Effect of peristaltic endoscope and heat transfer on the magnetohydrodynamic flow of non-Newtonian biviscosity fluid through an inclined annulus: Homotopy perturbation approach

This work focuses on the heat transfer analysis of the magnetohydrodynamic peristaltic flow of blood through the gap between two coaxial flexible tubes of different wavelengths. In this model, the non-Newtonian biviscosity fluid is assumed to be blood, which is flowing through the annulus region between the inclined tubes. The governing equations for the considered problem are simplified under the assumptions of a zero Reynolds number and long wavelength approximations. An analytical expression for the temperature is obtained in its closed form, while a semi-analytical solution for the axial velocity of the moving fluid is determined using the homotopy perturbation method. Expressions for various flow variables such as shear stress, volumetric flow rate, pressure rise, and frictional force at the surface of inner and outer tubes are also obtained. In this work, we discussed the impact of various flow parameters like the Hartmann number, Grashof number, heat source, upper limit apparent viscosity coefficient, amplitude ratios of inner and outer tubes, radius ratio, and wavelength ratio on the above flow variables. The streamline contour plots are also drawn for the realization of the flow pattern of the blood inside the endoscope. The comparison of shear stresses for the peristaltic and rigid endoscopes and the validation of the present result with the previously established results are also discussed. A noteworthy observation drawn from the present model is that the pressure gradient enhances for increasing values of wavelength ratio when the wavelength of the inner tube is less than the wavelength of the outer tube, whereas the pressure gradient gets suppressed for increasing values of wavelength ratio when the wavelength of the inner tube is greater than the wavelength of the outer tube. From the present analysis, it is also found that the shear stress tau rz of blood is the least for a peristaltic endoscope as compared to the rigid one. Therefore, this study may be applicable to medical practitioners for laparoscopic purposes, as a peristaltic endoscope may be a more appropriate device due to its flexibility than a rigid endoscope.