Entropy generation in convective radiative flow of a Casson nanofluid in non-Darcy porous medium with Hall current and activation energy: The multiple regression model

The present article’s primary goal is to analyze entropy generation on unsteady three dimensional thermally radiating magnetohydrodynamic flow of Casson nanofluid past a vertical stretching sheet embedded in a non-Darcy porous medium under the influence of mixed convection, Hall current, viscous dissipation, Ohmic heating, and heat generation. The combined effects of Brownian motion and thermophoretic diffusion are taken into consideration, and the impact of the chemical reaction initiated by activation energy is also incorporated in the flow-field. A mathematical model of the physical problem containing highly nonlinear coupled partial differential equations with convective boundary conditions is developed. Suitable similarity transformation is applied to convert the governing highly nonlinear coupled partial differential equations into nonlinear coupled ordinary differential equations, and then the resulting nonlinear coupled ordinary differential equations are numerically solved with the help of the spectral quasi-linearization method. A detailed investigation is performed to illustrate the impact of several pertinent flow parameters on the velocity, temperature, concentration, entropy generation and Bejan number profiles. In contrast, the numerical values of skin friction coefficients in x and z directions, local Nusselt number, and local Sherwood number are presented in tabular forms for varying values of pertinent flow parameters. Apart from this, linear and quadratic multiple regression analyses for the physical quantities of engineering interest have been executed to upgrade the present model’s efficiency and application in various industrial and engineering processes. With a variation in magnetic parameter, the maximum relative errors in the linear regression estimates for the skin- friction coefficients in x and z directions are found to be 2.28–2.37% and 0.85–1.72%, respectively. Besides, due to the enhancement in magnetic parameter, the maximum relative errors in the quadratic regression estimations for the reduced Nusselt number NuxRex−1/2 and the reduced Sherwood number ShxRex−1/2 are 0.56%−0.58% and 0.30%, respectively. It is observed that the error of each solution of the present physical problem approaches to be less than 10−8 in mere six iterations. Moreover, the findings of the current research work signify that the Brownian motion and thermophoretic diffusion minimize entropy generation adjacent to the sheet; on the contrary, activation energy intensifies entropy generation rate closer to the sheet. Furthermore, the appropriate resemblance is obtained through verifying the present results with previous existing results.