A diffuse interface–lattice Boltzmann model for conjugate heat transfer with imperfect interface

A diffuse interface-lattice Boltzmann model is proposed for modeling conjugate heat transfer problems with imperfect interfaces. According to the continuity condition of heat flux and jump condition of temperature across the imperfect interface, a unified sharp interface equation of the temperature field with a singular source term in the composite media domain is established. Then a diffuse interface equation is obtained by making a smoothed approximation of the unified sharp interface equation. The novel diffuse interface equation is restructured into a second-order heat diffusion equation with an anisotropic diffusion coefficient tensor. To numerically solve the second-order anisotropic diffusion equation, a multiple-relaxation-time (MRT) lattice Boltzmann (LB) scheme is employed. Several numerical simulations of benchmark test examples with analytical solutions are carried out to demonstrate the accuracy of the present model, including the steady-state heat diffusion in a two-layer medium with a flat interface, steady heat diffusion in a square domain with a curved interface and unsteady-state temperature diffusion with two-layer media. The numerical results show that the phenomenon of temperature jump across the imperfect interface can be successfully and correctly captured. Moreover, as an example of practical application, the new proposed diffuse interface model is utilized to predict the effective thermal conductivity of porous media with thermal contact resistance at pore scale. The variation law of the effective thermal conductivity is obtained for each parameter by studying the effects of thermal conductivity ratios of the dual-component material, the shape and volume fraction of blocks in the material, the interfacial thermal conductance coefficient, and the number of blocks on the effective thermal conductivity. Both uniform and random pore structures are considered. The previous theoretical equations strongly support the validity of the present model.