## Heat Transfer Miscellaneous

#### Heat-Transfer

1. 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. Stefan-Boltzmann constant is 5.668 × 110-8W/m2K4. The net radiative heat transfer (in kW) from the roof to the floor is _______.

1. Let the base be (1) and hemispherical furnace be (2)
∴ F11 + F12 = 1 ...(1)
F21 + F22 = 1 ...(2)
∵ F11 = 0
∴ F12 = 2
A1 F12 = A2 F21

 ∴ F21 = A1 F12 = πR2 F12 = 0.5F12 A2 2πR2

∴ F21 = 0.5 × 2.0.5
∴ F22 = 0.5
So, F11 = 0, F12 = 1, F21 = 0.5 < F22 = 0.5
Now Radiative heat transfer,
⇒ Q = A1 F12ε2 × 6(8004 – 6004) watt
∴ Q = π × 12 × 1 × 0.5 × 5.668 × 10– 8(8004 – 6004) watt
or Q = 24.9 kW.

##### Correct Option: C

Let the base be (1) and hemispherical furnace be (2)
∴ F11 + F12 = 1 ...(1)
F21 + F22 = 1 ...(2)
∵ F11 = 0
∴ F12 = 2
A1 F12 = A2 F21

 ∴ F21 = A1 F12 = πR2 F12 = 0.5F12 A2 2πR2

∴ F21 = 0.5 × 2.0.5
∴ F22 = 0.5
So, F11 = 0, F12 = 1, F21 = 0.5 < F22 = 0.5
Now Radiative heat transfer,
⇒ Q = A1 F12ε2 × 6(8004 – 6004) watt
∴ Q = π × 12 × 1 × 0.5 × 5.668 × 10– 8(8004 – 6004) watt
or Q = 24.9 kW.

1. 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

1. Heat lost by fluid = Heat gained by cold fluid

5 × 2000 × 150 – 100) = 10 × 4000 (Tco – Tci)
∴ Tco = 32.5°c

##### Correct Option: B

Heat lost by fluid = Heat gained by cold fluid

5 × 2000 × 150 – 100) = 10 × 4000 (Tco – Tci)
∴ Tco = 32.5°c