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GATE 2024 Chemical Engineering, Q34 · Heat Transfer

The correct answer is 48.

Question

The opposite faces of a metal slab of thickness 5 cm and thermal conductivity 400 W/(m·K) are maintained at 500°C500°C and 200°C.200°C. The area of each face is 0.02m2.0.02 m². Assume that the heat transfer is steady and occurs only in the direction perpendicular to the faces. The magnitude of the heat transfer rate, in kW, rounded off to the nearest integer, is _______

Official answer: 48

Why

GATE 2024 official key: 48. Steady, 1-D conduction perpendicular to the faces → Fourier's law Q =kAΔT/L= kA\Delta T/L applies directly: Q =400×0.02×(500−200)/0.05=48,000= 400 \times 0.02 \times (500−200)/0.05 = 48,000 W = 48 kW.

Explanation cross-checked for consistency. Final answer matches the official IIT answer key.

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