Categories: 7th Semester

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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