MHD PERISTALTIC FLOW OF A WALTER'S B FLUID WITH MILD STENOSIS THROUGH A POROUS MEDIUM IN AN ENDOSCOPE

In this work, the effects of partial slip and the magnetic field on peristaltic flow of an electrically conducting Walter's B fluid through a porous medium are discussed. The streaming is through a uniform and nonuniform annulus har'ing a mild stenosis. The influences of heat transfer and chemical reactions are taken into consideration. The governing equations of motion are scrutinized under the assumptions of long wavelength and low Reynolds number. The analytical solutions of these equations are given using the regular perturbation technique, which is based on a small wave number. The approximate analytical solutions of the pressure rise and friction force are estimated along a numerical integration. The effects of various physical parameters of the problem are discussed and illustrated graphically through a set of figures. It is found that the a vial velocity decreases with an increase of the Hartmann number, Walter's B fluid parameters, and maximum height of stenosis. Also, it is observed that the temperature decreases with the increase of the Brickmann number. In addition, it is found that the concentration increases with the increase of the Soret number. Furthermore, the streamlines are graphically shown. It is observed that the size of the trapped bolus increases with the decreasing of the Hartmann number and with the increasing of the permeability parameter. The present study is very important in many medical applications, such as the gastric juice motion in the small intestine when an endoscope is inserted through it.