Transient heat conduction in a plate subjected to heating and/or cooling by combined convection and radiation has been studied. The plate is assumed to be homogeneous, isotropic, and opaque to thermal radiation. The initial temperature distribution and the ambient environment as well as fluid temperatures are considered to be constant. In the analysis the transient heat-conduction equation and the boundary conditions are transformed to a nonlinear Volterra integral equation of the second kind for the surface temperature. This equation is solved numerically on a digital computer by the method of successive approximations. Precise results accurate to at least four significant figures have been obtained for a range of parameters of physical interest and are presented graphically as well as compared with approximate solutions and results available in the literature. Asymptotic solutions for small and large times are also given and their range of validity discussed. © 1968.
