Abstract
I 1950, Jaeger wrote . . . the complete solutions of transient problems on composite walls, even in the simplest case of two layers only, are so very complicated as to be practically useless. When one uses a modern high-speed computing machine, this remark is no longer true. 'A Fortran program for the IBM 7090 was written recently for calculating temperatures in a two-layer slab by means of an analytical solution. It did not take long to write the program, and results are obtained fairly quickly. It is the purpose of the present paper to give some of the details of this study in order to encourage others to write similar programs for their computing machines. The solution to the problem under consideration will be taken from Ref. 2 with certain modifications. For a twolayer slab it is convenient to have the origin of coordinates at the interface, so that a\, 61, a2, and 62 in Ref. 2 will be changed to — si, 0, 0, and s2, respectively. Then x will be replaced by —x in region 1. In addition, there will be changes in notation and trigonometric modification of equations. For example, K», &„, and yin there will be replaced by 1/ju;, jLttOjn , and HiSitOn here. Finally, the problem will be generalized by including heat generation in each medium. With these revisions in mind, the problem may be formulated as follows:
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