Numerical analysis of MHD mixed convection flow in a parallelogramic porous enclosure filled with nano uid and in the presence of magnetic field induction

The present study numerically investigated the mixed convection flow of nanouid in a lid-driven parallelogramic porous enclosure subjected to a magnetic field. The induced magnetic field was also considered in terms of the magnetic potential to solve the magnetohydrodynamic (MHD) flow and temperature equations. The Darcy- Brinkman-Forchheimer model with the Boussinesq approximation was adopted, and the finite volume method based on SIMPLE algorithm was utilized to solve the governing equations with appropriate boundary conditions in an orthogonal computational domain. The governing equations in a non-orthogonal physical domain were transformed into a computational domain in an orthogonal co-ordinate by co-ordinate transformations. It was shown that the flow field and heat transfer were greatly sensible for the skew angle variation. Magnetic potential circulated through the parallelogramic porous enclosure with either a high magnetic Reynolds number or magnetic permeability of the nanouid. Results also indicated that the inuence of the external magnetic field on fluid characteristics and heat transfer manifested various fashions, mainly depending on the effective area of the parallelogramic enclosure. Besides, the variations of heat transfer rates while adding nanoparticles or applying magnetic field were affected to some extent by porous medium permeability and Richardson number.