## Heat & Mass Transfer - Dec 2013

### Mechanical Engg. (Semester 6)

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.
**1 (a)** Explain briefly the mechanism of conduction, convection and radiation heat transfer.(6 marks)
**1 (b)** With sketches write down the mathematical representation of three commonly used different types of boundary conditions for one dimensional heat equation in rectangular coordinates.(8 marks)
**1 (c)** A plate of thickness 'L' whose one side is insulated and the other side is maintained at a temperature T_{1} is exchanging heat by convection to the surrounding area at a temperature T_{2}, with atmospheric air being the outside medium. Write mathematical formulation for one dimensional, steady state heat transfer, without heat generation.(6 marks)
**2 (a)** An electric cable of 10mm diameter is to be laid in atmosphere at 20°C. The estimated surface temperature of the cable due to heat generation is 65°C. Find the maximum percentage increase in heat dissipation, when the wire is insulated with rubber having K=0.155 W/mK, take h=8.5 W/m^{2}K.(6 marks)
**2 (b)** Differentiate between the effectiveness and efficiency of fins.(4 marks)
**2 (c)** In order to reduce the thermal resistance at the surface of vertical plane wall(50×50cm). 100 pin fins(1 cm diameter. 10Cm long) are attached. If the pin fins are made of coper having a thermal conductivity is 15 W/m^{2}K, calculate the decrease in the thermal resistance. Also calculate the consequent increase in heat transfer in heat transfer rate from the wall if it is maintained at a temperature of 200°C and surroundings are at 30°C.(10 marks)
**3 (a)** Show that the temperature distribution in body during Nevetonian having or cooling is given by $$\frac{T-T_{0}}{T_{1}-T_{0}}=\frac{\theta}{\theta_{1}}=Exp\left ( \frac{-hA_{s}t}{\rho CV} \right )$$.(6 marks)
**3 (b)** The steel ball bearing (K=50W/mK, α=.3×10^{-5}m^{2}/sec), 40mm at diameters are heated to temperature of 650°C, it is then quenched in a oil bath at 50°C, where the the transfer coefficient is estimated to be 300 W/m^{2}K. Calculate:

i)The time required for bearing to reach 200°C.

ii) The total amount of heat removed from a bearing during this time and

iii) The instantaneous heat transfer rate from the bearing, when they are first immersed in oil bath and when they reach 200°C(14 marks)
**4 (a)** With reference to fluid flow over a flat plate, discuss the concept of velocity boundary and thermal boundary, layer with nessary sketches.(5 marks)
**4 (b)** The exact expression for local Nuselt number for the laminar flow along a surface is given by $$Nu_{1}=\frac{h_{1}x}{k}=0.332 R^{1/2}_{ex}\ p^{1/3}$$ show that the average heat transfer coefficient from x=0 to x=L over the length 'L' of the surface is given by 2h_{t} where h_{t} is the local heat transfer coefficient at x=L.(5 marks)
**4 (c)** A vertical plate 15 cm high and 10cm wide is maintained at 140°C. Calculate the maximum heat dissipation rate from bothe the sides of the plates to air at 20°C. The radiation heat transfer coefficient is 9.0 w/m^{2}K. For air at 80°C, take r=21.09 × 10^{-6}m^{2}/sec, P_{r}=0.692, K_{f}=0.03 W/mK.(10 marks)
**5 (a)** Explain the physical significance of i) Nusselt number ii) Groshoff number.(4 marks)
**5 (b)** Air at 2 atm and 200°C is heated as it flows at a velocity of 12m/sec through a tube with a diameter of 3 cm. A constant heat flux condition is maintained at the wall and the wall temperature is 20°C above air temperature all along the length of the tube. Calculate : i) The heat transfer per unit length of tube. ii) The increase in bulk temperature of air over a 4m length of the tube.

take the following properties of air Pr=0.681.μ=2.57×10^{-5}kg/ms, K=0.0386 W/mK and C_{p}=1.025 kJ/kg K.(10 marks)
**5 (C)** Obtain a relationship between drag coefficient c_{∞} and heat transfer coefficient h_{∞} for the flow over a flat plate.(6 marks)
**6 (a)** Derive an expression for LMTD of a counter flow heart exchanger. State the assumptions made.(8 marks)
**6 (b)** What is meant by the term fouling factor? How do you determine it?(4 marks)
**6 (c)** Engine oil is to be cooled from 80°C to 5°C by using a single pass counter flow , concentric-tube heat exchanger with cooling water available at 20°C. Water flows inside a tube with an internal dia of 2.5cm with a flow rate of 0.08 kg/s and oil flows through the annulus at a rate of 0.16kg/s. The heat transfer coefficient for the water side and oil side are respectively h_{w}1000 W/m^{2}°C and h_{oil} 80W/m^{2}C. The fouling factors is F_{w} 0.00018m^{2}°C/W on both sides and the tube wall resistance in negligible. Calculate the tube length required.(8 marks)
**7 (a)** Sketch a pool boiling curve for water and explain briefly the various regimes in boiling heat transfer.(6 marks)
**7 (b)** Define mass transfer coefficient.(2 marks)
**7 (c)** A 12 cm outside diameter and 2m long tube is used in a big condenser to condense the steam at 0.4 bar. Estimate the unit surface conductance. i)in vertical position ; ii) in horizontal position. Also find the amount of condense formed per hour per hour in both the cases. The saturation temperature of the steam=74.5°C.

Average wall temperature=50°C.

the properties of water film at average temperature of $$\frac{75.4+50}{2}=62.7°C$$ are given below ρ =982.2 kg/m^{3}, h_{f}=24800kJ/kg,K=0.65 W/mK, μ=0.47×10^{-3}kg/ms.(12 marks)
**8 (a)** State and prove Wien's displacement law of radiation.(6 marks)
**8 (b)** The temperature of a black surface 0.2m^{2} in area is 540°C calculate:

i)The total rate of energy emission

ii)The intensity of normal radiation

iii) The wavelength of maximum monochromatic emissive power.(6 marks)
**8 (c)** Derive an expression for a radiation shape factor and show that it is function of geometry only.(8 marks)