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 outside radius r 2 that is cooled by ambient air The thermal conductivities of the particle and shell are k 1 and k 2 , respectively, where k 1 2k 2 (a) By a...

KNOWN Size and thermal conductivities of a spherical particle encased by a spherical shell FIND a Re ...

A spherical particle of radius r 1 experiences uniform thermal generation at a rate of q. The

Question:

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.

Chemical reaction Ambient air T h Control volume B Control volume A

(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.

Distribution
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