Peristaltic flow of hybrid nanofluid inside a duct having sinusoidally advancing boundaries and elliptic cross-section is mathematically investigated. The notable irreversibility effects are also examined in this mathematical research by considering a descriptive entropy analysis. In addition, this work provides a comparison analysis for two distinct nanofluid models: a hybrid model (Cu-Ag/water) and a phase flow model (Cu/water). A comprehensive graphical description is also provided to interpret the physical aspects of this mathematical analysis.

In this research, the electro-osmotic effects are highlighted for a blood-based hybrid nanofluid flow across an artery infected with multiple stenosis. The artery has permeable walls together with slip boundary effects. The slip and permeable boundary conditions model the more realistic blood flow problems. The governing equations of the problem are converted into non-dimensional form by introducing adequate dimensionless variables and acquired the exact solutions. The detailed study of heat transfer is given by Joule heating and viscous dissipation effects. The disorder of fluid flow is investigated by the mathematical study of entropy generation. Analytically attained solutions are examined graphically for both symmetric and non-symmetric shapes of stenosis. Streamlines are analyzed for varying values of flow rate Q and electro-osmotic parameter m. The flow velocity has smallest values on the axis of channel and gets higher value near the boundary walls. The temperature profile delineates opposite behavior to the velocity, and it is parabolic in nature. The velocity reduces towards the non-uniform stenosis except for electroosmotic parameter m. The temperature has larger magnitude in the case of anti-symmetric stenosis. Moreover, the stability of velocity solution is also analyzed.

This research article interprets the computational fluid dynamics analysis on blood flow inside a symmetric stenosed artery. The current problem models the blood flow inside the left coronary artery as having a symmetric stenosis in the central region. A comprehensive physiological examination of coronary artery disease is numerically evaluated by using the computational fluid dynamics toolbox Open-Field Operation And Manipulation. There are no assumptions of mild stenosis taken into account since the considered stenosis has an exactly measured length, height and position, etc. The blood flow problem is modeled for the non-Newtonian Casson fluid with unsteady, laminar, and incompressible flow assumptions. The underlying problem is solved numerically in its dimensional form. A thorough graphical analysis is provided on the blood flow simulations, pressure profile, velocity line graphs, pressure line graphs, and streamlines for the left coronary artery having a symmetric stenosis formation. The considered artery is divided into three sections, i.e. pre-stenosis, post-stenosis, and stenosis region, and the velocity and pressure line graphs are plotted for these considered regions. The graphical illustrations provide a detailed analysis of how the blood flow is affected inside the left coronary artery due to coronary artery disease. These pre- and post-stenosis velocity line graphs reveal two intriguing results: In the pre-stenosis zone, the velocity increases with increasing axial coordinate length, whereas in the post-stenosis region, the velocity decreases with rising axial coordinate length. It is evident that as the flow moves toward the stenosis region, the flow profile rises; yet, after passing through the stenosis zone, the flow profile begins to fall as the flow moves away from the stenosis region.

The Phan–Thien–Tanner non-Newtonian model of fluid flow is considered to mathematically model the cilia governed flow inside the human body. The collective action of cilia generates a rhythmic motion in form of metachronal wave traveling along the wall of channel. We have utilized the necessary assumptions to non-dimensionalize this complex problem and the exact solutions are obtained for the cilia governed flow problem. The graphical results are also incorporated to further discuss these solutions in detail. The wavy movements developed due to rhythmic actions of cilia are clearly evident in pressure gradient graphs. Further, a parabolic flow pattern is also observed in this ciliated channel flow problem. Streamlines disclose the trapping phenomenon and the multiple pumping regions can be seen in intrigued pressure rise graphical solutions.

In this research, we have considered the convective heat transfer analysis on peristaltic flow of Rabinowitsch fluid through an elliptical cross section duct. The Pseudoplastic and Dilatant characteristics of non-Newtonian fluid flow are analyzed in detail. The Rabinowitsch fluid model shows Pseudoplastic fluid nature for $$\sigma > 0$$σ > 0 and Dilatant fluid behaviour for $$\sigma < 0.$$σ < 0 . The governing equations are transformed to dimensionless form after substituting pertinent parameters and by applying the long wavelength approximation. The non-dimensional momentum and energy equations are solved analytically to obtain the exact velocity and exact temperature solutions of the flow. A novel polynomial of order six having ten constants is introduced first time in this study to solve the energy equation exactly for Rabinowitsch fluid flow through an elliptic domain. The analytically acquired solutions are studied graphically for the effective analysis of the flow. The flow is found to diminish quickly in the surrounding conduit boundary for Dilatant fluid as compared to the Pseudoplastic fluid. The temperature depicted the opposite nature for Pseudoplastic and Dilatant fluids. The flow is examined to plot the streamlines for both Pseudoplastic and Dilatant fluids by rising the flow rate.

Viscous flow between two sinusoidally deforming curved concentric tubes is mathematically investigated for the first time. Exact solutions are computed to analyse the flow between these two tubes and graphical outcomes are included for a thorough analysis of the solutions. The present article has prime applications in endoscopy as a novel peristaltic endoscope is introduced first time for a curved sinusoidal tube. This curved nature of outer sinusoidal tube with a flexible peristaltic endoscope placed inside it covers the topic of practical applications like endoscopy of human organs having curved shapes and the maintenance of complex machineries that involve complex curve structures. The usage of a flexible peristaltic endoscope inside a curved sinusoidal tube makes the process of catheterization more comfortable.