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An analytical solution of transient 3D heat equation based on integral transform method is derived. The result are compared with numerical solution, and good agreements are obtained. Minimization of response time and temperature distribution through a laser slab are tested. It is found that the increasing in the lateral convection heat transfer coefficient can significantly reduce the response time and the temperature distribution while no effect on response time is observed when changing pumping profile from Gaussian to top hat beam in spite of the latter reduce the temperature distribution, also it is found that dividing the pumping power between two slab ends might reduce the temperature distribution and it has no effect on thermal response time.
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