Temperature Profile in Semi-infinite Body With Exponential Source and Convective Boundary Condition

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Abstract
An analytical solution for the temperature profile in a semi-infinite body with an exponentially decaying (with position) source and convective boundary condition is obtained using Laplace transforms. The appropriate dimensionless parameters are identified and the temperature as a function of these parameters is presented in graphic form. With cooling at the exposed surface, the maximum temperature occurs in the interior of the slab instead of at the exposed surface. The location of the temperature maximum as a function of the various system parameters is presented in graphic form. Approximate relationships are presented for small values of dimensionless time.

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