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

Abstract

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 (c ) 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 (c ) 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 heat flux 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 (c ) of fluid is larger than that of solid, which will be eliminated in future work.

Revisiting the second-order convergence of the lattice Boltzmann method with reaction-type source terms

“…A common choice of the speed of sound c s is 1/ √ 3, which reduces the error in higher moments. The moments of the equilibrium distribution are truncated by some authors on the second order terms [5,9,10,12,37,[55][56][57][58][59], by not including the terms u 2…”

A spatially-varying relaxation parameter Lattice Boltzmann Method (SVRP-LBM) for predicting the effective thermal conductivity of composite material

“…The layers-in-series and the layers-in-parallel models are simplified representations of the highest and lowest estimated values in a two-phase composite material [1]. These two models also play very important roles in studying the interfacial effect between the two materials [28]. The theoretical models for predicting the ETCs of series and parallel models were derived based on circuit network of conductors [48], which can be expressed as equation ( 20) and ( 21), respectively.…”