Entropy generation and thermal analysis in quadratic translation of sodium alginate with MHD and porosity effects

Combined effects of magnetic field and porous media on non-Newtonian fluid flow are investigated in this work. Here, sodium alginate (C6H9NaO7) is used as a counter-example to Casson fluid, which is regarded as a non-Newtonian fluid. The fluid (along a vertical plate) experiences quadratic translational motion. This work considers the natural or free convection phenomenon. Based on accurate initial and boundary conditions, the problem is initially represented in terms of linear partial differential equations. The Laplace transform method (LTM) is applied to solve the post-transformation problem, and precise solutions are established for temperature and fluid velocity in terms of special functions (error and complementary error functions). Entropy generation (EG) and Bejan number (BN) analytical results are established in the presence of MHD and porosity effects. Expressions are provided for both the skin friction coefficient and the rate of heat transfer. Numerical solutions and graphs are obtained using the finite difference approach. The results of the investigation demonstrated that MHD and porosity have a significant impact on not only the flow analysis but also EG and BN. With a higher Hartmann number, it is discovered that the magnitude of the EG is greater than the BN, but the BN is changed in a more powerful way. According to the porosity effect, entropy generation decreases as a medium becomes more porous, while the BN rises.