A Generalized Function in Heat Conductivity Problems for Multilayer Structures with Heat Sources
An accurate analytical solution of the stationary problem of heat conductivity for a multilayer structure with heat sources under asymmetric boundary conditions of the third kind is obtained based on the use of the theory of generalized functions. Using the asymmetric unit function (Heaviside function), the problem for a multilayer structure is reduced to a single-layer with discontinuous (piecewise-continuous) medium properties. By introducing a new independent variable, the nonlinear differential equation (nonlinearity of the second kind—the thermal-physical properties depend on the spatial variable) is reduced to a linear one, direct integration of which allows obtaining an accurate analytical solution of the problem considered. Examples of investigations of the temperature fields for some certain multilayer structures are given.
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