GENERALIZED NUMERICAL-SOLUTION OF THE HEAT-CONDUCTION PROBLEM IN SOLIDS OF DIVERSE CONFIGURATION UNDERGOING CONVECTIVE COOLING

A numerical solution has been obtained for a very general thermophysical problem including a large number of heat conduction cases. An inhomogeneous partial differential equation of thermal conduction has been integrated by means of the finite-difference method. Inhomogeneous third-kind boundary conditions and an initial condition expressing a spatial unevenness of the temperature are applied to different geometries of the body. A mathematical model has been developed for determining the unsteady-state temperature field and the duration of the cooling (or heating) of solids of different configurations by using a universal approach. The three classical one-dimensional bodies (infinite slab, infinite cylinder and sphere) are studied, as well as various complicated multidimensional solids by using a rational approach for reducing the multidimensional problem to a one-dimensional one. (As has been accepted in heat-transfer theory, an m-dimensional solid (m = 1,2,3) means a body with an m-dimensional temperature field.) The initial temperature distribution and the ambient fluid temperature have been considered as arbitrary functions of the variable of space and time, respectively. Moreover, the volumetric specific power of the internal heat source is an arbitrary function of the spatial coordinate and time. An effective algorithm intended for numerical simulation software has been proposed. The model can also be applied to other physical transfer processes having mathematical descriptions analogous to that of heat conduction (molecular diffusion, etc.).