**Safia Akram 1,\*, Emad H. Aly 2,3, Farkhanda Afzal <sup>1</sup> and Sohail Nadeem <sup>4</sup>**


Received: 20 July 2019; Accepted: 13 August 2019; Published: 16 August 2019

**Abstract:** In the present analysis, peristaltic flow was discussed for MHD Newtonian fluid through the gap between two coaxial tubes, where the viscosity of the fluid is treated as variable. In addition, the inner tube was considered to be at rest, while the outer tube had the sinusoidal wave traveling down its motion. Further, the assumptions of long wave length and low Reynolds number were taken into account for the formulation of the problem. A closed form solution is presented for general viscosity using the Adomian decomposition method. Numerical illustrations that show the physical effects and pertinent features were investigated for different physical included phenomenon. It was found that the pressure rise increases with an increase in Hartmann number, and frictional forces for the outer and inner tube decrease with an increase in Hartmann number when the viscosity is constant. It was also observed that the size of the trapping bolus decreases with an increase in Hartmann number, and increases with an increase in amplitude ratio when the viscosity is parameter.

**Keywords:** peristaltic flow; an endoscope; variable viscosity; Adomian solutions; different wave forms
