Off-lattice Boltzmann simulation of conjugate heat transfer for natural convection in two-dimensional cavities.

This study addresses the inadequacy of isothermal wall conditions in predicting accurate flow features and thermal effects in multicomponent systems. A finite-difference characteristic-based off-lattice Boltzmann method (OLBM) with a source term-based conjugate heat transfer (CHT) model is utilized to analyze buoyancy-driven flows in two-dimensional enclosures. The source term-based CHT model [Karani and Huber, Phys. Rev. E 91, 023304 (2015)1539-375510.1103/PhysRevE.91.023304] is extended to handle curved conjugate boundaries. The proposed CHT-OLBM solver is verified using analytical solutions and reference data from the literature. The effects of wall conduction on conjugate natural convection (CNC) problems in square and horizontal annular cavities are systematically examined with a solid wall of a nondimensional thickness of 0.2. For the square cavity problem, the governing parameters considered are 10^{5}≤Gr≤10^{9} and χ=1,5,10, while for the horizontal annulus problem, the governing parameters are taken as 10^{5}≤Ra≤10^{7} and χ=1,5,10,100, where Gr is the Grashof number, Ra is the Rayleigh number, and χ is the thermal conductivity ratio. Qualitative analysis of the simulation results using isotherms and streamlines and quantitative analysis of the local fluid-solid interface temperature, solid wall temperature distribution, Nusselt number profiles, overall Nusselt number, and effective Grashof/Rayleigh number is conducted. The overall heat transfer reduction inside the cavities due to a solid wall is quantified, and correlations are obtained to represent the overall heat transfer inside both enclosures. The findings demonstrate the significance of CHT analysis, and the CHT-OLBM solver developed in this study can successfully investigate steady, unsteady, and chaotic CNC flows.