Bernstein operational matrix of differentiation to analyze the conductive, convective, and radiative non-linear sublimation model with temperature-dependent internal heat generation

Abstract

Theoretical modeling of solid-vapor phase change process, known as sublimation, is of much interest in the pharmaceutical industry and freeze-drying technology. While past theoretical studies on sublimation assume that the phase change material (PCM) remains in direct contact with the heat source or sink with no heat loss due to the surrounding temperature, in most practical scenarios, PCM experiences less heat on its surface due to the loss of some amount of heat in the surrounding environment. Considering the impact of heat radiation on the porous surface is essential for ensuring the precision of the phase change process. The present study reports a theoretical model of a sublimation problem where heat generation is in proportion to the local temperature and loss of heat due to thermal radiation occurs in the porous medium. In connection with thermal radiation, a convective boundary condition is assumed at the surface of the porous body. The solution of the non-linear mathematical model is determined numerically via the Bernstein operational matrix of differentiation method. It is found that temperature-dependent heat generation enhances the temperature within the porous medium and thus, the rate of sublimation increases, while it is delayed due to heat loss through the radiation.