MHD Mixed Convection of Nanofluid in a Lid-Driven Porous Trapezoidal Cavity with a Heated Obstacle

This study uses numerical simulation to model MHD mixed convection nanofluid flow within a permeable trapezoidal chamber with a heated obstacle. Considered are the volume fractions (1–5%) of copper (Cu), alumina (Al₂O₃), and silver (Ag) nano-sized particles when mixed with water (H₂O). With a constant velocity, upper wall moves left to right while bottom wall steps from right to left. A lower temperature is kept on upper wall, while left, right, and bottom walls are kept at warmed. There are two types of obstacles inside the enclosure: a constant square heated obstacle (case-I) and a heat-generating square obstacle (case-II). To investigate how the liquid flow and heat transport properties within the chamber are impacted with the Darcy number (Da) and Richardson number (Ri), the governing PDEs are solved by Galerkin weighted residual based finite element technique. Results are compared to published papers to validate the computational process. The findings are displayed using streamlines, isotherms, temperature, and velocity profiles, and mean Nusselt numbers. The outcomes demonstrate that when Richardson number rises, heat transportation rate increases. It is shown that an effective control parameter for temperature transport is Darcy number. Moreover, it is found that when only 5% nanoparticles are used, heat transport rate augment by 17.12%. Richardson number is an effective control parameter for heat transport via a porous material enclosure. Mass and heat transport rates both rise with an increment in the thermal Darcy number. Furthermore, the flow strength rises as Richardson number rises. Moreover, the average Nu increases by 15.27% for 5% nanoparticles volume at \(Da=1{0}^{-2}\) $Da=10^{-2}$ in case I whereas it increases only 0.3% for same number of nanoparticles in case II.