Flows of Second grade fluid with Soret and Dufour effects

Abstract

Boundary layer flow induced by the stretching surface frequently appear in the industrial and engineering applications. Examples of such practical applications are extrusion of plastic sheets, cooling of a metallic plate in a cooling bath, drawing of plastic films, paper production, hot rolling, wire drawing, glass fiber etc. A variety of flow problems having quiet relevance to the polymer extrusion is the flow generated by a stretching surface. A metal spinning process is the best example of such phenomenon. Another example is annealing and thinning of copper wires in which the final product depends on the stretching rate of the sheet with exponential variation of stretching velocity and temperature distributions. Some recent studies in this direction are [1-7]. Further the flow of an electrically conducting fluid with heat and mass transfer is important in many geothermal and industrial applications. Such fluids are useful in MHD accelerators, high temperature plasmas, power generators, cooling of nuclear reactors, MHD pumps and flow meters, in metallurgical process and many others (see [8-12]). The analysis of non-Newtonian fluids is a hot topic of research due to its several industrial and engineering applications. In particular, these fluids are encountered in material processing, bioengineering, chemical and nuclear industries, polymeric liquids and foodstuffs. Several fluids like shampoos, paints, ketchup, mud, apple sauce, soaps, certain oils and polymer solutions are the example of non-Newtonian fluids. The characteristics of all the non-Newtonian fluids cannot be explained through one constitutive relationship. Thus various models of non-Newtonian fluids have been proposed in the past. The non-Newtonian fluids are further divided into three categories namely differential, rate and integral types. Second grade fluid model is a subclass of differential type fluids which describes the normal stress effects. One and two dimensional flows of second grade fluid are analyzed in the past. For instance helical flows of second grade fluid between two infinite coaxial cylinders were investigated by Jamil et al. [13]. Electrically conducting flow of second grade fluid over a permeable stretching sheet with arbitrary velocity and appropriate wall transpiration was examined by Ahmad and Asghar [14]. The perturbation solutions for modified second grade fluid flow past a porous plate is examined by Pakdemirli et al. [15]. Differential transform analysis of flow of second grade fluid past a stretching or shrinking surface was reported by Rashidi et al. [16]. Hayat et al. [17] discussed the unsteady MHD flow of second grade fluid between two parallel disks. Jamil et al. [18] investigated the flow of fractional second grade fluid using finite Hankel and Laplace transforms method. Here the flow is induced due to the torsional and longitudinal oscillations of cylinder. Turkyilmazogolu [19] provided the multiple solutions of an electrically conducting second grade fluid flow past a shrinking surface with slip conditions. He computed the exponential type solutions and noticed that these are unique or multiple with slip conditions. Hayat et al. [20] developed the series solutions for boundary layer flow of second grade fluid with power law heat flux and heat generation/absorption.