## Heat Transfer - Dec 2015

### Mechanical Engineering (Semester 5)

TOTAL MARKS: 80

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

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

(3) Assume data if required.

(4) Figures to the right indicate full marks.

### Answer any four questions.

**1 (a)** Two pin fins are identical except that the diameter of one is twice of other. For which fin will (i) Fin Effectiveness (ii) Fin Efficiency be higher?(5 marks)
**1 (b)** What is Thermal Boundary Layer? Illustrate the same with help of a neat diagram.(5 marks)
**1 (c)** What is fouling in Heat Exchangers?(5 marks)
**1 (d)** During the ripening process of orange, the average heat energy release is estimated as 4715 KJ/m^{3}/hr. If the orange is assumed to be homogeneous sphere having K=0.175 W/mK, compute the temperature at center of orange.

Take diameter of orange = 90mm. Outer surface temperature of orange = 8°C.(5 marks)
**1 (e)** A Filament of a 75W light bulb may be considered as a black body radiating into a black enclosure of 70°C. The filament diameter is 0.1 mm and length 50mm. Considering the radiation, determine the filament temperature.(5 marks)
**2 (a)** A standard cast iron pipe (inner diameter=50 mm and outer diameter = 55 mm) is insulated with magnesium insulation (K=0.02 W/mK). Temperature at the interface between the pipe and insulation is 300°C, The allowable heat loss through the pipe is 600 W/m length of pipe for the safety; the temperature of the outside surface of insulation must not exceed 100°C, Determine minimum thickness of insulation required.

K for cast iron = 20 W/m°C.(8 marks)
**2 (b)** Derive a relation of heat transfer through fin with heat loosing at tip.(8 marks)
**2 (c)** Define thermal conductivity. How thermal conductivity is varied with temperature.(4 marks)
**3 (a)** Air at 200°C and at atmospheric pressure flows at a velocity of 2 m/s over a plate maintained at 1000°C. The length and width of the plate are 800mm and 400mm resp.

First half of the plate

Full plate and (iii) Next half of the plate.

Nu=0.332 Re^{0.5} Pr^{0.333} Properties of air at 600°C are ρ=1.06 kg/m^{3},

μ=7.211 kg/mh, v=18.97×10^{-6} m^{2}/s. Pr=0.696.

K for air 0.02894 W/m°C.(10 marks)
**3 (b)** With the help of Buckingham π-theorem show that for forced convection Nu=C Re^{m} Pr^{m}.(10 marks)
**4 (a)** Show that the radiant heat transfer between two infinitely large parallel plates seperated by n shields is $$ Q_{n -shields} = \dfrac {A \sigma (T^4_1 - T_2^4)}{(n+1)\left [ \frac {2}{\epsilon} -1 \right ]} $$(8 marks)
**4 (b)** The net radiation from the surface of two parallel plates maintained at temperature T_{1} and T_{2} is to be reduced by 79 times. Calculate the number of screens to be placed between the two surfaces to achieve this reduction in heat exchange. Assuming the emissivity of screens as 0.05 and that of the surface as 0.8.(8 marks)
**4 (c)** What is the mode of heat transfer in vacuum? Define Absorptivity, Reflectivity, Transmisivity and establish the relation among them.(4 marks)
**5 (a)** Derive the expression for log mean temperature difference (LMTD) in a parallel flow heat exchanger. State your assumptions.(8 marks)
**5 (b)** A counter flow heat exchanger is employed to cool 0.55 kg/s (Cp=2.45 kJ/kg°C) of oil from 115°C to 40°C by the use of water. The inlet and outlet temperature of cooling water are 15°C and 75°C respectively. The overall heat transfer coefficient is expected to be 1450 W/m^{2}C. Using NTU method. Calculate the following:

i) The mass flow rate of water.

ii) The effectiveness of the heat exchanger

iii) The surface area required.(8 marks)
**5 (c)** Classify Heat Exchangers on various arrangements.(4 marks)

### Answer (any two).

**6 (a) (i)** What is Filmwise and Dropwise condensation?(4 marks)
**6 (a) (ii)** Why Extended surface are used?(4 marks)
**6 (a) (iii)** How Numerical methods are used in conduction heat transfer.(4 marks)
**6 (b)** An egg with mean diameter of 4cm and initially at 20°C is placed in a boiling water pan for 4 min and found to be boiled to the consumers taste. For how long should a similar egg for same consumer be boiled when taken from refrigerator at 5°C? Take the following properties for egg: k=10 W/mK, ρ=1200 kg/m^{3}, C_{p}=2 kJ/kg K and h=100W/m^{2}K. Use lump theory.(8 marks)
**6 (c)** Explain the physical significance of Reynold number and Prandtl number.(4 marks)