Lattice Boltzmann simulations of heat transfer in flow past a cylinder and in simple porous media

The Lattice Boltzmann method has been further developed for flow and heat transfer computations in terms of two distribution functions. A modified boundary scheme for heat transfer has been proposed for curvilinear fluid–solid interfaces, based on a weighted relaxation time. Weight coefficients depend on the interface location with respect to the regular lattice. The approach has been validated for two cases in a simple and more complex geometry: a non-isothermal flow past a single circular cylinder and in simple porous (granular) media. Computations have been performed with the use of the new boundary scheme for curvilinear interfaces and compared to a standard scheme known from the literature. For the circular cylinder case, results for the local and averaged Nusselt numbers are validated with the outcome of other numerical methods and with experimental data. For the more complex geometry, two configurations are considered: a regular array of square cylinders and a random arrangement of circular cylinders to simulate a granular medium. The results for the Nusselt number are compared, after a suitable volume averaging, with available semi-empirical correlations.