5HE - Heat Transfer - April'1998

PART A - (20 x 2 = 40 marks)

- Write Fourier's law of heat conduction.
- Which metal has the highest value of thermal conductivity? Write its thermal conductivity value in S.I. unit.
- Define Prandtl number. What is its physical significance?
- What is forced convection?
- Define equivalent Thermal conductivity for a composite wall consisting of three heterogeneous layers of different materials.
- Which type of flow arrangement gives
- State Stefan-Boltzmann's law of thermal radiation.
- What is a grey body?
- Define 'Capacity' and 'Economy, of a steam-heated tubular evaporator.
- Define fouling factor.
- Define heat transfer coefficient
**.**Write its unit. - Define 'Effectiveness' of a heat exchanger.
- Why is multiple effect evaporation preferred over a single effect operation?
- How will you account for the effect of liquid head in evaporator design?
- What are regenerators?
- Name two molten metals. State their important properties as heat transfer Media.
- State the variables affecting the transfer of heat in packed beds.
- Write few important applications of fluidised beds from the view point of heat transmission.
- Explain 'leiden frost' phenomenon during boiling.
- How will you calculate LMTD correction factor?
- (a) Derive an expression for determining the rate of heat transfer through the thick wall of a hollow cylinder. Also, find the temperature profile and its nature. State your assumptions clearly.
(b) An insulated steam pipe having outer diameter of 3.0 cm is to be covered with two layers of insulation, each having a thickness of 2.5 cm. Average thermal conductivity of one material is 4 times that of the other. Assuming that the inner and outer surface temperatures of composite insulation are fixed, how much will the heat transfer be reduced when the better insulating material is next to the pipe than its outer layer?

Or

- (a) Explain the term 'Thermal Diffusivity'. Prove that for unsteady state heat conduction along X-axis,
where a
= Thermal diffusivity. Equation
(b) An insulated wall is to be constructed of common brick 20 cm thick, and metal lathe with plaster 2.5 cm thick, with intermediate layer of loosely packed rock wool. The outer surfaces of the brick and plaster are to be at a temperature of 600

^{o}C and 50^{o}C respectively. Calculate the thickness of insulation required in order that the heat loss per square meter shall not exceed 600 kcal/hr. The conductivity of brick, rock-wool and metal lathe with plaster are 0.32, 0.045 and 0.7 k cal/m.hr.^{o}C respectivelyUNIT II

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

N_{Nu}=f (N_{Re}, N_{Pr}) where N_{Nu}, N_{Re}, N_{Pr}represent Nusselt, Reynolds and Prandtl number respectively(b) Explain the physical significance of Nusselt and Reynold numbers.

Or

- (a) Discuss the various regimes of boiling heat transfer with the help of a boiling curve for water.
(b) What are molten metals? Explain their properties and advantages as heat transfer media with examples.

UNIT III

- (a) Classify heat exchangers. With the help of a neat sketch, explain the working and construction of a 1-2 exchanger.
(b) A heat exchanger heats 25,000 kg/hr of water entering at 80

^{o}C while cooling 20,000 kg/hr of water from 100^{o}C to 80^{o}C. Determine the heat transfer area necessary for (i) Parallel flow arrangement (ii) Counter flow arrangement. Given Overall heat transfer coefficient, U= 1,500 W/m^{2}.Or

- (a) Give a classification of furnaces and explain any one of them with a. neat sketch.
(b) Water enters a parallel flow double-pipe heat exchanger at 15

^{o}C, flowing at the rate of 1200 kg/hr. It is heated by oil( C_{p}=2000 J/kg.K), flowing at the rate of 500 kg/hr from an inlet temperature of 90^{o}C. For an area of 1 m^{2}and an overall heat transfer coefficient of 1,200 W/m^{2}.K determine the total heat transfer and the outlet temperatures of water and oil.UNIT IV

- (a) State Kirchoffs and Wien's laws of thermal radiation. Derive the Wien's law from basic Planck's distribution law
(b) A gray surface is maintained at a temperature of 860

^{o}C. If the maximum spectral entiesive power at that temperature is 1.5 x 10^{10}W/m^{2}, determine the emissivity of the body and the wavelength corresponding to maximum spectral intensity of radiation.Or

- (a)Write short notes on any THREE of the following

(i)Radiation from gases and clouds of particles.

(ii)Design of tubular furnaces.

(iii)Radiation exchange between large parallel gray planes.

(iv)Radiation shape factorUNIT V

- (a) With the help of a neat sketch, discuss the forward feed multiple effect evaporation system.
(b) 1.5 kg/s of a solution containing 1.0 wt.% solids is fed to a single effect evaporator at 303 K. It is to be concentrated to a solution of 1.5 wt.% solids. Evaporation takes place at atmospheric pressure. Saturated steam is supplied at 205 kN/m

^{2}for heating. If the overall heat transfer coefficient is 3000 W/m^{2}.K, what is the surface area required? Suitable assumptions may be made, if necessary. Saturation temperatures of steam at 205 kN/m^{2}= 125^{o}C and Latent heat of vapourization = 2,200 kJ/kg.Or

- 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

PART B - (5 x 12 = 60 marks)