Some explicit solutions to the multidimensional inverse problem of transient heat conduction

The inverse problem of heat conductivity and heat transfer coefficient determination is considered for the case of linear and nonlinear transient heat transfer. For linear heat transfer, these coefficients depend on the spatial variables and time, while in nonlinear heat transfer, they depend only on the temperature distribution. Under experimentally realizable assumptions, explicit equations for these coefficients are obtained which can be used as the basis of experimental methods for determining thermophysical variables, filtration properties, and other characteristics of fluids.