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The present article provides a detailed analysis of entropy generation on the unsteady three-dimensional incompressible and electrically conducting magnetohydrodynamic flow of a Casson nanofluid under the influence of mixed convection, radiation, viscous dissipation, Brownian motion, Ohmic heating, thermophoresis and heat generation. At first, similarity transformation is used to transform the governing nonlinear coupled partial differential equations into nonlinear coupled ordinary differential equations, and then the resulting highly nonlinear coupled ordinary differential equations are numerically solved by the utilization of spectral quasi-linearization method. Moreover, the effects of pertinent flow parameters on velocity distribution, temperature distribution, concentration distribution, entropy generation and Bejan number are depicted prominently through various graphs and tables. It can be analyzed from the graphs that the Casson parameter acts as an assisting parameter towards the temperature distribution in the absence of viscous and Joule dissipations, while it has an adverse effect on temperature under the impacts of viscous and Joule dissipations. On the contrary, entropy generation increases significantly for larger Brinkman number, diffusive variable and concentration ratio parameter, whereas the reverse effects of these parameters on Bejan number are examined. Apart from this, the numerical values of some physical quantities such as skin friction coefficients in x and z directions, local Nusselt number and Sherwood number for the variation of the values of pertinent parameters are displayed in tabular forms. A quadratic multiple regression analysis for these physical quantities has also been carried out to improve the present model’s effectiveness in various industrial and engineering areas. Furthermore, an appropriate agreement is obtained on comparing the present results with previously published results.

Unsteady hydromagnetic natural convection boundary layer flow of a viscous, incompressible, and electrically conducting dusty fluid past an impulsively moving vertical plate with ramped temperature in the presence of thermal radiation and transverse magnetic field is studied. Exact solutions of the governing equations for fluid and particle velocities and fluid and particle temperatures are obtained in closed form by Laplace transform technique. To compare the results obtained in this case with that of an isothermal plate, exact solutions of the governing equations are also obtained for an isothermal plate. The expressions for the skin friction and Nusselt number are also derived for both ramped temperature and isothermal plates. Numerical values of fluid and particle velocities and fluid and particle temperatures are displayed graphically for various values of pertinent flow parameters for both ramped temperature and isothermal plates, whereas numerical values of skin friction and Nusselt number for both ramped temperature and isothermal plates are presented in tabular form for pertinent flow parameters.