Mesoscopic approach for steady‐state free convection in a diamond array

The purpose of the present paper is testing an in‐house efficiency algorithm based on lattice Boltzmann method (LBM) and using it to resolve the obtained coupled nondimensional governing equations to analyze two‐dimensional free convection inside a cold outer cavity subjected to a heated cylindrical diamond array. Steady state or oscillatory results are obtained using the Bhatnagar‐Gross‐Krook collision model associated to the thermal LBM. Both the velocity and temperature fields are solved using the D2Q9 models. With different Rayleigh numbers (Ra), the tested free convection can either achieve to steady state or oscillatory. We extended our in house Fortran 90 code using curved boundary conditions and implemented them into a cavity with a diamond array. The numerical simulations were done using distinct Ra (10⁶ and 10 ⁷) and distances between the four neighboring circular cylinders aligned in a diamond array. The effects of several physical parameters, including Ra and position of the hot body array on flow and heat transfer characteristics are investigated. The obtained results are highlighted in the form of streamlines, isotherms, and velocities plots. We show in this paper the stability and the efficiency of the LBM to deal with a complex geometry and its ability to reach suitable convergence criteria for high Ra (10 ⁶ and 10 ⁷). The numerical results indicate that LBM can simulate numerical problems with a high Ra reaching a steady state where we can depict the change of the flow pattern and enhancement of the heat transfer in the presence of heated diamond array.