Boundary Characteristics for the Generalized Heat-Conduction Equation and Their Equivalent Representations

On the basis of the consideration of the boundary-value problem for the generalized equation of heat conduction in bounded nonuniform spaces with Dirichlet, Neumann, and Robin boundary conditions, corresponding sequences of boundary characteristics have been obtained. For each of these sequences, definite integro-differential representations (relations) have been constructed. It has been shown that approximate analytical solutions can be obtained for bounded nonuniform regions with variable transfer coefficients in the Cartesian, cylindrical, and spherical coordinate systems. On the basis of systems of algebraic equations, approximate analytical solutions have been constructed with approximately equal accuracies independently of the calculation scheme used (with the introduction of the temperature-disturbance front or without it, i.e., by multiple integration of the heat-conduction equation over the whole computational region). These solutions have a negligibly small error and, therefore, can be considered as conditionally exact.