Volume 4 • Issue 5 • 1000249 J Appl Computat Math ISSN: 2168-9679 JACM, an open access journal Open Access Research Article Applied & Computational Mathematics Chandra et al., J Appl Computat Math 2015, 4:5 http://dx.doi.org/10.4172/2168-9679.1000249 Keywords: MHD; Visco-elastic luid; hermal difusion; Variable suction; Variable permeability; Vertical porous plate; Heat and mass transfer Nomenclature C l Species concentration D Molecular difusivity Gr Grashof number of heat transfer K 1 Permeability of the medium k hermal difusivity Rc Elastic parameter Nu Nusselt number S Heat source parameter Sh Sherwood number T Non-dimensional temperature t Non-dimensional time u Non-dimensional velocity v o Constant suction velocity y Non-dimensional distance along y-axis Ԑ A small positive constant β Volumetric coeicient of expansion for heat transfer τ Density of the luid β 1 Volumetric coeicient of expansion with species concentration S o Frequency of oscillation υ Kinematic coeicient of viscosity σ Electrical conductivity ω Non-dimensional frequency of oscillation C Non-dimensional Species concentration Gc Grashof number for mass transfer g Acceleration due to gravity Kp Porosity parameter M Magnetic parameter B 0 Magnetic ield of uniform strength Pr Prandtl number Sc Schmidt number T 1 Temperature of the ield t l Time u l Velocity component along x-axis v Suction velocity y l Distance along y-axis *Corresponding author: Raju MC, Department of Mathematics, Annamacharya Institute of Technology and Sciences (Autonomous), Rajampet-516126, A.P, India, Tel: 9440355318; E-mail: mcrmaths@yahoo.co.in Received August 12, 2015; Accepted August 24, 2015; Published August 30, 2015 Citation: Chandra RP, Raju MC, Raju GSS (2015) Thermal and Solutal Buoyancy Effect on MHD Boundary Layer Flow of a Visco-Elastic Fluid Past a Porous Plate with Varying Suction and Heat Source in the Presence of Thermal Diffusion. J Appl Computat Math 4: 249. doi:10.4172/2168-9679.1000249 Copyright: © 2015 Chandra RP, 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. Abstract An analytical solution is investigated for a fully developed free convective low of a visco-elastic incompressible electrically conducting luid past a vertical porous plate bounded by a porous medium in the presence of thermal diffusion, variable suction and variable permeability. A magnetic ield of uniform strength is applied perpendicular to the plate and the presence of heat source is also considered. The novelty of the study is to investigate the effect of thermal diffusion on a visco-elastic luid in the presence of time dependent variable suction. The importance is due to the applications of this kind of visco-elastic luids in many industries. The coupled dimensionless non- linear partial differential equations are transformed into a set of ordinary differential equations by using multiple parameter perturbation on velocity whereas simple perturbation method on temperature and concentration. With corresponds to these, the expressions for skin friction, Nusselt number and Sherwood number are derived. The numerical computations have been studied through igures and tables. The presence of thermal diffusion increases luid velocity, whereas the inluence of the magnetic ield reduces it. In the case of heavier species, it is noticed that concentration increases with an increase in Soret number. Thermal and Solutal Buoyancy Effect on MHD Boundary Layer Flow of a Visco-Elastic Fluid Past a Porous Plate with Varying Suction and Heat Source in the Presence of Thermal Diffusion Chandra RP 1 , Raju MC 1 * and Raju GSS 2 1 Department of Mathematics, Annamacharya Institute of Technology and Sciences (Autonomous), Rajampet, A.P, India 2 Department of Mathematics, JNTUA College of Engineering, Pulivendula, A.P, India