Finite element analysis of nanofluid flow and heat transfer in a square cavity with two circular obstacles at different positions in the presence of magnetic field

A constructal design-based model is used to examine thermal management and heat augmentation inside a square cavity which is filled with Cu-water nanofluids. The concept of using varied pair impediments in the cavity is applied for the first time. A system of partial differential equations is used to derive the mathematical structure of the governing flow, which is then translated into a non-dimensional form using dimensionless variables. Numerical experiments are carried out by using a Galerkin finite element scheme for various values of the associated physical parameters. The effects of key parameters on streamlines, isotherms, dimensionless temperature, and Nusselt numbers are explored for various values of the Rayleigh number. Because of the synchronous motion, the streamlines and isotherms have a symmetrical distribution. The average Nusselt number drops as the Rayleigh number increases. It's worth noticing that as compared to the zero volume fraction parameter, the Nusselt number drops for all values of Ha. However, the Nusselt number increases dramatically for different values of phi.