591 2013,25(4):591-598 DOI: 10.1016/S1001-6058(11)60400-X Diffusion of chemically reactive species in Casson fluid flow over an unsteady permeable stretching surface * MUKHOPADHYAY Swati Department of Mathematics, The University of Burdwan, Burdwan-713104, W. B., India, E-mail: swati_bumath@yahoo.co.in VAJRAVELU Kuppalapalle Department of Mathematics, Department of Mechanical, Materials and Aerospace Engineering, University of Central Florida, Orlando, Florida 32816 - 1364, USA (Received May 30, 2012, Revised October 22, 2012) Abstract: In this paper we investigate the two-dimensional flow of a non-Newtonian fluid over an unsteady stretching permeable surface. The Casson fluid model is used to characterize the non-Newtonian fluid behavior. First-order constructive/destructive chemical reaction is considered. With the help of a shooting method, numerical solutions for a class of nonlinear coupled differential equations subject to appropriate boundary conditions are obtained. For the steady flow, the exact solution is obtained. The flow features and the mass transfer characteristics for different values of the governing parameters are analyzed and discussed in detail. Key words: chemical reaction, Casson fluid, mass transfer, unsteady stretching, suction/injection Introduction Processes involving the effects of mass transfer have attracted the attention of researchers due to app- lications in chemical processing equipments [1] . The driving force for mass transfer is the difference in con- centration. There are some fluids which react chemi- cally with some ingredients present in them. In the recent years, the boundary-layer flows of non-Newtonian fluids have been given considerable attention due to ever increasing engineering applica- tions. In order to obtain a thorough cognition of non- Newtonian fluids and their various applications, it is necessary to study their flow behaviors. It is well known that the mechanics of non-Newtonian fluids present a special challenge to engineers, physicists and mathematicians. The non-linearity can manifest itself in a variety of ways in many fields, such as food processing, drilling operations and bio-engineering. * Biography: MUKHOPADHYAY Swati (1975-), Female, Ph. D., Assistant Professor Corresponding author: VAJRAVELU Kuppalapalle, E-mail: kuppalapalle.vajravelu@ucf.edu The Navier-Stokes theory is inadequate for such fluids and no single constitutive equation is available in the literature which exhibits the properties of all fluids. Because of the complexity of these fluids, there is not a single constitutive equation which exhibits all prope- rties of such non-Newtonian fluids. Thus a number of non-Newtonian fluid models have been proposed. In literature, the majority of non-Newtonian fluid models are concerned with simple models like the power-law and grade two or grade three fluids [2,3] . These simple fluid models have shortcomings that render to results not having accordance with fluid flows in the reality. The power-law model has a vast usage in modeling fluids with shear-dependent viscosity but it cannot predict the effects of elasticity. The fluids of grade two or grade three can account for the effects of elasti- city but the viscosity in these models is not shear-de- pendent, and also they cannot predict the effects of stress relaxation. A subclass of rate type fluids namely the Maxwell model can predict the stress relaxation. This rheological model, also, excludes the complica- ting effects of shear-dependent viscosity from any boundary-layer analysis. There is another fluid model for non-Newtonian fluid, namely the Casson fluid, examples of which include jelly, tomato sauce, honey, soup, concentrated fruit juices, etc.. Human blood can