Thermal properties of composite materials and porous media: lattice-based Monte Carlo approaches

Ever since its development during World War II as part of the Manhattan Project, the Monte Carlo method has enjoyed countless applications in science and engineering. Intrinsically a computationally very demanding method, the Monte Carlo method has naturally become far more popular as computers have become faster, cheaper and more accessible. In transient thermal conduction problems, the Monte Carlo method using continuous random walks has been commonly used for many years to determine temperature profiles where there are arbitrarily shaped boundaries with arbitrarily varying boundary conditions. Quite recently, a lattice-based Monte Carlo method, which is basically a type of simulation initedifference method, has been developed to determine the effective thermal conductivity in some very simple models of two- and three-component composites and also simple models of porous media. In section 3.2 of this chapter we describe such calculations in detail. The Monte Carlo method also has the potential to be used to provide temperature profiles in composite/porous media models too. This area is yet to be developed. In Section 3.3 we describe some recent preliminary calculations by the present authors