GTU BE 7th Semester 170102 Theory of Heat Transfer Summer 2018 Question Paper

1
Seat No.: ________ Enrolment No.___________
GUJARAT TECHNOLOGICAL UNIVERSITY
BE – SEMESTER?VII ? EXAMINATION ? SUMMER 2018
Subject Code: 170102 Date: 01-05-2018
Subject Name: Theory of 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. Tables for properties of air and water are permitted.
Q.1 (a) A gray, diffuse opaque surface (Absorptivity a = 0.8) is at 100?C and receives an
irradiation 1000 W/m
2
. If the surface area is 0.1 m
2
, calculate
i. Radiosity of the surface
ii. Net radiative heat transfer rate from the surface
iii. Calculate above quantities if surface is black.
07
(b) A 1m long, 5 cm diameter, cylinder placed in an atmosphere of 40
o
C is provided
with 12 longitudinal straight fins (k = 75 W/m-K), 0.75 mm thick. The fin
protrudes 2.5 cm from the cylinder surface. The heat transfer coefficient is 23.3
W/m
2
-K. Calculate the rate of heat transfer if the surface temp. of cylinder is at
150
o
C.
07

Q.2 (a) A steam pipe pipe is covered with two layers of insulation, first layer being 3 cm
thick and second 5 cm. the pipe is made from steel (k = 58 W/m-K ) having ID
of 160 mm and OD of 170 mm. The inside and outside film coefficients are 30
and 5.8 W/m
2
-K , resp. Draw electrical analogy for system and calculate the heat
lost per meter of pipe, if the steam temperature is 300
o
C and air temperature is
50
o
C. The thermal conductivity of two materials are 0.17 and 0.093 W/m-K,
resp.
07
(b) Derive general heat conduction equation in Cylindrical coordinates. 07
OR
(b) What is the ?critical radius? of insulation on a small diameter wire and a steam
pipe. Explain its physical significance in both the cases & derive an expression
for the same.
07

Q.3 (a) Define velocity & thermal boundary layer thickness. 07
(b) State Buckingham?s ? Theorem. Explain the various parameters used in the
forced convection. Using Dimensional Analysis, obtain an expression for Nusselt
Number in terms of Re & Pr.
07
OR
Q.3 (a) Write Von-karman integral momentum equation, for the hydrodynamic laminar
boundary layer of fluid flowing over stationary plate. Using this equation, derive
the expression for hydrodynamic boundary layer thickness considering the cubic
velocity profile.
07
(b) Explain unsteady state heat transfer when Bi < 0.1 07 Q.4 (a) Explain term boiling also explain various regimes of boiling. 07
(b) Explain dropwise and filmwise condensation. 07
OR

1
Seat No.: ________ Enrolment No.___________
GUJARAT TECHNOLOGICAL UNIVERSITY
BE – SEMESTER?VII ? EXAMINATION ? SUMMER 2018
Subject Code: 170102 Date: 01-05-2018
Subject Name: Theory of 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. Tables for properties of air and water are permitted.
Q.1 (a) A gray, diffuse opaque surface (Absorptivity a = 0.8) is at 100?C and receives an
irradiation 1000 W/m
2
. If the surface area is 0.1 m
2
, calculate
i. Radiosity of the surface
ii. Net radiative heat transfer rate from the surface
iii. Calculate above quantities if surface is black.
07
(b) A 1m long, 5 cm diameter, cylinder placed in an atmosphere of 40
o
C is provided
with 12 longitudinal straight fins (k = 75 W/m-K), 0.75 mm thick. The fin
protrudes 2.5 cm from the cylinder surface. The heat transfer coefficient is 23.3
W/m
2
-K. Calculate the rate of heat transfer if the surface temp. of cylinder is at
150
o
C.
07

Q.2 (a) A steam pipe pipe is covered with two layers of insulation, first layer being 3 cm
thick and second 5 cm. the pipe is made from steel (k = 58 W/m-K ) having ID
of 160 mm and OD of 170 mm. The inside and outside film coefficients are 30
and 5.8 W/m
2
-K , resp. Draw electrical analogy for system and calculate the heat
lost per meter of pipe, if the steam temperature is 300
o
C and air temperature is
50
o
C. The thermal conductivity of two materials are 0.17 and 0.093 W/m-K,
resp.
07
(b) Derive general heat conduction equation in Cylindrical coordinates. 07
OR
(b) What is the ?critical radius? of insulation on a small diameter wire and a steam
pipe. Explain its physical significance in both the cases & derive an expression
for the same.
07

Q.3 (a) Define velocity & thermal boundary layer thickness. 07
(b) State Buckingham?s ? Theorem. Explain the various parameters used in the
forced convection. Using Dimensional Analysis, obtain an expression for Nusselt
Number in terms of Re & Pr.
07
OR
Q.3 (a) Write Von-karman integral momentum equation, for the hydrodynamic laminar
boundary layer of fluid flowing over stationary plate. Using this equation, derive
the expression for hydrodynamic boundary layer thickness considering the cubic
velocity profile.
07
(b) Explain unsteady state heat transfer when Bi < 0.1 07 Q.4 (a) Explain term boiling also explain various regimes of boiling. 07
(b) Explain dropwise and filmwise condensation. 07
OR

2
Q.4 (a) Define Re, Nu, Pr. Explain their importance in convection heat transfer. 07
(b) What are Fourier and Biot Number? What is the physical significance of these
numbers? Also Distinguish between Biot Number & Nusselt Number.
07

Q.5 (a) Derive equations of temperature distribution and heat dissipation for Fin
insulated at tip.
07
(b) How are the heat exchangers classified ? What is LMTD Correction Factor?
What are the fouling factors?
07
OR
Q.5 (a) Distinguish between: (i) A black body & grey body (ii) Specular & diffuse surfaces (iii)Absorptivity & Emissivity of a surface (iv) Total Emissivity & Equilibrium emissivity
07
(b) Define and explain Radiation shield and Radiation shape factor 07
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