Consider a 2D rectangular semi-infinite body for which temperature field is known at nodal points in both directions. The temperature is max at the top and goes to zero in the depth direction. In the horizontal direction, it is maximum at the center and goes to zero towards the sides. How to calculate the temperature differentials at various nodes especially at the boundaries of this body?
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The temperature as a function of time at any position in a semiinfinite solid subjected to an external heat flux conforming to equations 5 or 23 can be determined by means of equations 22 or 24, as derived. This method is concerned with the expression for heat flux, and is not dependent upon a knowledge of the surface temperature behavior. It is felt that this method of approach could be utilized in the solution of other problems involving a variable external heat flux, and that a family of solution equations could be obtained to include the most commonly encountered heat flow expressions. The degree of accuracy of this solution is a function of the magnitude of the time intervals chosen. It can be seen from the tables and curves that many points are necessary to determine a curve for each position, or depth, in the solid. Although relatively simple mathematically, the use of equations 22 or 24 can be rather tedious if high accuracy for a number of positions is desired. This type of solution, however, is ideally suited to machine programming because of its simplicity, and the use of a general program for digital computer use of each equation would, the author feels, prove advantageous to those requiring extended application of these solutions
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