Heat Transfer Miscellaneous
 A hemispherical furnace of 1 m radius has the inner surface (emissivity, ε = 1) of its roof maintained at 800 K, while its floor (ε = 0.5) is kept at 600 K. StefanBoltzmann constant is 5.668 × 110^{8}W/m^{2}K^{4}. The net radiative heat transfer (in kW) from the roof to the floor is _______.

View Hint View Answer Discuss in Forum
Let the base be (1) and hemispherical furnace be (2)
∴ F_{11} + F_{12} = 1 ...(1)
F_{21} + F_{22} = 1 ...(2)
∵ F_{11} = 0
∴ F_{12} = 2
A_{1} F_{12} = A_{2} F_{21}∴ F_{21} = A_{1} F_{12} = πR^{2} F_{12} = 0.5F_{12} A_{2} 2πR^{2}
∴ F_{21} = 0.5 × 2.0.5
∴ F_{22} = 0.5
So, F_{11} = 0, F_{12} = 1, F_{21} = 0.5 < F_{22} = 0.5
Now Radiative heat transfer,
⇒ Q = A_{1} F_{12}ε_{2} × 6(800^{4} – 600^{4}) watt
∴ Q = π × 1^{2} × 1 × 0.5 × 5.668 × 10^{– 8}(800^{4} – 600^{4}) watt
or Q = 24.9 kW.Correct Option: C
Let the base be (1) and hemispherical furnace be (2)
∴ F_{11} + F_{12} = 1 ...(1)
F_{21} + F_{22} = 1 ...(2)
∵ F_{11} = 0
∴ F_{12} = 2
A_{1} F_{12} = A_{2} F_{21}∴ F_{21} = A_{1} F_{12} = πR^{2} F_{12} = 0.5F_{12} A_{2} 2πR^{2}
∴ F_{21} = 0.5 × 2.0.5
∴ F_{22} = 0.5
So, F_{11} = 0, F_{12} = 1, F_{21} = 0.5 < F_{22} = 0.5
Now Radiative heat transfer,
⇒ Q = A_{1} F_{12}ε_{2} × 6(800^{4} – 600^{4}) watt
∴ Q = π × 1^{2} × 1 × 0.5 × 5.668 × 10^{– 8}(800^{4} – 600^{4}) watt
or Q = 24.9 kW.
 In a counter flow heat exchange, for the hot fluid the heat capacity = 2 kJ/kgK, mass flow rate = 5 kg/s, inlet temperature = 150°C, outlet temperature = 100°C. For the cold fluid, heat capacity = 4 kJ/kg K, mass flow rate = 10 kg/s, inlet temperature = 20°C. Neglecting heat transfer to the surroundings, the outlet temperature of the cold fluid in °C is

View Hint View Answer Discuss in Forum
Heat lost by fluid = Heat gained by cold fluid
5 × 2000 × 150 – 100) = 10 × 4000 (T_{co} – T_{ci})
∴ T_{co} = 32.5°cCorrect Option: B
Heat lost by fluid = Heat gained by cold fluid
5 × 2000 × 150 – 100) = 10 × 4000 (T_{co} – T_{ci})
∴ T_{co} = 32.5°c