## Heat & Mass Transfer - Jun 2014

### Mechanical Engineering (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)** What is thermal diffusivity? Explain importance in heat conduction problem.(4 marks)
**1 (b)** Describe different types of boundary conditions applied to heat Conduction problems.(4 marks)
**1 (c)** Consider a one dimensional steady state heat conduction in a plate with constant thermal conductivity in a region 0≤ ×≤ L. A plate is exposed to uniform heat flux q W/m^{2} at x= 0 and dissipates heat by convection at x-L with heat transfer coefficient h in the surrounding air at T_{∞}. Write the mathematical formulation of this problem for the determination of one dimensional, steady temperature distribution within the wall.(4 marks)
**1 (d)** An industrial freezer is designed to operate with an internal air temperature of-20°C when the external air temperature is 25°C and the internal and external heat transfer coefficients are 12 W/m^{2}°C and 8 W/m^{2}°C, respectively. The wall of the freezer are composite construction, comprising of an inner layer of plastic 3 mm thick with thermal conductivity of 1 W/m°C. An outer layer of stainless steel of thickness 1 mm and thermal conductivity of 16W/m°C. Sandwiched between these layers is a layer of insulation material with thermal conductivity of 0.07 W/m°C. Find the width of the insulation required to reduce the convective heat loss to 15 W/m^{2}.(8 marks)
**2 (a)** What is critical thickness of insulation on a small diameter wire or pipe? Explain its physical significance and derive an expression for the same.(10 marks)
**2 (b)** A set of aluminium fins (K=180 W/mK) that are to be fitted to a small air compressor. The device dissipates 1 KW by convecting to the surrounding air which is at 20°C. Each fin is 100 mm long, 30 mm high and 5 mm thick. The tip of each fin may be assumed to be adiabatic and a heat transfer coefficient of 15 W/m^{2}K acts over the remaining surfaces. Estimate the number of fins required to ensure the base temperature does not exceed 120°C.(10 marks)
**3 (a)** What are Biot and Fourier numbers? Explain their physical significance.(6 marks)
**3 (b)** What are Heisle charts? Explain their significance in solving transient convection problems.(6 marks)
**3 (c)** The temperature of a gas stream is measured with a thermocouple. The junction may be approximated as a sphere of diameter I mm, K=25 W/m°C, ρ = 8400 kg/m^{3} and C= 0.4 kJ/kg°C. The heat transfer coefficient between the junction and the gas stream is h= 560 W/m2°C. How long will it take for the thermocouple to record 99% of the applied temperature difference?(8 marks)
**4 (a)** Establish a relation between Nusselt, Prandtl and Grashof numbers using dimensional analysis.(8 marks)
**4 (b)** Explain velocity and thermal boundary layer.(6 marks)
**4 (c)** A 30 cm long glass plate is hung vertically in the ak at 27°C while its temperature is maintained at 77°C. Calculate the boundary layer thickness at the trailing edge of the plate. Take properties of air at mean temperature K-28.15× 10^{-3}W/mK, γ =18.41 × 10^{-6}m^{2}/s, P_{r}=0.7,β = 3.07 × 10^{-3} K^{-1 }(6 marks)
**5 (a)** Explain the significance of i) Reynolds number ii) Prandtl number, iii) Nusselt number, iv) Stanton number.(8 marks)
**5 (b)** Atmospheric air at 275 K and free stream velocity 20 m/s flows over a flat plate of length 1.5 m long maintained at 325 K. Calculate:

i) The average heat transfer coefficient over the region where the boundary layer is laminar.

ii) Find the average heat transfer over the entire length 1.5 m of the plate.

iii) Calculate the total heat transfer rate from the plate to the air over the length of 1.5 m and width 1 m. assume transition occurs at a Reynolds number 2×10^{5}. Take air Properties at mean temperature of 300K

K-0.026W/m°C, P_{r}=0.708,γ=16.8×10^{-6} m^{2}/s, μ=1.98×10^{-5}kg/ms(12 marks)
**6 (a)** Derive an expression for the,effectiveness of a parallel flow heat exchange.(10 marks)
**6 (b)** 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 1000 W/m^{2}°C and 80W/m^{2}C. The fouling factors are 0.00018m^{2}°C/W and 0.00018 m^{2}°C/W, the tube wall resistance is negligible. Calculate the tube length required. Take specific heat of water as 4180 J/kg°C and for oil, 2090J/kg°C.(10 marks)
**7 (a)** Explain film wise and drop wise condensation.(4 marks)
**7 (b)** Draw the boiling curve and discuss the different regimes of boiling.(8 marks)
**7 (c)** Derive an expression for the total mass of water vapour diffused from a water column to the air passing over the water container.(8 marks)
**8 (a)** Explain briefly the concept of a black body.(4 marks)
**8 (b)** State: (i) Kirchoff's law, ii) Plank's law, iii) Wien's displacement law.(6 marks)
**8 (c)** Calculate the net radiant heat exchange per mm^{2} area for two large parallel plates at temperature of 427°C and27°C respectively ε for hot plates is 0.9 and for cold plate it is 0.6. If polished aluminium shield is placed between them, find percentage reduction in the heat transfer. Assume ε for shield :0.4.(10 marks)