Similarity solution of unsteady MHD boundary layer flow of a nanofluid for free and forced convection around an inclined plate.

Abstract

This study investigates the unsteady magnetohydrodynamic (MHD) boundary layer flow of electrically conducting nanofluids over an inclined plate, considering both forced and free convection. This flow situation is relevant to various engineering applications, including solar water heaters, inclination sensors, heat removal in industrial processes, and even deterrence, power generation in nuclear reactors, and biomedical applications. The governing equations are transformed into ordinary differential equations using similarity solutions. These equations are then solved numerically with the sixth-order Runge-Kutta method and the Nachtsheim-Swigert iteration technique. The effects of various parameters, such as the buoyancy ratio, magnetic field strength, Brownian motion, thermophoresis, and unsteadiness, on the velocity, temperature, and concentration profiles are analyzed in detail through graphical representations and discussions. Furthermore, the influence of these parameters on the skin friction coefficient, Nusselt number (heat transfer), and Sherwood number (mass transfer) is presented in tabular form. The numerical results reveal that increasing the nanofluid viscosity leads to a rapid rise in the velocity profiles. Conversely, higher unsteadiness parameters are associated with decreases in both velocity and concentration profiles.