856 ENGINEERING THERMODYNAMICS
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\M-therm\Th15-4.pm5
- A spherical shaped vessel of 1.2 m diameter is 100 mm thick. Find the rate of heat leakage, if the
temperature difference between the inner and outer surfaces is 200°C. Thermal conductivity of the
material is 0.3 kJ/m-h-°C. [Ans. 2262 kJ/h] - Exhaust gases flowing through a tubular heat exchanger at the rate of 0.3 kg/s are cooled from 400°C to
120°C by water initially at 10°C. The specific heat of exhaust gases and water may be taken as 1.13 and
4.19 kJ/kg K respectively, and overall heat transfer co-efficient from gases to water is 140 W/m^2 K.
Calculate the surface area required when the cooling water flow is 0.4 kg/s.
(i) For parallel-flow ; (ii) For counter-flow. [Ans. (i) 4.0 m^2 , (ii) 3.37 m^2 ] - Water flows inside a tube 50 mm in diameter and 3 m long at a velocity of 0.8 m/s. Determine the heat
transfer co-efficient and the rate of heat transfer if the mean water temperature is 50°C and the wall is
isothermal at 70°C. For water at 60°C, take k = 0.66 W/m K, ν (kinematic viscosity) = 0.478 × 10–6 m^2 /s,
and Prandtl number = 2.98. [Ans. 4075 W/m^2 K ; 38.39 kW] - Liquid air at – 153°C is stored in the space of two concentric spheres of 21 cm and 30 cm diameters. The
surface emissivities are 0.03. Assume the outer surface temperature is 27°C. Considering only radiation
heat transfer and taking the latent heat of liquid air of 209 kJ/kg, find the rate of evaporation. Take
σ = 2.04 × 10–4 kJ/h-m^2 K^4 .[Ans. 21.7 kg/h] - A body at 1100°C in black surroundings at 550°C has an emissivity of 0.4 at 1100°C and an emissivity of
0.7 at 550°C. Calculate the ratio of heat loss by radiation per m^2 ,
(i) when the body is assumed to be grey with ε = 0.4
(ii) when the body is not grey. [Ans. (i) 70.22 kW, (ii) 62.42 kW] - A long steel rod, 20 mm in diameter, is to be heated from 427°C to 538°C. It is placed concentrically in
a long cylindrical furnace which has an inside diameter of 160 mm. The inner surface of the furnace is
at a temperature of 1093°C, and has an emissivity of 0.85. If the surface of the rod has an emissivity of
0.6, find the time required for the heating operation.
Take for steel : ρ = 7845 kg/m^3 and c = 0.67 kJ/kg K. [Ans. 29.88 s]