A lattice Boltzmann algorithm for simulating conjugate heat transfer through virtual heat capacity correction

A fundamental problem for lattice Boltzmann method (LBM) to simulate conjugate heat transfer between solid and fluid is that lattice Boltzmann equation (LBE) can only retrieve standard energy equation when solid has the same heat capacity (ρc) with that of fluid. When their heat capacities are different, the continuity of heat flux cannot be kept at the interface for conventional LBM. In present work, a lattice Boltzmann algorithm for simulating conjugate heat transfer through virtual heat capacity correction method is proposed to solve this problem. This algorithm, at first, assume that the solid has the same heat capacity (ρc) with that of fluid to keep the continuity of heat flux at the interface between solid and fluid, after that modify the temperature field and the distribution function according to real data of heat capacity of fluids or solids at the end of each time step. This algorithm also fits to conjugate heat conduction problems between solid and solid as long as we take one of the solids as a kind of fluid that does not flow. Several test cases including both steady and transient conjugate heat transfer with flat or curved interface are calculated to validate the present method. The results show that the proposed method has a very good performance in simulating solid-fluid and solid-solid conjugate heat transfer, which is easy in implementation, capable for solving both steady and transient heat transfer problems. Also, the present method can deal with curved interface easily without a necessary to find the normal direction of interface. However, this method suffers a stability problem while the heat capacity (ρc) of fluid is larger than that of solid, which will be eliminated in future work.