Effects of nonhomogeneous nanofluid model on convective heat transfer in partially heated square cavity with conducting solid block

In this study, the conjugate natural convection in a square cavity filled with Al ₂O ₃–water nanofluid with an inner conducting solid block is studied numerically using nonhomogeneous Buongiorno’s two-phase model. The left wall of the cavity is partially heated and the remaining parts of the wall are adiabatic, while the right wall is fully cooled. The top and bottom horizontal walls are adiabatic. The numerical simulations are based on the finite difference method. The results are simulated for various values of the nanoparticle volume fraction (0 ≤ ϕ≤ 0.04) , Rayleigh number (10 ²≤ Ra≤ 10 ⁶) , thermal conductivity of the conjugate square (k_w= 0.28 , 0.76 , 1.95 , 7.0) and 16.0 (epoxy_ 0.28, brickwork: 0.76, granite: 1.95, solid rock: 7, stainless steel: 16), the size of the inner solid (0 ≤ D≤ 0.7) , and the length of the heater (0.1 ≤ H≤ 1.0). The numerical results for the average and local Nusselt numbers, isotherms, distribution of nanoparticles, and streamlines are presented graphically. The findings indicate that increasing the average solid volume fraction and the size of the solid block as well as the thermal conductivity will enhance the rate of the heat transfer at low values of Rayleigh number Ra= 10 ³. On the other hand, increasing these parameters at high values of Rayleigh number (Ra> 10 ⁵) decreases the average Nusselt number.