Conjugate Heat Transfer Simulations Using Characteristic-Based Off-Lattice Boltzmann Method

The present study uses a characteristic-based off-lattice Boltzmann method with a conjugate heat transfer model to study natural convection inside a square enclosure with a finite-thickness conducting solid vertical wall. A conjugate heat transfer model based on source term formulation is implemented, which considers the effects of thermal inertia for steady and transient conditions. The Prandtl number, Pr, and the Grashof number, Gr, were set to \(0.7\) and \(10^{5}\) , respectively. Other parameters selected are the non-dimensional solid wall thickness ratio, \(w/L = 0, 0.12, 0.2\) , and the solid wall to fluid thermal conductivity ratio, \(\xi = 1, 5\) . The inclusion of the solid wall heat conduction has resulted in lower values of the average Nusselt number, \({\text{Nu}}_{{{\text{avg}}}}\) , which emphasizes the importance of conjugate heat transfer study for practical applications. Due to the presence of temperature gradients in the solid wall, the resulting fluid–solid interface temperature distribution is non-uniform, and the flow circulation pattern becomes asymmetric. As the value of \(w/L\) increases, a reduction in the value of \({\text{Nu}}_{{{\text{avg}}}}\) is observed. Similarly, for small values of \(\xi\) , the value of \({\text{Nu}}_{{{\text{avg}}}}\) is lower than the maximum values of \(4.082\) observed in the case of isothermal boundary condition.