Critical Analysis of Two-Dimensional Heat-Balance Equations for Composite Plates Obtained According to the Variational Principles of the Theory of Heat Conduction. II. Model Problem

We obtain analytic solutions of the model problem stationary heat conduction for a composite plate. These are constructed with help two methods aimed at reducing dimensionality, namely, method weighted residuals (the generalized Galerkin method) and variational method. consider homogeneous rectangular elongated plate made an anisotropic material in general form. The front faces structure thermally insulated; temperature is specified on one longitudinal end face plate, whereas flux given other face. It assumed that input data its solution independent coordinate. field approximated by second-order polynomial transverse also take into account boundary conditions imposed faces. shown that, case application residuals, resolving differential equation has second order. At same time, method, it fourth In obtained integral tangential direction constant equal to true value this quantity. using indicated oscillates orthogonal frequency amplitude these oscillations depend relative thickness structure. Moreover, can be higher than several orders magnitude. computed dimensionality similar oscillating character.