Free convection flow and heat transfer of nanofluids in a cavity with conjugate solid triangular blocks: Employing Buongiorno’s mathematical model

Abstract

This study aims to investigate the conjugate natural convection heat transfer of nanofluids in a square enclosure with two solid triangular walls. The left and right walls of the cavity are held at a constant temperature of Th and Tc, respectively, whereas the bottom and top are insulated. To assess the nanoparticles distribution inside the cavity that induced from the thermophoresis and Brownian motion, the Buongiorno’s model was used. The governing nonlinear equations were solved in a non-uniform unstructured grid by employing the Galerkin finite element method. The governing parameters are Rayleigh number (103≤ Ra ≤ 104), thermal conductivity ratio of solid walls to the fluid (1 ≤Rk≤ 500), thermal conductivity parameter (3 ≤ Nc ≤ 15), thermal viscosity parameter (3 ≤ Nv ≤ 15), Brownian motion parameter (5×10−7≤Nb≤5×10−6), Thermophoresis parameter (10−7≤Nb≤ 10−6), thickness of the triangular walls (0.1 ≤ m ≤ 0.75) and the position of the blocks (normal or reverse position). The numerical results are reported as contours of isotherms, streamlines, heatlines and isoconcentrations and the local and average Nusselt numbers. The results show that the presence of the triangular blocks boosts the overall rate of heat transfer. The average Nusselt number increases as the Rk decreases. The overall rate of heat transfer decreases when the triangular walls are placed in the reverse position.