Alternative multiple-relaxation-time lattice Boltzmann method for simulating conjugate heat transfer

In this paper, an alternative multiple-relaxation-time lattice Boltzmann (LB) scheme for conjugate heat transfer is proposed. We have derived the correct energy governing equation from the first law of thermodynamics and clarified that the thermal boundary for conjugate heat transfer should be the continuity of the conductive heat flux, which is essential to guarantee Galilean invariance. The development of the present model has two distinct features. First, the temperature evolution equation is modified to include the effect of the specific heat capacity. Second, the convection term is considered as a source term and is calculated in moment space, thus preserving the inherent advantages of the LB method without finite difference calculations. To verify the thermal governing equations, we conduct numerical simulations of heat conduction in a moving rod configuration with varying thermal capacities. Furthermore, to validate the present model's in accuracy, we examine several benchmark problems, including the effective thermal conductivity of parallel and series dual-component materials, steady and unsteady coupled heat transfer in horizontal interface channels, stable heat conduction in a two-layer annulus, natural convection in a square cavity with 16 solid blocks, and thermocapillary flow with two superimposed planar fluids. In the realm of application research, we apply our model to simulate the cooling process in random porous media. The results demonstrate that our model achieves satisfactory accuracy and exhibits a second-order convergence rate in space. The simulation results show the potential of the current LB method to simulate complex applications, highlighting its versatility and accuracy.