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Thermodynamics HW Solutions 92

Thermodynamics HW Solutions 92 - Chapter 2 Heat Conduction...

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Chapter 2 Heat Conduction Equation 2-43 A spherical shell of inner radius , outer radius , and thermal conductivity k is considered. The outer surface of the shell is subjected to radiation to surrounding surfaces at T . Assuming no convection and steady one-dimensional conduction in the radial direction, the radiation boundary condition on the outer surface of the shell can be expressed as r 1 r 2 surr r 1 r 2 T surr k ε −= k dT r dr Tr T () 2 2 4 εσ surr 4 2-44 A spherical container consists of two spherical layers A and B that are at perfect contact. The radius of the interface is r o . Assuming transient one-dimensional conduction in the radial direction, the boundary conditions at the interface can be expressed as t Trt AB (, ) ) 00 = r and k Trt x k x A A B B ) ) 2-45 Heat conduction through the bottom section of a steel pan that is used to boil water on top of an electric range is considered (Fig. P2-45). Assuming constant thermal conductivity and one-dimensional
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