Nonlinear thermal interaction between a heat-generating particulate bed and a solid

The process of combined conduction and radiation in a large, heat-generating, dry particulate bed in sudden contact with a semi-infinite solid is studied analytically by a successive approximation method and numerically by a finite difference method. The transient behavior of the system, in particular, the behavior of the temperature at the particulate bed-solid interface, is obtained as a function of two dimensionless controlling parameters. Also obtained are the conditions leading to incipient melting of the system. Based upon the finite difference solution, the present approximate method, which is shown to be rather simple and convenient to use, is found to yield rapidly converging and sufficiently accurate results