Patil Mallikarjun B Int. Journal of Engineering Research and Applications www.ijera.com ISSN: 2248-9622, Vol. 6, Issue 1, (Part – 3) January 2016, pp.07-18 www.ijera.com 7|Page Mixed Convection Flow and Heat Transfer of Micropolar Fluid in a Vertical Channel with Symmetric and Asymmetric Wall Heating Conditions Patil Mallikarjun B 1 , Chandrali Baishya 2 Department of Studies and Research in Mathematics, Tumkur University, Tumkur-572 103, Karnataka, India ABSTRACT Analytical solutions for fully developed mixed convection flow of a micro polar fluid with heat generation or heat absorption in a parallel plate vertical channel with symmetric and asymmetric wall temperature distribution has been presented. The two boundaries of the channel are kept either at equal or at different temperatures as isothermal-isothermal, isoflux-isothermal and isothermal-isoflux cases. Reverse flow conditions are observed with increase in micro vortex viscosity. Micro polar fluids display reduction in heat transfer rate. Key Words: Mixed convection, Viscous Dissipation and Micropolar fluid. I. INTRODUCTION The theory of micropolar and thermomicropolar fluids formulated by Eringen [1,2] has shown much interest in recent years because of its considerable attention due to there application in a number of processes that occur in industry. The applications include the extrusion of polymer fluids, solidification of liquid crystals, cooling of a metallic plate in a bath, animal blood, exotic lubricants and in colloidal suspensions. A detailed review of the published papers on these fluids can be found in the review article by Arimal et al. [3,4] and Eringen [5]. The essence of the theory of micropolar fluid flow lies in the extension of the constitutive equations for Newtonian fluids so that more complex fluids can be described by this theory. In this theory, the rigid particles contained in as small fluid volume element are limited to rotation about the center of the volume elements described by the micro rotation vector. Such fluids display the effects of local rotary inertia and couple stresses. Further the desired model of the non-Newtonian flow of fluids containing microconstitutents motivated the development of the theory. Subsequent studies have successfully applied the model to a wide range of applications including blood flows, porous media, lubricants, turbulent shear flows, flow in capillaries and micro channels etc. The interest in heat transfer problems involving non-Newtonian fluids has grown persistently in the past half century. Hinch [6] has given an excellent sequence of lectures on non-Newtonian fluids. Many practical applications of mixed convection exists, including in the fuel element of a nuclear reactor, in the heaters and coolers of mechanical or chemical devices, in the lubrication of machine parts etc. Chiu et.al [7] studied the effect of microstructure on the free convection heat transfer in enclosures. Chamkha , Grosan and Pop [8]studied both analytically and numerically the problem of fully developed free convection flow of a micropolar fluid between a parallel plate vertical channel with asymmetric wall distribution. Again the same authors in [9] studied the fully developed flow of a micropolar fluid in a mixed convection between a parallel-plate vertical channel with asymmetric wall temperature distribution. They observed flow reversal due to buoyancy force and they also derived criteria for the occurrence of the flow. Buoyancy and wall conduction effects on forced convection of micropolar fluid flow along a vertical slender flow circular cylinder have been studied by Cheng et.al [10]. However, the effect of heat absorption or heat generation on the mixed convection flow and heat transfer of a micropolar fluid in vertical channel geometry with symmetric and asymmetric wall conditions has not been studied. The aim of the present study is to discuss such situation. It is also of our interest to investigate the effect of material constant on the micropolar fluid on the flow and heat transfer through vertical channel with symmetric and asymmetric wall heating conditions with heat generation or heat absorption coefficient for three thermal boundary conditions. RESEARCH ARTICLE OPEN ACCESS