The coupling relation between the excess temperatures in an active element

Abstract

@(X, Y ) = O(X*, Y) O(X, Y*), (1) 0 (X*, Y*) where @(X, Y) is the dimensionless (excess) temperature and X*, Y*, X, Y are fixed and variable coordinates. In [2] on the basis of analyzing experimental data and known solutions of problems of heat conduction and the electromagnetic field in the interelectrode gap, it was shown that Eq. (I) is not always satisfied to a given accuracy, but only for a strictly defined set of thermal, geometric, and other parameters. Establishing the necessary and sufficient conditions for satisfying Eq. (I) is stimulated by the solution of a series of applied problems, especially for those experimental cases when it is complicated to measure, for example, the temperature inside an active element. THEOREM. Let a function of internal heat sources have the form w (x, Y) = w1 (x) w~ (Y), (2) where WI(X) and W2(Y) are continuous functions, which satisfy the differential equations W~xx = ~W~, W2vv = ~W~, O < X < I, O < F < R, (3 ) f o r t h e boundary c o n d i t i o n s W x (0, Y) BizW (0, Y) = O;