Numerical Study of Thermal Conduction and Convection Using Lattice Boltzmann and Finite Difference Methods

This paper presents a 2D numerical analysis of thermal conduction and convection phenomena using a hybrid Lattice Boltzmann-Finite Difference (LB-FD) model. The study focuses on the simulation of conjugate heat transfer in a cavity filled with air. This cavity is characterized by two cold vertical walls and a relatively thick bottom part, considered solid and heated from below. The study aims to examine the impact of the choice of solid material on the heat exchange process. Analysis of the findings indicates that increasing the value of the thermal conductivity of the material increases the rate of heat transfer inside the cavity. For example, for a Rayleigh number set at \({10}^{6}\) , the results show that heat exchange increases by 156.97% when the solid/air thermal conductivity ratio is increased from 1 to 800. The study suggests that the LB-FD approach is an appropriate method to simulate thermal conduction and convection phenomena and can be employed to study more complex thermal problems with conjugate heat transfer.