Question: A spherical particle of radius r 1 experiences uniform thermal generation at a rate of q. The particle is encapsulated by a spherical shell of
A spherical particle of radius r1 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 shell are k1 and k2, respectively, where k1 = 2k2.
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(a) By applying the conservation of energy principle to spherical control volume A, which is placed at an arbitrary location within the sphere, determine a relationship between the temperature gradient, dT/dr, and the local radius, r, for 0 < r < r).
(b) By applying the conservation of energy principle to spherical control volume B, which is placed at an arbitrary location within the spherical shell, determine a relationship between the temperature gradient, dT/dr, and the local radius, r, for r1 < r < r2.
(c) On T - r coordinates, sketch the temperature distribution over the range 0 < r1 < r2.
Chemical reaction Ambient air T h Control volume B Control volume A
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