## Heat Transfer - Dec 2016

### Mechanical Engg (Semester 5)

TOTAL MARKS: 100

TOTAL TIME: 3 HOURS
(1) Question 1 is compulsory.

(2) Attempt any **four** from the remaining questions.

(3) Assume data wherever required.

(4) Figures to the right indicate full marks.

### Solve any one question.Q1(a,b) Q2

**1(a)** Differentiate between steady and unsteady state heat traansfer. Give examples of each.(4 marks)
**1(b)** A furnace wall lining in made up of a material with k=2.5 W/mK. The temperatures of the inner and outler surfaces of this plane wall lining are 810°C and 330°C respectively. The outer surface of this exposed to ambient air 30°C with convective heat transfer coefficient = 10W/m^{2}K.

Calculate:

i) The rate of heat flow per unit area

ii) Thickness of lining in given situation.

iii) The thickness of lining required if the heat flow rate is to be reduced by 50%.(6 marks)
**10(a)** Draw labeled temperature profiles (with suitable temperature values) of the following types of heat exchangers:

i) Parallerl flow heat exchanger

ii) Counter flow heat exchanger

iii) Condenser,

iv) Evaporator.(4 marks)
**10(b)** Explain phenomenon of nucleate boiling.(6 marks)
**10c)** Derive the expression for LMTD for parallel flow heat exchanger.(8 marks)
**2** Heat is generated uniformly in a stainless steel plate having k=20 W/mK. The thickness of the plate is 1 cm and the heat generation is 500 MW/m^{3}. If the two sides of the plate are maintained at 100°C and 200°C, respectively. Solving the governing differential equation, calculate the tempreature at the center of plate.(10 marks)

### Solve any one question.Q3(a,b) Q4(a,b)

**3(a)** Derive the expression for Lumped heat capacity with usual notations.(8 marks)
**3(b)** In what medium is the lumped system analysis more likely to be applicable : in water or in air? Why?(2 marks)
**4(a)** An electric motor is to be connected by a horizontal steel shaft (k=42.56 W/mk), 25 mm in diameter to an impeller of a pump, circulating liquid metal at a tempreature of 540°C. If the tempreature of electric motor is limited to a maximum value 54°C with ambient air at 27°C and heat transfer coefficient of 40.7 W/m^{2}K, what length of shaft should be specified between motor and pump? Assume insulated tip condition, for fin analysis.(6 marks)
**4(b)** In some cases, addition of fins may actually decrease the heat transfer from surface. Justify the statement.(4 marks)

### Solve any one question.Q5(a,b,c) Q6(a,b,c)

**5(a)** Define and explain the significance of Prandtl number.(4 marks)
**5(b)** Identify the characteristics dimension for following cases in Natural convection:

i) Vertical cylinder,

ii) Horizontal cylinder,

iii) Horizontal plate,

iv) Sphere.(4 marks)
**5(c)** Water is flowing at the rate 50kg/min through a tube of inner diameter 2.5cm. The inner surface of tube is maintained at 100°C. If the temperature of water increases from 25°C to 55°C, find length of tube required. Nu=0.023 Re^{0.8}Pr^{0.4},

Properties of water:σ=977.8kg/m^{3},

k=0.6672W/m°C,

μ= 405×10^{-6}Ns/m^{2},

Cp=4.187kJ/kg°C.(8 marks)
**6(a)** Explain the significance of thermal boundary layer and velocity boundary layer.(4 marks)
**6(b)** A hot plate 1m×0.5m at 130°C is kept vertically in still air at 20°C. Find:

i) Heat transfer coefficient,

ii) Initial rate of cooling the plate in °C/min. Assume 0.5 m side is vertical and heat transfer takes place from both the sides of the plates. Take properties of air as Cp=1007J/kg °C,

k=0.029W/M°C,

υ=19.1×10^{-6}m^{2}/s,

Pr=0.7 Assume mass of plate =20kg and specific heat of plate =40J/kg°C Use Nu= 0.59 (GrPr)^{1/4}.(8 marks)
**6(c)** Define and expalin significance of Nussel number.(4 marks)

### Solve any one question.Q7(a,b,c) Q8(a,b)

**7(a)** if the shape factor of a surface with respect toitself is 0.6. what may be the nature of this surface? Explain with the help of sketch. Also sketch and explain the types of surface which has no (zero) shape factor with respect to itself.(4 marks)
**7(b)** A gray opaque surface has an absorptivity=0.8. It is maintained at 100°C/ It receives an irradiation of 1,000W/m^{2}. Its surface area is 0.1m^{2} Calculate,

i) Radiosity of the surface,

ii) Net radiative heat transfer rate from the surface. Recalculate the above quantities, if the surface is black.(8 marks)
**7(c)** What is the significance of radiation shield? List few applications of radiation shield.(4 marks)
**8(a)** Explain with suitable illustration how the concept of surface resistance and space resistacne is used for solving radiation heat transfer problems?(8 marks)
**8(b)** Determine the heat lost by radiation pre meter length of a 100 mm diameter pipe at 300°C if it is.

i) Located in large room of brick wall whose tempreature is 20°C.

ii) Located i a 200 mm diameter brick conduit at a tempreature of 20°C.

ϵ_{pipe}= 0.79,

ϵ_{brick}=0.93.(8 marks)

### Solve any one question.Q9(a,b,c) Q10(a,b,c)

**9(a)** Write a note on Forced convection boiling (Flow boiling).(6 marks)

### Solve any one question.Q1(a,b,c) Q2(a,b,c)

**9(b)** A chemical having specific heat of 3.3kJ/kgK following at the rate of 20,000kg/hr enters a parallel flow heat exchange at 120°C. The flow rate of cooling water is 50,000kg/hr with an inlet tempreature of 20°C. The heat tranfer area is 10m^{2} and overall heat transfer coefficient is 1050W/m^{2}°C. Taking specific hat of water as 4.186kJ/kgK, find

i) Effectiveness of het exchanger

ii) Outlet tempreature of water and chemical.(8 marks)
**9(c)** Define NTU. What does it represent? Is as heat exchanger with a very large NTU(say 10) necessarily a good one to buy?(4 marks)