Determine the heat transfer through a plane of length 4 m, height 3 m and thickness 0.2 m. The temperatures of inner and outer surfaces are 150°C and 90°C respectively. Thermal conductivity of the wall is 0.5 W/mK.

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Determine the heat transfer through a plane of length 4 m, height 3 m and thickness 0.2 m. The temperatures of inner and outer surfaces are 150°C and 90°C respectively. Thermal conductivity of the wall is 0.5 W/mK.

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ESE Mechanical 2015 Paper 1: Official Paper

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1800 W
2000 W
2200 W
2400 W

Answer 1

Concept:

By Fourier’s law of heat conduction

\(Q = \; - kA\frac{{dT}}{{dx}}\)

k = thermal conductivity (W/m-k), A = area of cross section (m²), dT is temperature difference between the two ends of plate and dx is the thickness of the plate

Calculation:

Given, k = 0.5 W/mK, length = 4 m height = 3 m, dx = 0.2 m, T₁ = 150°C and T₂ = 90°C,

A = 3m × 4 m = 12 m²

dT = 90 -150 = -60°C

\(Q = - kA\frac{{dT}}{{dx}} =- 0.5 × 12 × \frac{{\left( { - 60} \right)}}{{0.2}} = 1800\;W\)

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Determine the heat transfer through a plane of length 4 m, height 3 m and thickness 0.2 m. The temperatures of inner and outer surfaces are 150°C and 90°C respectively. Thermal conductivity of the wall is 0.5 W/mK.

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