THE THERMAL RESPONSE OF A METAL SLAB TO A CLASS OF RADIALLY DEPENDENT HEAT INPUTS
OHIO STATE UNIV RESEARCH FOUNDATION COLUMBUS ANTENNA LAB
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The temperature fields are deduced for an infinite metal slab of finite thickness produced by a heat flux input which depends on the radial coordinate. The formal solution is obtained by means of transform techniques, and several alternative approaches to their evaluation are presented. Two heat flux inputs are considered in detail. They are the Gaussian input and the uniform input over a circular area of the front surface. Such inputs might be used, for example, as models for a study of the thermal-elastic effects of a laser beam focused on a metal slab. Several asymptotic expansion are presented for the small-time response of the temperature fields under various assumptions on the heat flux input. An extension of the results of Oosterkamp has been derived as well as a verification of the validity of the approximations through the derivation of an upper bound on the error.
- Lasers and Masers