Analyzing the 3D-MHD flow of a sodium alginate-based nanofluid flow containing alumina nanoparticles over a bi-directional extending sheet using variable porous medium and slip conditions

The sodium alginate (SA)-based nanofluid flow comprising alumina nanoparticles on a bi-directional extending sheet has many applications, which include thermal management, automotive radiators, industrial heat exchangers, conductive coatings, flexible electronics, electromagnetic shielding, solar panels, etc. A numerical study based on the SA-based nanofluid flow containing alumina nanoparticles over a bi-directional extending sheet in the presence of variable Darcy porous media has not yet been examined. Therefore, this study focuses on numerically investigating the flow behavior of a nanofluid of SA containing nanoparticles of alumina (Al2O3) over a bi-directional extending sheet. The variable Darcy porous media, magnetic field, thermal radiation, and thermal-dependent and space-dependent heat sources are applied to examine heat transfer flow. The velocity and thermal slip conditions have been used in the present model. The model is first shown as partial differential equations and is then converted to ordinary differential equations (ODEs). A numerical technique called bvp4c MATLAB function is applied to solve the modeled ODEs. The model is validated with previously published results. From the obtained results, it is found that high magnetic factor increases the thermal distribution, skin frictions, and heat transfer rate and reduces the velocity profiles along both directions. The Casson factor reduces the skin friction, heat transfer rate, and velocity profiles along both directions while increasing the thermal distribution. High velocities and temperature distributions of a SA-based nanofluid flow containing alumina nanoparticles are found for the scenario of no-slip condition when matched to the slip condition. It is concluded from the observed results that the percentage increase is higher for the no-slip conditions compared to the slip conditions.