Sciknow Publications Ltd. HMMT 2014, 2(2):28-46 Open Journal of Heat, Mass and Momentum Transfer DOI: 10.12966/hmmt.04.02.2014 ©Attribution 3.0 Unported (CC BY 3.0) Chemical Reaction Effects on Mixed Convection Flow of Two Immiscible Viscous Fluids in a Vertical Channel J. Prathap Kumar, J. C. Umavathi * and Shreedevi Kalyan Department of Mathematics, Gulbarga University Gulbarga, Karnataka, India *Corresponding author (Email: jc_uma11@yahoo.com) Abstract - The objective of this paper is to study the heat and mass transfer in vertical infinite parallel plates in the presence of first order chemical reaction. The channel is filled with viscous, immiscible fluids. Fluids in both the regions are incompressible and the transport properties are assumed to be constant. The governing equations which are coupled and highly nonlinear are solved analytically using regular perturbation method and numerically using finite difference method. Separate solutions are matched at the interface by using suitable matching conditions. The effects of various pertinent parameters on the heat and mass transfer characteristics are discussed numerically and represented graphically. The thermal Grashof number and mass Grashof number enhances the flow in both regions in the presence or in the absence of first order chemical reaction. The viscous dissipation, viscosity ratio, width ratio and conductivity ratio enhances the flow, where as the first order chemical reaction parameter suppresses the flow in both the regions. The volumetric flow rate, Nusselt number, total species rate and the total heat rate added to the flow are also explored. It is also found that the numerical and analytical solutions agree very well for small values of the perturbation parameter. Keywords - Chemical reaction parameter, viscous dissipation, Regular perturbation method, Finite Difference Method 1. Introduction Convective flows are of great interest in a number of industrial applications such as fiber and granular insulations, geothermal systems etc. Many analysis of laminar convection in vertical parallel plate channels are available in the literature. These analyses can be classified into free convection and mixed convection, symmetric and asymmetric heating with uniform wall temperature or uniform wall heat fluxes. Generally, the developing flow is analyzed by numerical technique [1], the fully developed flow is analyzed analytically [2] and experimental work is also available [3]. The mixed convection in narrow vertical ducts without the effect of viscous dissipation has been investigated by Pop et al. [4]. Storesletten and Pop [5] have extended the problem of buoyancy-driven viscous flow in a vertical parallel plane channel posed by Banks and Zalurska [6] to the case of a vertical porous layer with non-uniform wall temperature. The effect of viscous dissipation has been included in the study of the combined free and forced convection in a porous medium between two vertical walls by Ingham et al. [7]. More recent contributions to the effect of viscous dissipation in addition to the buoyancy effects have been published by Nield [8], and by Magyari et al. [9]. Analytical Taylor series solutions have been reported for the mixed convection in a vertical channel for isoflux- isothermal wall conditions by Barletta et al. [10]. The same approach has been applied to the mixed convection channel flow of clear fluids for the case of symmetrical isothermal-isothermal wall conditions by Barletta et al. [11]. All the mentioned studies pertain to a single-fluid model. Most of the problems relating to the petroleum industry, geophysics, plasma physics, magneto-fluid dynamics, etc., involve multi fluid flow situations. The problem concerning the flow of immiscible fluids has a definite role in chemical engineering and in medicine [12]. There have been some experimental and analytical studies on hydrodynamic aspects of the two-fluid flow reported in the literature. Bird et al. [13] obtained an exact solution for the laminar flow of two immiscible fluids between parallel plates. Bhattacharya [14] investigated the flow of two immiscible fluids between two rigid parallel plates with a time-dependent pressure gradient. These examples show the importance of knowledge of the laws governing immiscible multiphase flows for proper understanding of the processes involved. In modeling such problems, the presence of a second immiscible fluid phase adds a number of complexities as to the nature of interacting transport phenomena and interface conditions between the phases. There has been some theoretical and experimental