Perturbation Solution for Radiating Viscoelastic Fluid Flow and Heat Transfer with Convective Boundary Condition in Nonuniform Channel with Hall Current and Chemical Reaction
A mathematical analysis has been performed for heat and mass transfer of a time-dependent MHD flow of an electrically conducting viscoelastic fluid in nonuniform vertical channel with convective boundary condition. The fluid flow is considered between a vertical long wavy wall and a parallel flat wall saturated with the porous medium. The effects of thermal radiation, heat absorption, chemical reaction, and Hall current are taken into account. The prevailing nonlinear partial differential equations are derived by considering Boussinesq approximation, and the same equations are solved analytically using perturbation technique. Further the expressions for skin friction, Nusselt number, and Sherwood number are presented. The effects of various pertinent parameters on different flow fields are analyzed graphically and tabularly. It is found that effects of Hall parameter and Biot number are unfavorable on velocity profiles, but this trend is reverse for the effect of thermal and solutal Grashof numbers. The expressions of different flow fields satisfy the imposed boundary conditions, which is shown in all graphs; this implies accuracy of the solution. 1. Introduction The study of viscoelastic fluid has become important in the last few years. Qualitative analysis of these studies has significant bearing on several industrial applications such as polymer sheet extrusion from a dye and drawing of plastic firms. When manufacturing processes at high temperature need cooling, the flow may need viscoelastic fluid to produce a good effect or reduce the temperature. On the other hand, the flow and heat transfer of a viscoelastic fluid between parallel plates have significant role in many engineering fields such as petroleum production, chemical catalytic reactors, and solar power collectors. Boundary layer treatment for an idealized viscoelastic fluid was introduced by Beard and Walters [1]. There has been a continued interest in the investigation of natural convection heat transfer of non-Newtonian fluid, which exhibits the viscoelasticity. Recently, Rajagopal and Na [2] have studied the heat transfer analysis in the forced convection flow of a visco-elastic fluid by considering the Walters model. The problem of MHD flow and heat transfer has wide range of applications in emerging fields due to an electro-magnetic field are relevant to many practical applications in geophysical and astrophysical situations, the metallurgy industry, and cooling of continuous strips and filaments drawn through a quiescent fluid. Sarpkaya [3] was the first who had studied the MHD
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