Effects of Mass Transfer, Radiation, Joule Heating, and Viscous Dissipation on Steady MHD Marangoni Convection Flow over a Flat Surface with Suction and Injection

The combined effects of radiation and mass transfer on a steady MHD two-dimensional Marangoni convection flow over a flat surface in presence of Joule heating and viscous dissipation under influence of suction and injection is studied numerically. The general governing partial differential equations are transformed into a set of nonlinear ordinary differential equations by using unique similarity transformation. Numerical solutions of the similarity equations are obtained using the Runge-Kutta method along with shooting technique. The effects of governing parameters on velocity, temperature, and concentration as well as interface velocity, the surface temperature gradient, and the surface concentration gradient were presented in graphical and tabular forms. Comparisons with previously published work are performed and the results are found to be in excellent agreement. 1. Introduction In recent years, many researchers have investigated the Marangoni convection and applied such convection to their problems. This is mainly because it is important in crystal growth melts and greatly influences other industrial processes. Nishino and Kawamura [1] stated that Marangoni convection negatively affects the quality of silicon crystals for semiconductors and the convection also occurs in heat pipe for heat radiation devices of personal computers. The surface tension gradient variations along the interface may induce the Marangoni convection. In particular, the surface tension gradients that are responsible for Marangoni convection can be due to gradients of temperature (thermal convection) and/or concentration (solutal convection). A lot of analyses in Marangoni convection have been discovered in various geometries and conditions. Some of experimental works linked to Marangoni convection were discussed in several papers by Arafune and Hirata [2], Arafune et al. [3], Galazka and Wilke [4], Neumann et al. [5], Arendt and Eggers [6], Xu et al. [7], and Christopher and Wang [8]. On the other hand, the study of Magnetohydrodynamics (MHD) is important in the heat and mass transport process. The study of heat transfer is integral part of natural convection flow and belongs to the class of problems in boundary layer theory. The quality of heat transferred is highly dependent upon the fluid motion within the boundary layer. A large number of physical phenomena involve natural convection that was studied by Jaluria [9], which are enhanced and driven by internal heat generation. In such flows the buoyancy force is incremented due to heat generation resulting in modification