Series solutions of unsteady MHD flow of a non-newtonian fluid near the forward stagnation point

Abstract

Unsteady flow of a viscous incompressible electrically conducting non-Newtonian power- law fluid near the forward stagnation point of a two-dimensional body in the presence of a magnetic field is studied by means of an analytic technique, namely, the homotopy analysis method. Accurate analytic approximations are obtained, which are uniformly valid for all dimensionless time in the whole region 0 ≤ η< ∞. Effects of integral power- law index of the non-Newtonian fluids for κ =1 , 2, 3 and magnetic number M ≤ 10 on the flow are considered. To the best of authors' knowledge, such kinds of analytic solutions have been never reported. Introduction. Non-Newtonian fluids are very important fluids, which are widely used in industry. Most particulate slurries (china clay and coal in water, sewage sludge, etc.), multiphase mixtures (oil-water emulsions, gas-liquid disper- sions, such as froths and foams, butter) are non-Newtonian fluids. Further exam- ples, including a variety of non-Newtonian characteristics, include pharmaceutical formulations, cosmetics and toiletries, paints, synthetic lubricants, biological fluids (blood, synovial fluid, saliva), and foodstuffs (jams, jellies, soups, marmalades). Indeed, behaviours of the non-Newtonian fluids are so widespread that it would be no exaggeration to say that the Newtonian fluid behaviours are an exception rather than the rule. Since the non-Newtonian fluids have more complicated equa- tions that relate the shear stresses to the velocity field than the Newtonian fluids have, additional factors must be considered in examining various fluid mechanics (see, Irvine and Karni (1)). Several models have been proposed to describe the non-Newtonian behaviour of fluids. Among these models, which are known to follow the empirical Ostwaald- de Waele model, the so-called power-law model, in which the shear stress varies according to a power function of the strain rate, has received wide acceptance. Boundary layer assumptions were successfully applied to this model and much work has been done on it. Schowalter (2) and Acrivos et al. (3) initially theoretically analyzed the steady boundary layer flow of incompressible non-Newtonian power- law fluids and found the existence of the similarity solutions. Kim et al. (4) made a detailed analysis to obtain possible similarity solutions of the steady boundary layer equations of a non-Newtonian fluid. Yukselen and Erim (5) considered the curvature effects on the boundary layer of a non-Newtonian fluid. Thompson and Snyder (6), and Kim and Eraslan (7) investigated the effect of wall mass injection on the flow of a non-Newtonian power-law fluid over a flat plate, near a stagnation point and past a wedge. Akcay and Yukselen (8) analyzed the boundary layer of a non-Newtonian fluid flow with fluid injection on a semi-infinite flat plate, which moves with a constant velocity in the direction opposite to that of the