Heat Transfer Miscellaneous Easy Questions and Answers | Page - 25

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

1. 22 kW.
1. 25 kW.
1. 24.9 kW.
1. 24. kW.

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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.

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. 7.5
1. 32.5
1. 45.5
1. 70.0

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Heat lost by fluid = Heat gained by cold fluid

5 × 2000 × 150 – 100) = 10 × 4000 (T_co – T_ci)
∴ T_co = 32.5°c

Correct 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