Lattice Boltzmann formulation for conjugate heat transfer in heterogeneous media

Abstract

In this paper, we propose an approach for studying conjugate heat transfer using the lattice Boltzmann method (LBM). The approach is based on reformulating the lattice Boltzmann equation for solving the conservative form of the energy equation. This leads to the appearance of a source term, which introduces the jump conditions at the interface between two phases or components with different thermal properties. The proposed source term formulation conserves conductive and advective heat flux simultaneously, which makes it suitable for modeling conjugate heat transfer in general multiphase or multicomponent systems. The simple implementation of the source term approach avoids any correction of distribution functions neighboring the interface and provides an algorithm that is independent from the topology of the interface. Moreover, our approach is independent of the choice of lattice discretization and can be easily applied to different advection-diffusion LBM solvers. The model is tested against several benchmark problems including steady-state convection-diffusion within two fluid layers with parallel and normal interfaces with respect to the flow direction, unsteady conduction in a three-layer stratified domain, and steady conduction in a two-layer annulus. The LBM results are in excellent agreement with analytical solution. Error analysis shows that our model is first-order accurate in space, but an extension to a second-order scheme is straightforward. We apply our LBM model to heat transfer in a two-component heterogeneous medium with a random microstructure. This example highlights that the method we propose is independent of the topology of interfaces between the different phases and, as such, is ideally suited for complex natural heterogeneous media. We further validate the present LBM formulation with a study of natural convection in a porous enclosure. The results confirm the reliability of the model in simulating complex coupled fluid and thermal dynamics in complex geometries.

A lattice Boltzmann model for heat transfer in heterogeneous media

“…There is no obvious difference between them. The continuity of temperature and of temperature gradient across the interface of solid media can be guaranteed exactly in the present numerical prediction, which is important for conjugate heat transfer simulation [17][18][19][20][21]. Furthermore, in the models proposed in Refs.…”

“…Compared with some of the available LB approaches for conjugate heat transfer simulation [17][18][19][20], the present model is easier to be implemented as here no interface should be treated explicitly. Although the complexity induced by interface treatment can be avoided in several previous LB models [21,22], they suffer a number of obvious shortcomings. In Ref.…”

“…Furthermore, in the models proposed in Refs. [17][18][19][20][21], the thermophysical properties of each solid material layer should be assumed spatially identical, but such assumption may not meet the requirements of real situations. In the present model, such restriction does not exist and the thermophysical properties of each solid material layer can vary arbitrarily.…”

“…In Ref. [21], to meet the conjugate heat transfer condition, a source term was designed and added to the LB evolving equation. However, the source term is a nonlocal operator with only first-order accuracy.…”

“…combustion), these two assumptions can hardly be met. Recently, some scholars discussed how to model conjugate heat transfer by the LB method [17][18][19][20][21][22]. For conjugate heat transfer, the investigated domain is consisted of several different medium layers, and the specific heat capacity and/or thermal conductivity of the medium layers may be different with each other.…”