S-functions in a regional analytical modeling of heating modes of electrode modules of MHD-generators wall channels - Слесаренко, Анатолій Павлович; Кобринович, Юлія Олегівна; Загоруйко, Станіслав Юрійович (Eastern-European Journal of Enterprise Technologies, 2012)
The article suggests a new regional structural methodology of mathematical modeling of thermal processes in composite electrode modules of walls of MHD generators. The effect of cooling systems of the electrode modules and the impact of 20% and 50% heater entrainment on the nature of the thermal process change in the electrode modules are taken into account. There is the analysis of dependence between growth of heater entrainment and increase of temperature gradient in the rest of heater. It was revealed that the temperature of the central part of the heater surface reduced to 200 K at 50% entrainment (uniformly along the length of the slot), and increased to 200 K at 50% heater entrainment for a parabolic profile. Regional analytical structures of solution of appropriate problems of heat conductivity exactly satisfy the boundary conditions of problems and the conditions of the thermal contact at the boundaries of the contact of heterogeneous mediums. They are universal, concerning the change of geometric shapes of areas of study and boundaries of the contact of heterogeneous mediums. The accurate information about the geometry of the boundaries of areas and boundaries of the contact is given by S-functions, allowing for the first time in the world scientific practice to solve the inverse problems of differential geometry for given areas of any given ​​complex shape. The functions of temperature, determined by conservative structures of solution, are continuous and limited, and have continuously differentiable limited derivatives. The splines and regional structures of solution are more native in approximation theory for boundary value problems than polynomials and general structures of solution