The lattice Monte Carlo method for solving phenomenological mass and heat transport problems

Abstract

In this review paper, we introduce the recently developed Lattice Monte Carlo method for addressing and solving phenomenologically-based mass and heat transport problems especially for composite and porous materials. We describe in detail the application of this method to calculate effective mass diffusivities and to determine concentration profiles. Next, we describe in detail the application of this method to the calculation of effective thermal conductivities/thermal diffusivities and the determination of temperature profiles. Where possible, results of the method are compared with exact results or those from application of the Finite Element method. Excellent agreement is demonstrated.