Heat transfer analysis of a peristaltically induced creeping magnetohydrodynamic flow through an inclined annulus using homotopy perturbation method

Abstract The present work aims to focus on the heat transfer analysis of the peristaltic flow of biviscosity fluid in an annular region between two coaxial flexible tubes with different amplitudes and phases under the influence of a radially varying magnetic field and constant rotation. In this model, the non‐Newtonian biviscosity fluid is flowing through the annulus region between the two concentric inclined tubes. The outer flexible tube is permeable and supposed to satisfy the Saffman slip condition. The governing equations for the considered problem are simplified under the assumptions of a creeping flow and long‐wavelength approximations. Semi‐analytical expressions for the axial velocity and temperature profile are obtained using the homotopy perturbation method. Here, the expressions for shear stress and stream function are also obtained. In this work, the authors discussed the impact of various flow parameters like the Hartmann number, rotation of the frame, permeability parameter, phase difference, amplitude ratios of inner and outer tubes, radius ratio, and inclination angle on the above flow variables. The streamline contour plots are also drawn for the realization of the fluid flow inside the annular endoscopic region. A noticeable result which is drawn from the present study is that phase difference and amplitude ratio are responsible for reduction and enhancement in temperature and axial velocity of the moving fluid, respectively. It is also found from the present examination that the rise in the strength of the applied magnetic field enhances the transverse fluctuations of peristaltically propagating waves. The comparison of the sinusoidal waveform with the various types of waveforms, such as triangular, trapezoidal, and square waveforms, in the case of a peristaltic endoscope is also discussed. The proposed model may give insights into designing a novel endoscope and decide whether such types of peristaltic endoscopes have exemplary implementations for surgical and mechanical purposes.