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The present studies deal with the peristaltic motion of an incompressible Williamson fluid model in an endoscope. The governing equations of Williamson fluid model are first simplify using the assumptions of long wavelength and low Reynolds number. The four types of solutions have been presented for velocity profile named (i) exact solution, (ii) perturbation solution, (iii) HAM solution, and (iv) numerical solutions. The comparisons of four solutions have been found a very good agreement between all the solutions. In addition, the expressions for pressure rise and velocity against various physical parameters are discussed through graphs.

In this article, we considered the peristaltic flow of Newtonian incompressible fluid of chyme in small intestine. The analysis has been performed using an endoscope. The peristaltic flow of chyme is modeled by assuming that the peristaltic wave is formed in non-periodic mode comprising two sinusoidal waves of different wave lengths propagating with same speed along the outer wall of the tube. Heat transfer mechanisms have been taken into account, such that the constant temperature and are assigned to inner and outer tubes, respectively. A complex system of equations has been simplified using long wavelength and low Reynolds number approximation because such assumptions exist in small intestine. Exact solutions have been carried out for velocity temperature and pressure gradient. Graphical results have been discussed for pressure rise, frictional forces, temperature, and velocity profile. Comparison of present results with the results of the existing literature have been presented through figures. Trapping phenomena have been presented at the conclusion of the article.

In the present paper, we have studied the effects of endoscope and heat transfer on the peristaltic flow of second grade fluid through an inclined tube. The endoscope is a solid circular cylinder which is inserted in a peristaltic tube, and the flow takes place through the gap between endoscope and the peristaltic tube. The endoscope is maintained at a temperature $T_1$, while the outer tube has a sinusoidal wave traveling down its wall and is exposed to temperature $T_0$. The flow is investigated in a wave frame of reference moving with the velocity of the wave. The equations governing the flow of second grade fluid are modeled in cylindrical coordinates. Using perturbation method, the solutions are obtained for the stream function, pressure gradient and temperature fields. The pressure difference and frictional force at both the walls are calculated using numerical integration. The graphical results are presented to interpret the effect of various physical parameters of interest. It is found that, velocity increases with an increase in inclination angle and the best pumping rate appear in the vertical tube as compared to the horizontal tube. It is also found that, the heat generation parameter has an increasing effect on the velocity of the fluid.