNIVERSITY

BE- SEMESTER–V (NEW) EXAMINATION – WINTER 2024
Subject Code:3151909 Date:28-11-2024
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) Distinguish between the conduction, convection and radiation modes of heat 03
transfer with suitable example.
(b) Draw temperature variation for the condenser of the domestic refrigerator 04
and evaporator of the thermal power plant.
(c) Derive equation of logarithmic mean temperature difference for parallel flow 07
heat-exchanger.

Q.2 (a) “Generally fin is provided to increase the heat transfer rate but by providing 03
fin heat transfer may decrease” Justify the statement in context to heat
transfer.
(b) a) Explain the situation when the addition of fins to a surface is not useful. 04
b) Under what situations does the fin efficiency becomes 100%.
(c) Write the most general equation in Cartesian coordinates for heat transfer by 07
conduction.
Hence, deduce the above equation for the following cases with suitable
assumptions; (i) Laplace equation, (ii) Poisson equation, and (iii) Fourier
equation.
OR
(c) A steel fin (k=55W/mK) with a cross-section of an equilateral triangle, 5mm 07
on the side is 80mm long. It is attached to a plane wall maintained at 3500C.
The ambient air temperature is 400C and unit surface conductance is
100W/m2K. Calculate the heat dissipation rate by assuming the fin as a rod
with the tip of the fin is insulated.

Q.3 (a) What is critical radius of insulation? Explain its importance in electrical and 03
thermal system.
(b) Compare the value of effectiveness for the counter and parallel flow for 04
regenerator for NTU = 2.5.
(c) Explain with neat sketch, the various regimes in boiling and explain the 07
condition for the growth of bubbles. What is the effect of bubble size on
boiling?
OR
Q.3 (a) Write three properties of shape factor. 03
(b) Write the general differential equation in Cartesian coordinates for 3D 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 a uniform rate within the
material.

1
 (c) State the relationship between Nusselt number, Grashoff number and Prandtl 07
number in case of heat transfer by nature convection from a vertical plate.

Q.4 (a) Justify the use of polished surfaces in thermal insulation systems from the 03
perspective of radiation.
(b) Define Biot number and Fourier number, and point out their physical 04
significance.
(c) Define radiation shield. Prove that if radiation shields of the emissivity same 07
as the emissivity of two parallel plates is inserted between two parallel plates
net heat transfer rate due to radiation is reduced to half as compared to
without shield.
OR
Q.4 (a) Differentiate mean film temperature and bulk mean temperature. 03
(b) What is lumped system analysis? What are the assumption made in the 04
lumped system analysis and when it is applicable?
(c) What is heat exchanger? Classify the heat exchanger types with example. 07

Q.5 (a) What is the significance of thermal conductivity in material selection for heat 03
exchangers and insulators? Discuss its role in optimizing heat transfer.
(b) Why is it important to analyze heat conduction through composite walls in 04
industrial applications? Explain in brief, how to calculate the overall heat
transfer rate in such systems.
(c) An egg with mean diameter of 4 cm and initially at 20°C is placed in a 07
boiling water pan for 4 minutes and found to be boiled to the consumer’s
test. For how long should a similar egg for same consumer be boiled when
taken from a refrigerator at 5°C.
Take following properties for egg :
k =10W / m0C , ρ=1200kg /m3 , c =2kJ / kg0C , h =100W /m2 0C

OR
Q.5 (a) What is the relevance of one-dimensional heat conduction analysis in 03
practical applications? Explain with the example of heat transfer through a
plane wall or cylinder.
(b) Discuss the principle behind why black surfaces absorb more radiant energy 04
and how it enhances the efficiency of solar panels in converting sunlight to
electricity.
(c) A cylinder in vertical position is having dimension of 18 cm diameter and 07
length 1.5 m is maintained at a temperature of 1000C. It is kept in atmosphere
having temperature 200C.
Calculate the heat lost by cylinder surface to the atmosphere by free
convection.
Properties of air at mean film temperature 600C are as follows :
ρ=1.06kg/m3, υ=18.97*10-6m2/s, k=0.1042kJ/m.hr.0C, Cp=1.004kJ/kg0C.
Use the relation Nu=0.10(Gr.Pr)1/3
(The symbols have their usual meanings)

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

2
 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 (NEW) EXAMINATION – WINTER 2023
Subject Code:3151909 Date:07-12-2023
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.

Q.1 (a) Explain critical radius of insulation and its importance in electrical and 03
thermal systems heat transfer problems.
(b) With appropriate diagram explain the temperature variation in parallel flow 04
heat exchanger, counter flow heat exchanger, temperature distribution for
evaporator and condenser.
(c) A thermopane window consist of two 5 mm thick glass (k=0.78 W/m-K) 07
sheets separated by 10 mm stagnant air gap (k=0.025 W/m-K). The
convection heat transfer coefficient for inner and outer air are 10 W/m2-K
and 50 W/m2-K, respectively. (a) Determine the rate of heat loss per m2 of
the glass surface for a temperature difference of 60 Celsius between the
inside and outside air (b) compare the result with the heat loss, if the window
had only a single sheet of glass of thickness 5 mm instead of thermopane (c)
compare the result with the heat loss, if window has no stagnant air (i.e., a
sheet of glass, 10 mm thick.

Q.2 (a) What is lumped system analysis? Under what conditions it is applicable? 03
(b) What are the fundamental dimensions? Express thermal resistance, thermal 04
diffusivity and convective heat transfer coefficient in fundamental
dimensions.
(c) Find out the amount of heat transferred through an iron fin of length 50 mm, 07
width 100 mm and thickness 5 mm. Assume k = 58.33 W/m-K and h = 11.66
W/m2-K for the material of the fin and temperature at the base of the fin as
80 Celsius. Also determine the temperature at tip of the fin, if the
atmospheric temperature is 20 Celsius.
OR
(c) Derive general heat conduction equation in cylindrical coordinate system. 07
𝜕 2 𝑡 1 𝜕𝑡 1 𝜕 2 𝑡 𝜕 2 𝑡 𝑞𝑔 1 𝜕𝑡
+ + + + =
𝜕𝑟 2 𝑟 𝜕𝑟 𝑟 2 𝜕∅2 𝜕𝑧 2 𝑘 𝛼 𝜕𝜏

Q.3 (a) Define Absorptivity, reflectivity and transmissivity with proper example. 03
(b) What is the efficiency and effectiveness of fin? 04
(c) Dry saturated steam at 10 bar enters a counter flow heat exchanger at the rate 07
of 15 kg/s and leaves at 300 Degree Celsius. The entry of gas at 600 Degree
Celsius is with mass flow rate of 25 kg/s. If the condenser tubes are 30 mm
diameter and 3 m long, make calculations for the heating surface area and
the number of tubes required. Neglect the resistance offered by the metallic
tubes. Take the following properties for steam and gas: For steam: tsat=180
o
C (at 10 bar), Cps=2.7 kJ/kgK, hs=600 W/m2K for Gas: Cpg=1 kJ/kgK,
hg=250 W/m2K
OR
1
Q.3 (a) Define thermal diffusivity and explain its physical significance. 03
(b) What is meant by transient heat transfer? Mention some of the situations 04
where transient conduction occurs.
(c) Derive the equation of effectiveness for the parallel flow heat exchanger 07
1−𝑒𝑥𝑝[−𝑁𝑇𝑈(1+𝐶)]
∈= (1+𝐶)
Q.4 (a) State and prove Kirchoff’s law of radiation. 03
(b) Differentiate between mechanism of heat transfer by free and forced 04
convection. Mention some of the areas where these mechanisms are
predominant.
(c) Following data are obtained from a metallic cylinder of 15 mm diameter and 07
100 mm in length heated internally by an electric heater and subjected to
cross flow of air in a low-speed wind tunnel: velocity of free stream air = 15
m/s, temperature of free stream air = 25 oC, average temperature of cylinder
surface = 130 oC, power dissipation by heater is 63 W. Calculate the
experimental convective heat transfer coefficient for such a system. Compare
this value with that obtained from the correlation suitable for this
arrangement.
0.25
𝑁𝑢 = 0.26 𝑅𝑒 0.6 𝑃𝑟 0.36 (𝑃𝑟⁄𝑃𝑠)
Thermophysical properties of air at the mean bilk temperature at 25 Celsius
are: k =2.6325 x 10-2 W/m2K, υ = 15.53 x 10-6 m2/s, Pr = 0.702, Prs = 0.685
OR
Q.4 (a) What do you mean by geometrical or shape factor in case of radiation 03
exchange between two surfaces?
(b) The expression ℎ 𝑙 ⁄𝑘 gives the Biot number as well as the Nusselt number. 04
What is the difference between the two?
(c) Explain the essential features of Blasius method of solving laminar boundary 07
layer equations for flat plate. Derive expressions for boundary layer
thickness and local skin friction coefficient from this solution.
Q.5 (a) Explain the physical mechanism of boiling. 03
(b) Explain construction and working of heat-pipe. 04
(c) Two concentric spheres 25 cm and 35 cm in diameter with the space between 07
them evacuated are used to store liquid air (-150 oC) in a room at 20 oC. The
surfaces of the spheres are flushed with aluminum ( 𝜖 = 0.04). Calculate the
rate of evaporation of liquid air if the latent heat of vaporization of liquid air
is 218 kJ/kg. Assume that other modes of heat transfer are absent.
OR
Q.5 (a) List the applications of boiling heat transfer. 03
(b) How does film wise condensation differ from drop wise condensation? 04
Which type has a higher heat transfer film coefficient and point out the
reason thereof.
(c) Derive a general relation for the radiation shape factor in case of radiation 07
between two surfaces.

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

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 – WINTER 2022
Subject Code:3151909 Date:06-01-2023
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) Define the conduction, convection and radiation modes of heat transfer 03
with suitable example.
(b) Describe the thermal conductivity and explain its significance in heat 04
transfer.
(c) A steel fin (k = 54 W/mK) with a cross section of an equilateral triangle, 07
5 mm in side and 80 mm long. It is attached to a plane wall maintained
at 400°C. The ambient air temperature is 50°C and convective heat
transfer coefficient at surface is 90 W/m2K. Calculate the heat
dissipation rate from the rod.

Q.2 (a) Define fin efficiency and fin effectiveness. 03

(b) Give eight examples related to heat transfer from the routine life. 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
(c) Derive general heat conduction equation in cylindrical coordinates 07

Q.3 (a) Define Grashof number. Explain its significance in natural convection 03
heat transfer.
(b) Differentiate between: 04
1) Nusselt number and Reynolds number.
2) Free convection and forced convection.
(c) Using Buckingham – π theorem show that Nusselt number for free 07
convection is a function of Grashof Number and Prandtl number.
OR
Q.3 (a) Describe mean film temperature and bulk mean temperature. 03
(b) Explain the concept of thermal boundary layers. 04
(c) A horizontal fluorescent tube which is 3.8 cm in diameter and 120 cm 07
long stands in still air at 1 bar and 20 oC. If the surface temperature is 40
o
C and radiation is neglected, calculate heat transfer rate by convection.
Use Nu = 0.53 (Gr.Pr)0.25
From Air Table (Properties of Air) at Tmf
ν =15.06 X 10-6 m2/sec
Pr=0.701
K= 2.673 X 10-2 W/mK

1
Q.4 (a) Define absorptivity, emissivity and monochromatic emissive power. 03
(b) Describe shape factor. Discuss salient features of shape factor. 04
(c) Define total emissive power (Eb) and intensity of radiation (Ib). Show 07
that Eb = π×Ib
OR
Q.4 (a) It is desirable to wear white clothes instead of black during the summer 03
season. Give reason.
(b) Draw temperature variation for condenser and evaporator of thermal 04
power plant.
(c) Two large parallel plates with Є = 0.4 each are maintained at different 07
temperatures and are exchanging heat only by radiation. Two equally
large radiation shields with surface emissivity 0.04 are introduced in
parallel to the plates. Find the percentage reduction in net radiation heat
transfer.

Q.5 (a) Justify that a good absorber is also a good emitter for radiation heat 03
transfer.
(b) Give broad classification of heat exchangers. 04
(c) Derive the equation of LMTD for counter-flow heat exchangers. 07
OR
Q.5 (a) Define fouling factor in case of heat exchanger? List the causes of 03
fouling.
(b) Discuss the various regimes of boiling. 04
(c) Define condensation? Explain film-wise condensation and drop-wise 07
condensation.

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

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