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Consider a pair of concentric cylinders with a height of 24 mm. The smaller cylinder has a radius of 12 mm. The inner and outer radius of the larger, hollow cylinder is 24 mm and 25 mm, respectively. The same boundary condition and the initial condition from the shell and specimen tutorial will be used: Convection on the outer surface of the larger, hollow cylinder, and two radiation boundary conditions for each emitting surface. The larger, hollow cylinder will be set to 22 degress Celsius and the smaller cylinder will be set to -273.15 degrees Celsius.

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Analytic Solution

Assume only the inner surface of the larger, hollow cylinder and the cylindrical surface of the smaller cylinder are emitting radiation. Also assume the surfaces are gray and diffuse. The net radiation of an emitting surface of this concentric cylinder, two-surface enclosure is give below:

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In this convention, the subscript "1" denotes the smaller cylinder and the subscript "2" denotes the larger, hollow cylinder. Since this is a two-surface enclosure problem, we can expect the view factor for each surface to be 1. All the radiation emitted by one surface is intercepted by the other surface. The notation of the above equation is the net radiation of the smaller cylinder.

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