5HE Heat Transfer - Oct'1997

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

- Define 'temperature field' and 'temperature gradient'
- What is thermal diffusivity? Write its unit.
- Define natural or free convection.
- Write three dimensional heat transfer equation under unsteady state in cartesian co-ordinates.
- What is the difference between Biot number and Nueselt number?
- Differentiate between nucleate and film boiling.
- Why is mean temperature difference estimated in the heat exchanger design?
- Design of condenser is carried out on the basis of condensation. (Dropwise/Filmwise)
- What is Stefan - Boltzmann's law of thermal radiation?
- Define the terms emissivity and absorptivity in radiation heat transfer.
- What is Duhring's rule?
- How will you account for the effect of liquid head in evaporator design?
- Write broad classification of furnaces.
- What is thermal boundary layer?
- Which flow arrangement gives maximum efficiency in shell and tube heat exchanger and why?
- What is Wilson's plot?
- What are molten metals? Name two molten metals.
- Name the important parameters affecting the rate of heat transfer in packed bed.
- In forced convection, Nusselt number is a function of which dimensionless groups.
- In a heat exchanger, what does the term 'Transfer Unit' refer to ?
**PART B - (5 x 12 = 60 marks)**UNIT 1

- (a) Derive an expression for the rate of heat transfer through a composite plane wall consisting of three heterogeneous layers having thermal conductivity; K1,K2 and K3 respectively.
(b) A plane brick wall, 25 cm thick, is faced with 5 cm thick concrete layer. If the temperature of the exposed brick face is 70

^{o}C and that of the concrete is 25^{o}C, find out the heat lost per hour through a wall of 15 m x10 m. Also, determine the interface temperature. Thermal conductivity of the brick and concrete are 0.7 W/m.K and 0.95 W/m.K respectively.Or

- (a) Derive an expression for the temperature profile in a thick walled cylinder during heat transfer by conduction under steady state
(b) A steel pipe (K = 50 W/m.K) of I.D. = 100 mm and O.D. = 110 mm is to be covered with two layers of insulation, each having a thickness of 50 mm. Thermal conductivity of the first insulation material is 0.06 W/m.K and that of the second is 0.12 W/m.K. Calculate the loss of heat per metre length of pipe and the interface temperature between the two layers of insulation when the temperature of the inside tube surface is 250

^{o}C and that of the outside surface of the insulation is 50^{o}C.UNIT II

- (a) Discuss briefly the effect of turbulence on boundary layers. Under forced flow conditions, how does Prandtl number affect the relative thickness of thermal and hydrodynamic boundary layers?
(b) Air at 20

^{o}C is flowing along a heated flat plate at 150^{o}C at a velocity of 3 m/sec. The plate is 2 m long and 1.5 m wide. Calculate the thickness of the hydrodynamic boundary layer and the skin friction coefficient at 30 cm from the leading edge of the plate. Kinematic viscosity of air at 20^{o}C is 15.06 x 10^{-6}m^{2}/secOr

- (a) Derive an expression for forced convective heat transfer through a conduit using dimensional analysis.
(b) Determine the rate of heat loss from a 100 mm diameter steam pipe placed horizontally in ambient air at 30

^{o}C. The length of the pipe is 4 m and wall temperature, Tw = 170^{o}C.

Use the following empirical expression:

Nu=0.53 (Gr x Pr)^{1/4}

Properties of air at 100^{o}C are as following

b =1/373 K^{-1 }g = 23.13 x 10^{-6 }m^{2 }/sec

K= 0.0325 W/m.K

Pr = 0.7

Nu = 114UNIT III

- (a) Derive an expression for calculating the effectiveness of a parallel flow heat exchanger.
(b) A parallel flow heat exchanger has to cool 2500 kg/hr of oil from 70

^{o}C to 30^{o}C. Cooling water enters the exchanger at 10^{o}C and leaves at 20^{o}C. Specific heat of oil is 2.1 kJ/kg.K. Determine the effectiveness of the heat exchanger and heat transfer capacity.Or

- (a) Derive an expression to evaluate the mean temperature difference in a single pass counterflow shell and tube heat exchanger.
(b) A heat exchanger heats 25,000 kg/hr of water entering at 30

^{o}C while cooling 20,000 kg/hr of water from 100^{o}C to 80^{o}C. Determine the area necessary for (i)Parallel flow arrangement

(ii)Counter flow arrangement.

Overall heat transfer coefficient may be assumed as 1,600 W/m^{2}K.UNIT IV

- Write short notes on any THREE of the following:

(a) Tubular furnaces and their applications.

(b) Radiation from luminous flames

(c) Concept of black and gray body

(d) Radiation error in temperature measurement.Or

- (a) Explain Kirchoffs law of radiation.
(b) Determine the net heat transfer by radiation between the two surfaces A and B per hour per unit area if the temperatures of A and B are 800

^{o}C and 350^{o}C respectively. Emissivities of A and B are 0.9 and 0.25 respectively . Both surfaces are gray and are infinite parallel lines, 3.5 m apart.UNIT V

- A single effect evaporates operates at 13 kN/m
^{2}. What will be the heating surface necessary to concentrate 1.5 kg/s of 10% caustic soda to 40%, assuming a value of overall heat transfer coefficient as 1.5 kW/m^{2}K? Steam has been used for heating at 390 K and heating surface is 1 m below the liquid level.

Data given: Boiling point elevation = 30 K

Feed temperature = 290 K

Specific heat of the feed = 4.0 kJ/kg.K

Specific heat of the product = 3.26 kJ/kg.K

Specific gravity of the boiling liquid = 1.40 kJ/kg.K

Or

- (a) Draw a neat sketch of backward feed multiple effect evaporation system and discuss the salient features. When is backward feed operation preferred over forward feed?
(b) A triple effect evaporator concentrates, a liquid with no appreciable elevation in boiling point. If the temperature of the steam to the first effect is 395 K and vacuum in the last effect brings down the boiling point to 325 K, what are the approximate boiling points of liquid in first and second effect? Assume the overall heat transfer coefficient as 3.1, 2.3 and 1.1 kW/m

^{2.}K in first, second and third effects respectively.