Question

A spherical particle of radius ri experiences uniform thermal generation at a rate of q. The particle is encapsulated by a spherical shell of outside radius r2 that is cooled by ambient air. The thermal conductivities of the particle and the shell are kı and k2, respectively, where kı - 2k2. Chemical reaction 9 Ambient air oo 1 Control volume B Control volume A (a) By applying conservation of energy principle to spherical control volume A, which is placed at ar arbitrary location within the sphere, determine a relationship between the temperature gradient dT/dr and the local radius r, for O 5 r STı. [ans:..4 itr+ 3 dr (b) Bv applving the conservation of energy principle to spherical control volume B, which is placed at an arbitrary location within the spherical shell, determine the relationship between the temperature gradient dT/dr and the local radius r, for r1.< r S T2- dr (c) On T-r coordinates, sketch the temperature distribution over the range 0 T2.

Answer 1

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