Investigating convective and conductive heat transfer in square and circular heated bodies: A novel approach using coupled Runge-Kutta and lattice Boltzmann method

This study presented a novel approach to solving thermal problems (convection and conduction) using the multirelaxation time lattice Boltzmann method (MRT-LBM) coupled with Runge-Kutta finite difference schemes to perform numerical simulations of natural convection in a conjugate heat condition for two types of geometries recognized by the scientific community within a square cavity. The study examined the effects of Rayleigh number (Ra) and the solid/fluid conductivity ratio (Kr = Ks/Kf) on flow and heat transfer. In contrast to previous studies, this research varied the Kr ratio from 1 to 1000 for the square body and from 1 to 100 for the circular body. The results displayed that heat transfer and flow characteristics become more complex and turbulent as the Ra increases. Moreover, as the Kr ratio increased, heat transfer from the solid bodies to the fluid was enhanced, with an improvement of 238% for the circular obstacle case, while the square obstacle case showed a 29.8% enhancement. Additionally, an increase in fluid motion within the cavity, controlled by the Rayleigh number, results in an improvement of approximately 288% for Ra = 106 compared to Ra = 103 for the circular obstacle and a 71.4% increase for the square obstacle. This study provided valuable insights into natural convection phenomena in a conjugate heat condition of the two bodies confined within a cavity and has potential applications in various industrial and engineering fields.