In this paper, we investigate the effect of variation in thermal conductivity on several transient heat transfer problems with the lattice Boltzmann method (LBM). First, benchmark problems involving radiation and/or conduction with constant thermal conductivity are simulated. Then we consider the case of variable thermal conductivity with temperature in solving 2D coupled conduction-radiation heat transfer problem and natural convection in differentially heated enclosure. Both the energy equation and the radiative transfer equation (RTE) were solved using exclusively the lattice Boltzmann method. Good agreement with available data in literature was obtained.

In this paper, we extend the enthalpic formulation introduced in previous work of Hamila et al. [1], to solve transient conduction heat transfer during melting of phase change material. The volume fraction of liquid phase is described by a Heaviside step function smoothly approximated by a logistic curve having a common "S" shape, also called sigmoid curve. Several conduction test problems during melting of some specific phase change material are simulated and comparisons are made with the control volume solutions. The simulation of conduction heat transfer during melting of commercial PCM filling the cavity, in which one or more circular solid blocks (with enhanced thermophysical properties) are embedded, is performed. The proposed formulation can handle accurately conduction heat transfer problem with phase change including interface evolving over time. Special attention is given to distinction between thermophysical properties of solid and liquid phase which are not equal.