5HE - Heat Transfer - October'1998

**PART A - (20 x 2 = 40 marks)**

- Define 'Thermal Conductivity'. Write its S.I. unit.
- How does thermal conductivity vary with temperature for solid metallic substances and gases?
- Under which conditions, fins are used on the heat transfer surface?
- What is the relationship between dimensioniess groups, obtained by dimensional analysis for free convective heat transfer operations?
- Write the Nusselt's equation for condensation to determine film thickness.
- How does boundary layer influence the rate of heat transfer? Explain.
- Write the physical significance of Nusselt number.
- Write the relationship between individual and overall heat transfer coefficients for a double pipe heat exchanger with hot and cold working fluids.
- Write two applications for heat transfer in packed beds in chemical industry.
- What is subcooled boiling?
- What are the advantages of plate heat exchanger?
- What is Wilson's plot?
- Design of commercial condensers is done on the basis of ------- condensation (dropwise/filmwise).
- What is the effect of non-condensables, present in vapours, on rate of heat transfer?
- What do you understand by 'Radiation Error' in temperature measurement?
- What do you understand by NTU? How does it affect the efficiency of a parallel flow single pass heat exchanger?
- What are the applications of tubular furnaces?
- What is the principle of a thermo-compression evaporator?
- What is 'Boiling Point Elevation'? How will you account it during evaporator design?
- Write unsteady state heat conduction equation (three dimensional) in Cartesian co-ordinates for a solid metallic slab.
**PART B - (5 x 12 = 60 marks)**UNIT I

- (a) Derive an expression for determining the rate of
heat transfer and the temperature distribution through a plane vertical wall if thermal conductivity varies with temperature as follows :

K = K_{o}(1 + bT)

State your assumptions clearly.(b) What are the various modes of heat transfer through solids, liquids and gases? Discuss the analogy between flow of heat and electricity.

Or

- (a) Derive an expression for heat conduction through the metallic wall of a hollow sphere at steady state. Prove that the area for heat transfer through a spherical wall can be expressed as follows :
A =(A1A2)
^{1/2}, where A1, and A2 represent the inside and outside surface area.(b) A 150 mm diameter (O.D.) steam pipe is covered with two layers of lagging, each 40 mm thick. It carries steam at a pressure of 3.6 MN/m

^{2}. Estimate the heat loss per hour for a 50 m length of the lagged pipe. What would be the surface temperature of the lagging? Ambient temperature is 27^{o}C.

Data given:

Thermal conductivity of inner layer = 0.07 W/m.K

Thermal conductivity of outer layer = 0. 1 W/m.K

Outer surface heat transfer coefficient =3 W/m^{2}.K Saturation temperature of steam at 3.6 MN/m^{2}= 244.2^{o}C

Neglect the thickness of steam pipe and internal surface resistance.UNIT II

- (a) Using dimensional analysis, prove that heat transfer coefficient during free convection can be represented by the following relationship:

Nu = f(Gr,Pr)where Nu,Gr and Pr represent Nusselt, Grashof and Prandtl number respectively.(b) A horizontal cylinder, 3.0 cm in diameter and 0.8 m length, is suspended in water at 200C. Calculate the rate of heat transfer if the cylinder surface is at 55C. Given Nu = 0.53 (Gr x Pr)

^{1/4}

The properties of water at average temperature are as follows:

Density, r = 990 kg/m^{3}

Viscosity, m = 2.47 kg/hr.m

Thermal conductivity, k = 0.534 kcal/hr.m.^{o}C

C_{p}= 1 kcal/kg.^{o}C.Or

- (a) Discuss the regimes of boiling heat transfer with the help of a boiling curve. Why are heat transfer coefficients lowered in film boiling as compared to nucleate boiling?
(b) What are the factors affecting the condensation during film wise condensation? Explain their effects. Why are commercial condensers designed on the basis of film wise condensation?

UNIT III

- Differentiate between recuperators and regenerators. Draw a neat sketch of the shell and tube heat exchanger and explain its construction.
Or

- A refrigerator is designed to cool 300 kg/hr of hot fluid of specific heat, 3000 J/kg.K using a parallel flow arrangement. 1200 kg/hr of cooling water is available for cooling purposes at a temperature of 15
^{o}C. If the overall heat transfer coefficient is 1,500 W/m^{2}.K, calculate the outlet temperatures of the cooled liquid and water and also the effectiveness of the heat exchanger.

Given:

Surface area of the heat exchanger = 0.3 m^{2}

Heat capacity of water = 4186 J/kg.KUNIT IV

- (a) Discuss the two different theories, proposed to explain the phenomenon of radiation. State the Planck's distribution law.
(b) A small body at 15

^{o}C is placed inside a large furnace whose walls are maintained at 800^{o}C. The total absorptivity of the body at 15^{o}C varies with the temperature of the incident radiation as follows:

Determine the rate of absorption and emission of radiation by the small body.Temperature (K) 288 500 1,073 a 0.8 0.65 0.5 Or

- (a) Discuss the radiation from gases and vapours with specific reference to carbon di-oxide and water which are always present in industrial furnaces.
(b) Two concentric spheres, 21 cm and 30 cm in diameter, with the space between them evacuated, are to be used to store liquid air (-153

^{o}C) in a room at 27^{o}. The surface of the spheres are flushed with Aluminium (e = 0.03) and the latent heat of vapourization of liquid air is 209 kJ/kg. Find the rate of evaporation of liquid air.UNIT V

- With the help of neat sketches, discuss the classification of evaporators. Also, why is multiple effect operation preferred over a single effect evaporation unit?
Or

- (a) What are the liquid characteristics to be taken into account during selection and design of evaporators? (4)
(b) A solution containing 3 kg salt per 100 kg solution is evaporated to 15% solids concentration in an evaporator. Heat capacity of the solution is 0.98 kcal/kg.

^{o}C and that of the 15% solution is 0.90 kcal/kg.^{o}C. Feed temperature is 20^{o}C. Boiling point in the evaporator is 104^{o}C. It requires 540 kcal to evaporate 1 kg of water from the boiling solution. Steam gives only its latent heat of vaporization, 525 kcal/kg. How many kg of steam is required per kg of feed?