Three-dimensional flow analysis of Carreau fluid model induced by peristaltic wave in the presence of magnetic field

Abstract

This work investigates the impact of magnetohydrodynamics (MHD) on a non-Newtonian peristaltic flow of Carreau fluid in a uniform duct of rectangular cross section. An applied magnetic field is considered whereas the induced magnetic field is taken to be zero here due to small magnetic Reynolds number. Non-Newtonian fluid model is impossible to describe with the help of single constitutive relationship among strain and stress rate. These kinds of constitutive equations give a very complicated mathematical models and thus, mathematicians, physicist, modelers and computer scientist face multiple kinds of problems during the development of numerical and analytical methods. Generally, non-Newtonian fluids are classified into three categories such as the rate type, differential type, and integral type. Carreau fluid model is one of them. The governing nonlinear equations are studied under the considerations of long wavelength and the inertial forces have been ignored. Flow is examined in a wave frame of reference with the velocity of the wave. Such types of flow with magnetic effect are beneficial in drug delivery systems and also helpful to control the flow. Further in microfluidics, magnetohydrodynamics helps to produce a nonpulsating and stable flow in a design of complex microchannel. Analytical solutions of nonlinear partial differential equations are obtained by employing a perturbation method with the combination of eigenfunction expansion method. Numerical computation has been successfully used in order to analyze the pumping characteristic of the flow. Peristaltic pumping is also an engrossing mechanism in a human body that helps to propagate various kinds of biological fluids in different parts of a human body. Velocity behavior is analyzed and presented in both two and three-dimensional profile. Contours are also drawn with the help of streamlines against various involved parameters. Particularly, the obtained results are presented graphically to explore the impact of all the sundry parameters for velocity, pressure gradient, and pressure rise. An excellent comparison is also presented with previously published data to validate the current methodology and results. This problem has multiple numbers of applications in different fields of biomedical engineering including the three-dimensional fluid flow under the influence of elastic waves, blood flow dynamics in a living body.