Heat Transfer
Jump to paper
2021102502
B.Tech Examination, 2021
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
Ask AI
Q1
Choose the correct answer of the following (any seven):
a)Heat transfer takes place according to ______ law of thermodynamics.
b)In system ($T$ being time and temperature), what is the dimension of thermal conductivity?
c)With an increase in the thickness of insulation around a circular pipe, heat loss to surroundings is due to
d)The thermal conductivity of thermal insulation applied to a hollow spherical vessel containing very hot material is . The convective heat transfer at the outer surface of insulation is . What is the critical radius of the sphere?
e)The time constant of a thermocouple is the time taken to attain
f)A radiation shield should
g)In a counter flow heat exchange, cold fluid enters at and leaves at , whereas the hot fluid enters at and leaves at . The mean temperature difference for this case is
h)Which of the following numbers represents the ratio of kinematic viscosity to thermal diffusivity?
i)The reciprocity theorem states that
j)method is particularly useful in thermal design of heat exchangers when
Ask AI
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 , thermal conductivity , and surface area . The two sides of the wall are maintained at constant temperatures of and , respectively. Determine, (i) the variation of temperature within the wall and the value of temperature and (ii) the rate of heat conduction through the wall under steady conditions.
Ask AI
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 .
c)Consider a high and wide glass window with a thickness of and thermal conductivity of . 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 while the temperature of the outdoors is . Take the heat transfer coefficients on the inner and outer surfaces of the window to be and , which includes the effects of radiation.
Ask AI
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 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 $$\frac{T(x) - T_\infty}{T_b - T_\infty} = e^{-x \sqrt{hp/k A_c}}$$
Ask AI
Q5
Answer the following:
a)What is the physical significance of Biot number ? Represent diagrammatically the effect of 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 , , and . The heat transfer coefficient between the junction and the gas steam is . How long will it take for the thermocouple to record percent of the applied temperature difference?
Ask AI
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.
Ask AI
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 and a free-stream velocity flows across a circular cylinder of diameter . The surface of the cylinder is maintained at a uniform temperature . (i) Calculate the average heat transfer coefficient . (ii) Determine the heat transfer rate per length of the cylinder. (iii) Find the average drag coefficient . (iv) Calculate the drag force acting per length of the cylinder.
Ask AI
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 is , while the flow rate of oil through the outer annulus is . The oil and water enter at temperatures of and , respectively. How long must the tube be made if the outlet temperature of the oil is to be ?
Ask AI
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 cubical furnace, whose surfaces closely approximate black surfaces. The base, top and side surfaces of the furnace are maintained at uniform temperatures of , and 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.
Ask AI
2020102502
B.Tech 5th Semester Exam., 2020
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):
Ask AI
Q1.1
Which of the following is the case of heat transfer by radiation?
Ask AI
Q1.2
On a heat transfer surface, fins are provided to
Ask AI
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
Ask AI
Q1.4
The thermal resistance of a hollow cylinder is represented as
Ask AI
Q1.5
The Biot number can be thought of as the ratio of
Ask AI
Q1.6
The free convection heat transfer is significantly affected by
Ask AI
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
Ask AI
Q1.8
What is the basic equation of radiation from which all other equations of radiation can be derived?
Ask AI
Q1.9
The hydrodynamic and thermal boundary layers are identical at Prandtl number equal to
Ask AI
Q1.10
The normal automobile radiator is a heat exchanger of the type
Ask AI
Q.2 Solve all questions :
Ask AI
Q2.1
What are the different modes of heat transfer? How does heat conduction differ from heat convection?
Ask AI
Q2.2
State the Fourier's law of heat conduction.
Ask AI
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.
Ask AI
Q.3 Solve both questions :
Ask AI
Q3.1
Adding insulation on a cylindrical surface will always decrease heat transfer rate. True or False. Explain.
Ask AI
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.Ask AI
Q.4 Solve both questions :
Ask AI
Q4.1
What is boundary condition? Mention the different types of boundary conditions.
Ask AI
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} $

Ask AI
Q.5 Solve all questions :
Ask AI
Q5.1
What are the inherent dimensionless parameters for forced convection?
Ask AI
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?
Ask AI
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.
Ask AI
Q.6 Solve both questions :
Ask AI
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.
Ask AI
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).
Ask AI
Q.7 Solve all questions :
Ask AI
Q7.1
What do you mean by fully developed boundary flow? Explain with suitable diagram.
Ask AI
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.
Ask AI
Q7.3
Physically, what does the Grashof number represent?
Ask AI
Q.8 Solve all questions :
Ask AI
Q8.1
What is fouling factor? Explain its effect in heat exchanger design.
Ask AI
Q8.2
Define heat exchanger effectiveness.
Ask AI
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.
Ask AI
Q.9 Solve all questions :
Ask AI
Q9.1
State the Fick's law of diffusion.
Ask AI
Q9.2
Determine the view factor of the cylindrical surface with respect to the base, when $ L = 2r $. Consider $ F_{12} = 0.16 $.

Ask AI
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 $.
Ask AI
2020V4102502
B.Tech 5th Semester Exam., 2020
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):
Ask AI
Q1.1
Which of the following is the case of heat transfer by radiation?
Ask AI
Q1.2
On a heat transfer surface, fins are provided to
Ask AI
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
Ask AI
Q1.4
The thermal resistance of a hollow cylinder is represented as
Ask AI
Q1.5
The Biot number can be thought of as the ratio of
Ask AI
Q1.6
The free convection heat transfer is significantly affected by
Ask AI
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
Ask AI
Q1.8
What is the basic equation of radiation from which all other equations of radiation can be derived?
Ask AI
Q1.9
The hydrodynamic and thermal boundary layers are identical at Prandtl number equal to
Ask AI
Q1.10
The normal automobile radiator is a heat exchanger of the type
Ask AI
Q.2 Solve all questions :
Ask AI
Q2.1
What are the different modes of heat transfer? How does heat conduction differ from heat convection?
Ask AI
Q2.2
State the Fourier's law of heat conduction.
Ask AI
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.
Ask AI
Q.3 Solve both questions :
Ask AI
Q3.1
Adding insulation on a cylindrical surface will always decrease heat transfer rate. True or False. Explain.
Ask AI
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.Ask AI
Q.4 Solve both questions :
Ask AI
Q4.1
What is boundary condition? Mention the different types of boundary conditions.
Ask AI
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} $

Ask AI
Q.5 Solve all questions :
Ask AI
Q5.1
What are the inherent dimensionless parameters for forced convection?
Ask AI
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?
Ask AI
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.
Ask AI
Q.6 Solve both questions :
Ask AI
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.
Ask AI
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).
Ask AI
Q.7 Solve all questions :
Ask AI
Q7.1
What do you mean by fully developed boundary flow? Explain with suitable diagram.
Ask AI
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.
Ask AI
Q7.3
Physically, what does the Grashof number represent?
Ask AI
Q.8 Solve all questions :
Ask AI
Q8.1
What is fouling factor? Explain its effect in heat exchanger design.
Ask AI
Q8.2
Define heat exchanger effectiveness.
Ask AI
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.
Ask AI
Q.9 Solve all questions :
Ask AI
Q9.1
State the Fick's law of diffusion.
Ask AI
Q9.2
Determine the view factor of the cylindrical surface with respect to the base, when $ L = 2r $. Consider $ F_{12} = 0.16 $.

Ask AI
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 $.
Ask AI