Boundary Layer Analysis of MHD Heat and Mass Transfer with Double Diffusive Effects on a Wedge Surface under Robin-Type Boundary Conditions

Abstract

This work presents a numerical investigation of steady magnetohydrodynamic (MHD) boundary-layer flow with coupled heat and mass transfer over a wedge surface. The fluid is assumed to be electrically conducting, and the flow is influenced by an externally applied transverse magnetic field. Double-diffusive effects arising from simultaneous thermal and solutal buoyancy forces are incorporated into the formulation. The wedge geometry is described through the classical Falkner--Skan similarity transformation, while the thermal and concentration fields at the surface are modeled using Robin-type (convective) boundary conditions, which account for finite heat and mass exchange with the surrounding medium. The governing partial differential equations are transformed into a system of coupled, nonlinear ordinary differential equations and solved numerically using a shooting technique in conjunction with a Runge--Kutta--Fehlberg integration scheme. A detailed parametric study is conducted to examine the influence of the magnetic parameter $M$, wedge angle parameter $\beta$, Prandtl number $Pr$, Schmidt number $Sc$ on the velocity, temperature, and concentration distributions, as well as on the associated Nusselt and Sherwood numbers. The results indicate that the presence of a magnetic field suppresses the fluid velocity due to the Lorentz force, while simultaneously thickening the thermal and concentration boundary layers. Increasing wedge angle and buoyancy effects enhance surface transport rates, whereas higher Prandtl and Schmidt numbers lead to thinner thermal and concentration layers, respectively. The convective boundary conditions are found to significantly alter the surface gradients of temperature and concentration, resulting in notable variations in heat and mass transfer rates. The numerical results show excellent agreement with available benchmark solutions in limiting cases, thereby validating the accuracy of the present approach.