Subtopic: Steady state heat transfer in conduction, convection and radiation
Question Statement:
One-dimensional generalized heat conduction equation representing temperature distribution in a sphere, based on thermal conductivity k, specific heat capacity Cp, density ρ, and energy generation E, can be written as (1/rⁿ)·∂/∂r(rⁿ·k·∂T/∂r) + E = ρCp·∂T/∂t, where the value of n is
Options:
(A) 1
(B) 2
(C) 3
(D) 4
Official Answer Key:
B
Step-by-Step Solution & Explanation
The generalized 1-D conduction equation with geometry factor n takes n = 0 for a plane wall (Cartesian), n = 1 for a cylinder, and n = 2 for a sphere — the spherical Laplacian in r involves r² in exactly this position. Hence n = 2, matching (B).
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