The thermal response of a metal slab to a class of radially dependent heat inputs

Summary 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.Several representations of the Green's function are obtained as well as two approximate representations. One of these approximations converges well for time large the other for time small.A small time asymptotic expansion is given for input flux densities which satisfy certain smoothness requirements.Two inputs have been considered in detail. One is the uniform spot and the other is the Gaussian. An extension of the results obtained by Oosterkamp³) has been obtained along with an estimate of the validity.The work reported in this paper was supported in part by Contract AF 30(602)-2305 between The Ohio State University Research Foundation and Rome Air Development Center, Griffiss Air Force Base, New York.