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2021 2020 2020 (V4)
2021 102502

B.Tech Examination, 2021

Time 3 hours
Full Marks 70
Instructions:
  • The marks are indicated in the right-hand margin.
  • There are NINE questions in this paper.
  • Attempt FIVE questions in all.
  • Question No. 1 is compulsory.

Questions

Q1

Choose the correct answer of the following (any seven):

a)

Heat transfer takes place according to ______ law of thermodynamics.

a)

(i) zeroth

b)

(ii) first

c)

(iii) second

d)

(iv) third

b)

In M-L-T-θM\text{-}L\text{-}T\text{-}\theta system ($T$ being time and θ\theta temperature), what is the dimension of thermal conductivity?

a)

(i) ML−1T−1θ−3ML^{-1}T^{-1}\theta^{-3}

b)

(ii) MLθ−1T−3ML\theta^{-1}T^{-3}

c)

(iii) MLT−1θ−1MLT^{-1}\theta^{-1}

d)

(iv) MLT−2θ−1MLT^{-2}\theta^{-1}

c)

With an increase in the thickness of insulation around a circular pipe, heat loss to surroundings is due to

a)

(i) convection increases while that due to conduction decreases

b)

(ii) convection decreases while that due to conduction increases

c)

(iii) convection and conduction decrease

d)

(iv) convection and conduction increase

d)

The thermal conductivity of thermal insulation applied to a hollow spherical vessel containing very hot material is 0.5 W/m-K0.5\text{ W/m-K}. The convective heat transfer at the outer surface of insulation is 10 W/m2-K10\text{ W/m}^2\text{-K}. What is the critical radius of the sphere?

a)

(i) 0.1 m0.1\text{ m}

b)

(ii) 0.2 m0.2\text{ m}

c)

(iii) 1.0 m1.0\text{ m}

d)

(iv) 2.0 m2.0\text{ m}

e)

The time constant of a thermocouple is the time taken to attain

a)

(i) the final temperature to be measured

b)

(ii) 50%50\% of the value of initial temperature difference

c)

(iii) 63.2%63.2\% of the value of initial temperature difference

d)

(iv) to reach 100 ∘C100\text{ }^\circ\text{C} from 0 ∘C0\text{ }^\circ\text{C}

f)

A radiation shield should

a)

(i) have high transmissivity

b)

(ii) absorb all the radiations

c)

(iii) have high reflective power

d)

(iv) partly absorb and partly transmit the incident radiation

g)

In a counter flow heat exchange, cold fluid enters at 40 ∘C40\text{ }^\circ\text{C} and leaves at 60 ∘C60\text{ }^\circ\text{C}, whereas the hot fluid enters at 160 ∘C160\text{ }^\circ\text{C} and leaves at 140 ∘C140\text{ }^\circ\text{C}. The mean temperature difference for this case is

a)

(i) 20 ∘C20\text{ }^\circ\text{C}

b)

(ii) 80 ∘C80\text{ }^\circ\text{C}

c)

(iii) 100 ∘C100\text{ }^\circ\text{C}

d)

(iv) indeterminate

h)

Which of the following numbers represents the ratio of kinematic viscosity to thermal diffusivity?

a)

(i) Grashof number

b)

(ii) Prandtl number

c)

(iii) Mach number

d)

(iv) Nusselt number

i)

The reciprocity theorem states that

a)

(i) F12=F21F_{12} = F_{21}

b)

(ii) A1F12=A2F21A_1 F_{12} = A_2 F_{21}

c)

(iii) A1F12=A2F12A_1 F_{12} = A_2 F_{12}

d)

(iv) A2F12=A1F21A_2 F_{12} = A_1 F_{21}

j)

ϵ-NTU\epsilon\text{-NTU} method is particularly useful in thermal design of heat exchangers when

a)

(i) the outlet temperatures of the fluid streams are not known as a priori

b)

(ii) the outlet temperature of the fluid streams are known as a priori

c)

(iii) the outlet temperature of the hot fluid stream is known but that of cold fluid stream is not known as a priori

d)

(iv) inlet temperature of the fluid streams are not known as a priori

Q2

Answer the following:

a)

How does the slope of the temperature profile in a wall depend on its thermal conductivity?

b)

What is thermal contact resistance? A wall consists of two layers of insulation pressed against each other. Do you need to be concerned about the contact resistance at the interface in a heat transfer analysis or can we just ignore it? Justify your answer.

c)

Consider a large plane wall of thickness L=0.2 mL = 0.2\text{ m}, thermal conductivity K=1.2 W/m KK = 1.2\text{ W/m K}, and surface area A=15 m2A = 15\text{ m}^2. The two sides of the wall are maintained at constant temperatures of T1=120 ∘CT_1 = 120\text{ }^\circ\text{C} and T2=50 ∘CT_2 = 50\text{ }^\circ\text{C}, respectively. Determine, (i) the variation of temperature within the wall and the value of temperature x=0.1 mx = 0.1\text{ m} and (ii) the rate of heat conduction through the wall under steady conditions.

Q3

Answer the following:

a)

What is the physical significance of critical radius of insulation?

b)

Show that the critical radius of insulation for a cylindrical body can be represented as rcr=k/h (m)r_{cr} = k/h\text{ (m)}.

c)

Consider a 0.8 m0.8\text{ m} high and 1.5 m1.5\text{ m} wide glass window with a thickness of 8 mm8\text{ mm} and thermal conductivity of K=0.78 W/m-KK = 0.78\text{ W/m-K}. Determine the steady rate of heat transfer through this glass window and the temperature of its inner surface for a day during which the room is maintained at 20 ∘C20\text{ }^\circ\text{C} while the temperature of the outdoors is −10 ∘C-10\text{ }^\circ\text{C}. Take the heat transfer coefficients on the inner and outer surfaces of the window to be h1=10 W/m2-Kh_1 = 10\text{ W/m}^2\text{-K} and h2=40 W/m2-Kh_2 = 40\text{ W/m}^2\text{-K}, which includes the effects of radiation.

Q4

Answer the following:

a)

How do fins affect the heat transfer rate?

b)

What is the difference between the fin efficiency and the fin effectiveness?

c)

Derive the expression of 1-D1\text{-D} steady fin equation with no heat generation. Also show from the same that the temperature distribution for an infinitely long fin along the axial direction can be represented as $$\frac{T(x) - T_\infty}{T_b - T_\infty} = e^{-x \sqrt{hp/k A_c}}$$

Q5

Answer the following:

a)

What is the physical significance of Biot number (Bi)(\text{Bi})? Represent diagrammatically the effect of Bi\text{Bi} on steady-state temperature distribution in a plane wall with surface convection.

b)

What is lumped system analysis? When is it applicable?

c)

The temperature of a gas steam is measured with a thermocouple. The junction may be approximated as a sphere of diameter D=1 mmD = 1\text{ mm}, k=25 W/(m ∘C)k = 25\text{ W/(m }^\circ\text{C)}, ρ=8400 kg/m3\rho = 8400\text{ kg/m}^3 and cp=0.4 kJ/(kg ∘C)c_p = 0.4\text{ kJ/(kg }^\circ\text{C)}. The heat transfer coefficient between the junction and the gas steam is h=560 W/(m2 ∘C)h = 560\text{ W/(m}^2\text{ }^\circ\text{C)}. How long will it take for the thermocouple to record 9999 percent of the applied temperature difference?

Q6

Answer the following:

a)

What is the physical significance of the Nusselt number?

b)

'In a liquid to gas heat exchanger the fins are commonly used on the liquid side to enhance the heat transfer.' Write True of False. Justify with explanation.

c)

What is the difference between evaporation and boiling? Draw the boiling curve and identify the different boiling regimes.

Q7

Answer the following:

a)

Physically, what does the Grashof number represent? What is the value for critical Grashof number for flow over a vertical plate?

b)

Atmospheric air at T∞=250 KT_\infty = 250\text{ K} and a free-stream velocity u∞=30 m/su_\infty = 30\text{ m/s} flows across a circular cylinder of diameter D=2.5 cmD = 2.5\text{ cm}. The surface of the cylinder is maintained at a uniform temperature Tw=350 KT_w = 350\text{ K}. (i) Calculate the average heat transfer coefficient hmh_m. (ii) Determine the heat transfer rate QQ per 1 m1\text{ m} length of the cylinder. (iii) Find the average drag coefficient CDC_D. (iv) Calculate the drag force FF acting per 1 m1\text{ m} length of the cylinder.

Q8

Answer the following:

a)

Classify heat exchanger according to flow type and construction.

b)

A counter flow, concentric tube heat exchanger is used to cool the lubricating oil for a large industrial gas turbine engine. The flow rate of cooling water through the inner tube (Di=25 mm)(D_i = 25\text{ mm}) is 0.2 kg/s0.2\text{ kg/s}, while the flow rate of oil through the outer annulus (Do=45 mm)(D_o = 45\text{ mm}) is 0.1 kg/s0.1\text{ kg/s}. The oil and water enter at temperatures of 100 ∘C100\text{ }^\circ\text{C} and 30 ∘C30\text{ }^\circ\text{C}, respectively. How long must the tube be made if the outlet temperature of the oil is to be 60 ∘C60\text{ }^\circ\text{C}?

Q9

Answer the following:

a)

Define a gray body. What is the criterion to call a body gray?

b)

What is the view factor? Write the reciprocity relation for view factor.

c)

Consider the 5 m×5 m×5 m5\text{ m} \times 5\text{ m} \times 5\text{ m} cubical furnace, whose surfaces closely approximate black surfaces. The base, top and side surfaces of the furnace are maintained at uniform temperatures of 800 K800\text{ K}, 1500 K1500\text{ K} and 500 K500\text{ K} respectively. Determine, (i) the net rate of radiation heat transfer between the base and the top surface, (ii) the net rate of radiation heat transfer between the base and the side surfaces and (iii) the net radiation heat transfer from the base surface.

2020 102502

B.Tech 5th Semester Exam., 2020

Time 03 Hours
Full Marks 70
Instructions:
  • The marks are indicated in the right-hand margin.
  • There are NINE questions in this paper.
  • Attempt FIVE questions in all.
  • Question No. 1 is compulsory.
  • Students should be allowed to use the heat transfer charts.

Q.1 Choose the correct answer of the following (any seven):

Q1.1

Which of the following is the case of heat transfer by radiation?

a)

Blast furnace

b)

Heating of building

c)

Cooling of parts in furnace

d)

Heat received by a person from fireplace

e)

All of the above

Q1.2

On a heat transfer surface, fins are provided to

a)

increase temperature gradient so as to enhance heat transfer

b)

increase turbulence in flow for enhancing heat transfer

c)

increase surface area to promote the rate of heat transfer

d)

decrease the pressure drop of the fluid

Q1.3

Consider two walls, A and B, with the same surface areas and the same temp. drops across their thickness. The ratio of K is $ K_A/K_B = 4 $ and the ratio of $ L_A/L_B = 2 $. The ratio of heat transfer rates through the walls $ Q_A/Q_B $ is

a)

0.5

b)

1

c)

2

d)

4

Q1.4

The thermal resistance of a hollow cylinder is represented as

a)

2πkln⁡(r2/r1)\frac{2\pi k}{\ln(r_2/r_1)}

b)

r2−r14πr2r1k\frac{r_2 - r_1}{4\pi r_2 r_1 k}

c)

ln⁡(r2/r1)2πkL\frac{\ln(r_2/r_1)}{2\pi k L}

d)

ln⁡(r2/r1)2πr2r1kL\frac{\ln(r_2/r_1)}{2\pi r_2 r_1 k L}

Q1.5

The Biot number can be thought of as the ratio of

a)

the conduction to convection thermal resistance

b)

the convection to conduction thermal resistance

c)

the thermal energy storage capacity to conduction resistance

d)

the thermal energy storage capacity to convection resistance

Q1.6

The free convection heat transfer is significantly affected by

a)

Reynolds number

b)

Grashof number

c)

Prandtl number

d)

Stanton number

Q1.7

In a counterflow heat exchange, cold fluid enters at $ 30^\circ C $ and leaves at $ 50^\circ C $, whereas the hot fluid enters at $ 150^\circ C $ and leaves at $ 130^\circ C $. The mean temperature difference for this case is

a)

20∘C20^\circ C

b)

80∘C80^\circ C

c)

100∘C100^\circ C

d)

indeterminate

Q1.8

What is the basic equation of radiation from which all other equations of radiation can be derived?

a)

Stefan-Boltzmann equation

b)

Planck's equation

c)

Wien's equation

d)

Rayleigh-Jeans formula

Q1.9

The hydrodynamic and thermal boundary layers are identical at Prandtl number equal to

a)

0.5

b)

1

c)

10

d)

50

Q1.10

The normal automobile radiator is a heat exchanger of the type

a)

direct contact

b)

parallel flow

c)

counterflow

d)

cross-flow

Q.2 Solve all questions :

Q2.1

What are the different modes of heat transfer? How does heat conduction differ from heat convection?

Q2.2

State the Fourier's law of heat conduction.

Q2.3

A plane wall is a composite of two materials, A and B. The wall material A has uniform heat generation $ q_g = 1.5 \times 10^6 \text{ W/m}^3 $, $ k_A = 75 \text{ W/mK} $ and thickness $ L_A = 50 \text{ mm} $. The wall material B has no heat generation with $ k_B = 150 \text{ W/mK} $ and thickness $ L_B = 20 \text{ mm} $. The inner surface of material A is well-insulated, while the outer surface of material B is cooled by a water stream with $ T_\infty = 30^\circ C $ and $ h = 1000 \text{ W/m}^2\text{K} $. Determine the temperature of the insulated surface and the temperature of the cooled surface.

Q.3 Solve both questions :

Q3.1

Adding insulation on a cylindrical surface will always decrease heat transfer rate. True or False. Explain.

Q3.2

In a cylindrical fuel element for a gas-cooled nuclear reactor, the generation rate of thermal energy within the fuel element due to fission can be approximated by the relation $ q(r) = q_0 \left[ 1 - \left(\frac{r}{a}\right)^2 \right] \text{W/m}^3 $ where a is the radius of the fuel element and $ q_0 $ is constant. The boundary surface $ r = a $ is maintained at a uniform temperature $ T_0 $.
(i) Assuming one-dimensional, steady-state heat flow, develop a relation for the temperature drop from the centerline to the surface of the fuel element.
(ii) For a radius of $ a = 30 \text{ mm} $, the thermal conductivity $ k = 10 \text{ W/(m}^\circ\text{C)} $ and $ q_0 = 2 \times 10^7 \text{ W/m}^3 $, calculate the temperature drop from the centerline to the surface.

Q.4 Solve both questions :

Q4.1

What is boundary condition? Mention the different types of boundary conditions.

Q4.2

A thin fin of length L has its two ends fixed to two parallel walls at temperatures $ T_1 $ and $ T_2 $, the temperature of the environment being $ T_\infty $. Show that the expression for one-dimensional temperature distribution along the length of the fin can be represented as: $ \theta = \theta_1 \frac{\sinh m(L-x)}{\sinh mL} + \theta_2 \frac{\sinh mx}{\sinh mL} $

Question Diagram

Q.5 Solve all questions :

Q5.1

What are the inherent dimensionless parameters for forced convection?

Q5.2

In the fully developed region of flow in a circular tube, will the velocity profile change in the flow direction? How about the temperature profile?

Q5.3

Consider the velocity and temperature profiles for a fluid flow in a tube with diameter of 50 mm can be expressed as $ u(r) = 0.05 \left[ 1 - \left(\frac{r}{R}\right)^2 \right] $ and $ T(r) = 400 + 80 \left(\frac{r}{R}\right)^2 - 30 \left(\frac{r}{R}\right)^3 $ with units in m/s and K, respectively. Determine the average velocity and the mean temperature from the given velocity and temperature profiles.

Q.6 Solve both questions :

Q6.1

What is the physical significance of Biot number (Bi)? Represent diagrammatically the effect of Bi on steady-state temperature distribution in a plane wall with surface convection.

Q6.2

A long cylinder of radius 150 mm and at an initial uniform temperature of 530 °C is suddenly exposed to an environment at 30 °C. The convection heat transfer coefficient between the surface of the cylinder and the environment is $ 380 \text{ W/m}^2\text{K} $. The thermal conductivity and thermal diffusivity of the cylinder material are $ 200 \text{ W/mK} $ and $ 8.5 \times 10^{-5} \text{ m}^2\text{/s} $ respectively. Determine (i) the temperature at a radius of 120 mm and (ii) the heat transferred per meter length of the cylinder 265 seconds after the cylinder is exposed to the environment (use Heisler charts).

Q.7 Solve all questions :

Q7.1

What do you mean by fully developed boundary flow? Explain with suitable diagram.

Q7.2

Derive the 2-D differential form of conservation of energy equation for the laminar, incompressible flow over a flat plate with constant fluid properties.

Q7.3

Physically, what does the Grashof number represent?

Q.8 Solve all questions :

Q8.1

What is fouling factor? Explain its effect in heat exchanger design.

Q8.2

Define heat exchanger effectiveness.

Q8.3

Derive for parallel flow heat exchanger $ \epsilon = \frac{1 - \exp[-NTU(1+C)]}{1+C} $ where, $ C = \frac{C_{min}}{C_{max}} $, NTU = Number of transfer units.

Q.9 Solve all questions :

Q9.1

State the Fick's law of diffusion.

Q9.2

Determine the view factor of the cylindrical surface with respect to the base, when $ L = 2r $. Consider $ F_{12} = 0.16 $.

Question Diagram
Q9.3

Two infinite parallel plates are maintained at temperatures $ T_1 $ and $ T_2 $ with $ T_1 > T_2 $. To reduce the rate of radiation heat transfer between the plates, they are separated by a thin radiation shield which has different emissivities on opposite surfaces. One surface has an emissivity of $ \epsilon_s $ and the other surface of $ 2\epsilon_s $ where $ \epsilon_s < 0.5 $. Determine the orientation of the shield, i.e., whether the surface of $ \epsilon_s $ or the surface of emissivity $ 2\epsilon_s $ would be facing towards the plate at temperature $ T_1 $, for the larger value of the shield temperature $ T_s $.

2020 V4 102502

B.Tech 5th Semester Exam., 2020

Time 03 Hours
Full Marks 70
Instructions:
  • The marks are indicated in the right-hand margin.
  • There are NINE questions in this paper.
  • Attempt FIVE questions in all.
  • Question No. 1 is compulsory.
  • Students should be allowed to use the heat transfer charts.

Q.1 Choose the correct answer of the following (any seven):

Q1.1

Which of the following is the case of heat transfer by radiation?

a)

Blast furnace

b)

Heating of building

c)

Cooling of parts in furnace

d)

Heat received by a person from fireplace

e)

All of the above

Q1.2

On a heat transfer surface, fins are provided to

a)

increase temperature gradient so as to enhance heat transfer

b)

increase turbulence in flow for enhancing heat transfer

c)

increase surface area to promote the rate of heat transfer

d)

decrease the pressure drop of the fluid

Q1.3

Consider two walls, A and B, with the same surface areas and the same temp. drops across their thickness. The ratio of K is $ K_A/K_B = 4 $ and the ratio of $ L_A/L_B = 2 $. The ratio of heat transfer rates through the walls $ Q_A/Q_B $ is

a)

0.5

b)

1

c)

2

d)

4

Q1.4

The thermal resistance of a hollow cylinder is represented as

a)

2πkln⁡(r2/r1)\frac{2\pi k}{\ln(r_2/r_1)}

b)

r2−r14πr2r1k\frac{r_2 - r_1}{4\pi r_2 r_1 k}

c)

ln⁡(r2/r1)2πkL\frac{\ln(r_2/r_1)}{2\pi k L}

d)

ln⁡(r2/r1)2πr2r1kL\frac{\ln(r_2/r_1)}{2\pi r_2 r_1 k L}

Q1.5

The Biot number can be thought of as the ratio of

a)

the conduction to convection thermal resistance

b)

the convection to conduction thermal resistance

c)

the thermal energy storage capacity to conduction resistance

d)

the thermal energy storage capacity to convection resistance

Q1.6

The free convection heat transfer is significantly affected by

a)

Reynolds number

b)

Grashof number

c)

Prandtl number

d)

Stanton number

Q1.7

In a counterflow heat exchange, cold fluid enters at $ 30^\circ C $ and leaves at $ 50^\circ C $, whereas the hot fluid enters at $ 150^\circ C $ and leaves at $ 130^\circ C $. The mean temperature difference for this case is

a)

20∘C20^\circ C

b)

80∘C80^\circ C

c)

100∘C100^\circ C

d)

indeterminate

Q1.8

What is the basic equation of radiation from which all other equations of radiation can be derived?

a)

Stefan-Boltzmann equation

b)

Planck's equation

c)

Wien's equation

d)

Rayleigh-Jeans formula

Q1.9

The hydrodynamic and thermal boundary layers are identical at Prandtl number equal to

a)

0.5

b)

1

c)

10

d)

50

Q1.10

The normal automobile radiator is a heat exchanger of the type

a)

direct contact

b)

parallel flow

c)

counterflow

d)

cross-flow

Q.2 Solve all questions :

Q2.1

What are the different modes of heat transfer? How does heat conduction differ from heat convection?

Q2.2

State the Fourier's law of heat conduction.

Q2.3

A plane wall is a composite of two materials, A and B. The wall material A has uniform heat generation $ q_g = 1.5 \times 10^6 \text{ W/m}^3 $, $ k_A = 75 \text{ W/mK} $ and thickness $ L_A = 50 \text{ mm} $. The wall material B has no heat generation with $ k_B = 150 \text{ W/mK} $ and thickness $ L_B = 20 \text{ mm} $. The inner surface of material A is well-insulated, while the outer surface of material B is cooled by a water stream with $ T_\infty = 30^\circ C $ and $ h = 1000 \text{ W/m}^2\text{K} $. Determine the temperature of the insulated surface and the temperature of the cooled surface.

Q.3 Solve both questions :

Q3.1

Adding insulation on a cylindrical surface will always decrease heat transfer rate. True or False. Explain.

Q3.2

In a cylindrical fuel element for a gas-cooled nuclear reactor, the generation rate of thermal energy within the fuel element due to fission can be approximated by the relation $ q(r) = q_0 \left[ 1 - \left(\frac{r}{a}\right)^2 \right] \text{W/m}^3 $ where a is the radius of the fuel element and $ q_0 $ is constant. The boundary surface $ r = a $ is maintained at a uniform temperature $ T_0 $.
(i) Assuming one-dimensional, steady-state heat flow, develop a relation for the temperature drop from the centerline to the surface of the fuel element.
(ii) For a radius of $ a = 30 \text{ mm} $, the thermal conductivity $ k = 10 \text{ W/(m}^\circ\text{C)} $ and $ q_0 = 2 \times 10^7 \text{ W/m}^3 $, calculate the temperature drop from the centerline to the surface.

Q.4 Solve both questions :

Q4.1

What is boundary condition? Mention the different types of boundary conditions.

Q4.2

A thin fin of length L has its two ends fixed to two parallel walls at temperatures $ T_1 $ and $ T_2 $, the temperature of the environment being $ T_\infty $. Show that the expression for one-dimensional temperature distribution along the length of the fin can be represented as: $ \theta = \theta_1 \frac{\sinh m(L-x)}{\sinh mL} + \theta_2 \frac{\sinh mx}{\sinh mL} $

Question Diagram

Q.5 Solve all questions :

Q5.1

What are the inherent dimensionless parameters for forced convection?

Q5.2

In the fully developed region of flow in a circular tube, will the velocity profile change in the flow direction? How about the temperature profile?

Q5.3

Consider the velocity and temperature profiles for a fluid flow in a tube with diameter of 50 mm can be expressed as $ u(r) = 0.05 \left[ 1 - \left(\frac{r}{R}\right)^2 \right] $ and $ T(r) = 400 + 80 \left(\frac{r}{R}\right)^2 - 30 \left(\frac{r}{R}\right)^3 $ with units in m/s and K, respectively. Determine the average velocity and the mean temperature from the given velocity and temperature profiles.

Q.6 Solve both questions :

Q6.1

What is the physical significance of Biot number (Bi)? Represent diagrammatically the effect of Bi on steady-state temperature distribution in a plane wall with surface convection.

Q6.2

A long cylinder of radius 150 mm and at an initial uniform temperature of 530 °C is suddenly exposed to an environment at 30 °C. The convection heat transfer coefficient between the surface of the cylinder and the environment is $ 380 \text{ W/m}^2\text{K} $. The thermal conductivity and thermal diffusivity of the cylinder material are $ 200 \text{ W/mK} $ and $ 8.5 \times 10^{-5} \text{ m}^2\text{/s} $ respectively. Determine (i) the temperature at a radius of 120 mm and (ii) the heat transferred per meter length of the cylinder 265 seconds after the cylinder is exposed to the environment (use Heisler charts).

Q.7 Solve all questions :

Q7.1

What do you mean by fully developed boundary flow? Explain with suitable diagram.

Q7.2

Derive the 2-D differential form of conservation of energy equation for the laminar, incompressible flow over a flat plate with constant fluid properties.

Q7.3

Physically, what does the Grashof number represent?

Q.8 Solve all questions :

Q8.1

What is fouling factor? Explain its effect in heat exchanger design.

Q8.2

Define heat exchanger effectiveness.

Q8.3

Derive for parallel flow heat exchanger $ \epsilon = \frac{1 - \exp[-NTU(1+C)]}{1+C} $ where, $ C = \frac{C_{min}}{C_{max}} $, NTU = Number of transfer units.

Q.9 Solve all questions :

Q9.1

State the Fick's law of diffusion.

Q9.2

Determine the view factor of the cylindrical surface with respect to the base, when $ L = 2r $. Consider $ F_{12} = 0.16 $.

Question Diagram
Q9.3

Two infinite parallel plates are maintained at temperatures $ T_1 $ and $ T_2 $ with $ T_1 > T_2 $. To reduce the rate of radiation heat transfer between the plates, they are separated by a thin radiation shield which has different emissivities on opposite surfaces. One surface has an emissivity of $ \epsilon_s $ and the other surface of $ 2\epsilon_s $ where $ \epsilon_s < 0.5 $. Determine the orientation of the shield, i.e., whether the surface of $ \epsilon_s $ or the surface of emissivity $ 2\epsilon_s $ would be facing towards the plate at temperature $ T_1 $, for the larger value of the shield temperature $ T_s $.

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