Critical Analysis of Two-Dimensional Heat-Balance Equations for Composite Plates Obtained According to the Variational Principles of the Theory of Heat Conduction. I. General Two-Dimensional Theories

We apply variational principles to consider two approaches the construction of two-dimensional equations theory stationary heat conduction composite plates. The temperature plates is approximated by a polynomial in transverse coordinate with unknown coefficients expansion. Within framework first approach, thermal boundary conditions on front surfaces are neglected but obtained Euler and corresponding edges consistent from thermophysical point view because, according these equations, heat-balance equation true for any subdomain plate entire structure (as whole). second taken into account. This circumstance explains necessity introducing undetermined Lagrange multipliers, i.e., leads solution problem conditional extremum. It shown that inconsistent (contradictory) because holds neither plate, nor