Hindawi Publishing Corporation Journal of Applied Mathematics Volume 2013, Article ID 806724, 9 pages http://dx.doi.org/10.1155/2013/806724 Research Article On Convective Dusty Flow Past a Vertical Stretching Sheet with Internal Heat Absorption Raj Nandkeolyar and Precious Sibanda School of Mathematics, Statistics & Computer Science, University of KwaZulu-Natal, Private Bag X01, Scottsville, Pietermaritzburg 3209, South Africa Correspondence should be addressed to Precious Sibanda; sibandap@ukzn.ac.za Received 4 July 2013; Accepted 18 November 2013 Academic Editor: Subhas Abel Copyright © 2013 R. Nandkeolyar and P. Sibanda. his is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. he steady two-dimensional boundary layer low of a viscous, incompressible, and electrically conducting dusty luid past a vertical permeable stretching sheet under the inluence of a transverse magnetic ield with the viscous and Joule dissipation is investigated. he luid particles are assumed to be heat absorbing and the temperature at the surface of the sheet is a result of convective heating. he governing nonlinear partial diferential equations are transformed to a set of highly nonlinear coupled ordinary diferential equations using a suitable similarity transformation and the resulting system is then solved numerically. It is found inter alia that the contributions of viscous and Joule dissipation in the low are to increase the thickness of the thermal boundary layer. 1. Introduction he study of boundary layer lows through continuously stretching sheet has attracted many researchers due to its bearing in many luid engineering processes such as extru- sion processes, melt spinning, hot rolling, wire drawing, glass-iber production, manufacture of plastics, polymer and rubber sheets, performance of lubricants and paints, and movement of biological luids Crane [1] irst considered the steady two-dimensional boundary layer low of a Newtonian luid driven by a stretching elastic sheet moving in its own plane with a velocity varying linearly with the distance from a ixed point. Later, this work was extended by many researchers to investigate diferent aspects of the low and heat transfer in a luid of ininite extent surrounding a stretching sheet [2–7]. Magnetohydrodynamic low through stretching sheets in the presence of free convective heat transfer has been investigated by a number of researchers due to its applications in metallurgical industry, such as the cooling of continuous strips and ilaments drawn through a quiescent luid. It is known that the properties of the inal product depend signiicantly on the rate of cooling during the manufac- turing processes. he rate of cooling can be controlled by drawing the strips in an electrically conducting luid subject to a magnetic ield, so that a inal product of desired characteristics can be obtained [8, 9]. he free convection efect on MHD heat and mass transfer of a continuously moving permeable vertical surface was studied numerically by Yih [10]. He found that the Nusselt number and the Sherwood number increase with the increase in suction through the permeable wall. Ishak et al. [11] investigated the mixed convection boundary layer in the stagnation- point low towards a stretching vertical sheet. Ishak et al. [12] also made an analysis for the steady two-dimensional magnetohydrodynamic low of an incompressible viscous and electrically conducting luid over a stretching sheet in its own plane. In this study, the stretching velocity, the surface temperature, and the transverse magnetic ield were assumed to vary in a power law with the distance from the origin. Pal and Mondal [13] investigated the hydromagnetic non- Darcy low and heat transfer characteristics over a stretching sheet taking into account the efect of Ohmic dissipation and thermal radiation. he internal heat absorption/generation exerts signiicant inluence on the rate of heat transfer from a heated surface in several practical situations [14–17]. he efect of internal heat absorption/generation plays important role in the heat transfer of luids undergoing exothermic