Study of Newtonian and non Newtonian fluids by Sumudu transform techniques

Abstract

The Navier-Stokes equations are good model for the flow of a wide class of newlinefluids. The underlying constitutive model is a linear Newtonian relationship newlinebetween shear stress and shear rate is governed by fluid s (constant) viscosity. newlineThe exact solutions of few Navier- Stokes equations are known because of the newlinenon-linearity which occurs in the inertial part of these equations. However, newlinemany flow situations of interest are such that a number of terms in the newlineequations of motion either disappear automatically or can be neglected, and newlinethe resulting equations reduce to a form that can be readily solved. There are newlinemany fluids with complex microstructure such as biological fluids, as well as newlinepolymeric liquids, suspension, liquid crystal which are used in current newlineindustrial processes that show nonlinear viscoelastic behavior, that can not be newlinedescribed by the classical linearly Newtonian model. For such fluids nonlinearity newlineoccurs not only in the inertial part but also in the viscosity part of the newlinegoverning equations. The number of exact solutions becomes rare as newlinecompared to the analytical solutions of Navier-Stokes equations. But the newlineinadequacy of Navier-Stokes theory to describe rheological complex fluids has newlineled to the development of several theories of non-Newtonian fluids. Amongst newlinethese, the fluids of second and third-grade have acquired a special status. newline