Abstract
Abstract The present work is devoted to the collocation solution of some stationary temperature problems in regions with geometrical symmetry, temperature symmetry and/or antisymmetry with respect to 2 and 4 axes. Such problems are encountered e.g. in solving tube sheets of heat exchangers. The success of collocation solution depends on the suitability of the temperature function used. At first, two (auxiliary) temperature functions are derived using the simple harmonic series, one being symmetrical and the other antisymmetrical about the x-axis. Further, the method of deriving 7 harmonic temperature functions and their resulting forms is given for 3 (4) types of problems with geometrical symmetry about 2 (4) axes. The obtained functions satisfy a priori all conditions of symmetry and/or antisymmetry of the problem. The coefficients of the temperature functions are determined by the boundary point least squares method. KOLOKT, a program set up for the desk computer HP 9845 is described and some results are given. The technique described can be applied also to the derivation of stress functions and to the solution of thermal stresses.
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