Conjugate Effects of Heat and Mass Transfer on MHD Free Convection Flow over an Inclined Plate Embedded in a Porous Medium Farhad Ali, Ilyas Khan, Samiulhaq, Sharidan Shafie* Department of Mathematical Sciences, Faculty of Science, Universiti Teknologi Malaysia, Skudai, Johor, Malaysia Abstract The aim of this study is to present an exact analysis of combined effects of radiation and chemical reaction on the magnetohydrodynamic (MHD) free convection flow of an electrically conducting incompressible viscous fluid over an inclined plate embedded in a porous medium. The impulsively started plate with variable temperature and mass diffusion is considered. The dimensionless momentum equation coupled with the energy and mass diffusion equations are analytically solved using the Laplace transform method. Expressions for velocity, temperature and concentration fields are obtained. They satisfy all imposed initial and boundary conditions and can be reduced, as special cases, to some known solutions from the literature. Expressions for skin friction, Nusselt number and Sherwood number are also obtained. Finally, the effects of pertinent parameters on velocity, temperature and concentration profiles are graphically displayed whereas the variations in skin friction, Nusselt number and Sherwood number are shown through tables. Citation: Ali F, Khan I, Samiulhaq, Shafie S (2013) Conjugate Effects of Heat and Mass Transfer on MHD Free Convection Flow over an Inclined Plate Embedded in a Porous Medium. PLoS ONE 8(6): e65223. doi:10.1371/journal.pone.0065223 Editor: Derek Abbott, University of Adelaide, Australia Received February 1, 2013; Accepted April 23, 2013; Published June 28, 2013 Copyright: ß 2013 Ali et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. Funding: The authors have no support or funding to report. Competing Interests: The authors have declared that no competing interests exist. * E-mail: ridafie@yahoo.com Introduction The conjugate phenomenon of heat and mass transfer occurs as a result of combined buoyancy effects of thermal diffusion and diffusion through chemical species, which plays an important role in geophysics, aeronautics and chemical engineering. Some industrial applications are found in food drying, food processing and polymer production [1]. Hence, a considerable amount of attention has been focused in recent years by various scientists and engineers to study problems involving the conjugate phenomenon of heat and mass transfer either analytically or numerically (see [2– 7] and the references therein). On the other hand, the studies on the magnetohydrodynamic (MHD) free convection flow with simultaneous effects of heat and mass transfer are encountered in electric power generation, metallurgy, astrophysics and geophys- ics, solar power technology, space vehicle, nuclear engineering application and other industrial areas [8,9]. Ahmad and Sarmah [10] examined the thermal radiation effect on a transient MHD flow with mass transfer past an impulsively started infinite vertical plate. Rajput and Kumar [11] studied the MHD flow past an impulsively started vertical plate with variable temperature and mass diffusion. They used the Laplace transform method to find the exact solutions for velocity, temperature and concentration. In a subsequent year Rajput and Kumar [12] extended Rajput and Kumar [11] by taking the thermal radiation effect. Oscillatory flow of a viscous, incompressible electrically conducting fluid with heat radiation is analyzed by Singh [13] and established the closed form solutions. Ahmad [14] studied MHD transient free convection and mass transfer flow of a viscous, incompressible and electrically conducting fluid in the presence of thermal diffusion and thermal radiation. He obtained exact solutions for velocity, temperature and concentration using the Laplace transform method. Recently, Turkyilmazoglu and Pop [15] extended the work of Ahmad [14] by introducing a heat source term and by taking two different types of thermal boundary conditions namely prescribed wall temperature and prescribed heat flux. In their exact analysis, they found that the solutions of Ahmad [14] are not error free, therefore, they used a better approach in the formulation and used a proper radiation term. Furthermore, the free convection flow over vertical surfaces immersed in porous media has paramount importance because of its potential applications in soil physics, geohydrology, and filtration of solids from liquids, chemical engineering and biological systems [16,17]. Osman et al. [18] studied analytically the thermal radiation and chemical reaction effects on unsteady MHD free convection flow in a porous medium with heat source/ sink. By taking the porous medium effect, Sami et al. [19] provided an exact analysis to the study of the magnetohydrodynamic free convection flow of an incompressible viscous fluid past an infinite vertical oscillating plate with uniform heat flux. An in other investigation, Sami et al. [20] studied the MHD free convection flow in a porous medium with thermal diffusion and ramped wall temperature. They obtained exact dimensionless solutions of momentum and energy equations, under Boussinesq approxima- tion using the Laplace transforms. In addition to this, many researchers (for example, see Makinde [21,22], Makinde and Olanrewaju [23], Khan et al. [24], Pal and Mondal [25], Rajesh [26], Prasad et al. [27], Magyari and Pantokratoras [28], Turkyilmazoglu [29–32], Chandrakala [33], Narahari and Yunus [34], Narahari and Ishakh [35], Seth et al [36], Mishra et al. [37] PLOS ONE | www.plosone.org 1 June 2013 | Volume 8 | Issue 6 | e65223