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This study utilises mathematical modelling and computations to analyse the magnetohydrodynamic (MHD) effects on non-Newtonian Eyring–Powell fluid flow in an inclined non-uniform channel under long-wavelength, low Reynolds number conditions. The governing equations are solved by applying slip boundary conditions to determine the velocity, temperature, concentration, and streamline profiles. The key findings show that the magnetic parameter dampens the flow rate. The relationship between the variable viscosity, velocity, and temperature is nonlinear. The wall rigidity parameter and axial velocity are directly proportional until a threshold. Increasing inclination angles distorts streamlines. The magnetic field alters concentration contours and thermal transport. MATLAB parametric analysis explores MHD effects. This study enhances the understanding of inclined channel fluid dynamics, offering insights into variable viscosity, magnetic fields, wall properties, and impacts of inclination angles on non-Newtonian flow characteristics. This knowledge can optimise industrial MHD conduit/channel transport applications.

This study delves into the intricacies of the peristaltic mechanism exhibited by a non-Newtonian Ree-Eyring Nano-liquid, investigating its behavior in the presence of varying liquid properties and heat and mass transfer phenomena. The objective of the present investigation is to conduct a thorough analysis of this mechanism, taking into account the influence of wall properties and the dynamic nature of liquid properties. The Buongiorno nanofluid model is adopted to investigate heat and mass transfer phenomena, while the Ree-Eyring non-Newtonian fluid model is employed to comprehend the complex rheological characteristics of the fluid. This complex process's modeling involves utilizing long wavelengths and low Reynolds number approximations. The resulting non-linear ordinary differential equations are addressed using the homotopy perturbation technique, incorporating appropriate non-dimensional parameters. A strong correlation is observed between homotopy perturbation results and previously existing literature. The magnetic field is a critical factor in shaping the fluid flow behavior, while the interplay between variable liquid properties and nanofluid characteristics significantly affects temperature profiles. The Ree-Eyring fluid and magnetic parameters enhance the heat and mass transfer coefficient. This research advances the understanding of peristalsis in the context of Ree-Eyring Nano-liquids, holding promising implications for diverse applications in both technical and medical domains. [ABSTRACT FROM AUTHOR]

The electroosmotic force effect on the peristaltic motion of the third-grade fluid is considered in a uniform channel. The governing equations that supplement the flow are designed for long wavelengths and low Reynolds numbers. Solutions are obtained for velocity, temperature, concentration, and trapping by considering the variable liquid properties for analyzing the various parameter effects. These effects are depicted through graphs and the relevance is discussed. The variable fluid properties have a declining impact on the velocity and temperature fields. Increasing the Helmholtz–Smoluchowski velocity values decreases the velocity field. Temperature decreases as the Deborah number increases. The velocity slip characteristics rise, and the trapping bolus's size shrinks. The results of this paper may be beneficial in understanding the control of microvascular transport in the time of fractionation of blood into plasma and erythrocytes. [ABSTRACT FROM AUTHOR]

The dynamics of blood carrying microscopic copper particles through overlapping stenotic arteries is an important research area needed for scrutinizing and exploring dynamics through blood vessels. Adipose tissue deposition and other elements of atherosclerosis generate the uncommon artery disease known as arterial stenosis. It limits blood flow and raises the risk of heart disease. Using the Casson model, it is feasible to shed light on the peristaltic blood flow of copper nanoparticles over an overlapping stenotic artery. Nothing is known about the study of heat sink/source, buoyancy and Lorent force, and volume fraction because the focus is on the dynamics of blood carrying minute copper particles through an overlapping stenotic artery. When the Lorentz force is significant, the transport mentioned above was evaluated utilizing stenosis approximations to examine the stream function, wall shear stress, Nusselt number, and flow resistance distribution. In addition, temperature solutions were identified analytically, whereas a perturbation approach acquired velocity solutions. Temperature distribution and velocity are greater in stenosed arteries than in unstenosed arteries. Furthermore, extreme velocity and temperature rise as it reaches the core of the artery and falls as one approaches the wall. When the heat source parameter values increase due to an improvement in the fluid's thermal state, the temperature distribution increases. [ABSTRACT FROM AUTHOR]

In recent years, a great deal of interest has been generated in modern micro‐ and nanotechnologies for micro/nano‐electronic devices. These technologies are increasingly utilizing sophisticated fluid media to enhance performance. Among the new trends is the simultaneous adoption of nanofluids and biological micro‐organisms. Motivated by bio‐nanofluid vertical channel oxygenators in medical engineering, in the current work, a mathematical model is developed to examine the flow of mixed convective couple‐stress nanofluids in a vertical channel with a transverse magnetic field, fluid viscosity that changes with temperature, and thermal conductivity. The non‐Newtonian model follows Brownian motion and heat spread by nanoparticles in a fluid under coupled stress. Highly linked, nonlinear regulating equations are translated into nondimensional equations using relevant variables. The governing equations are then turned into a form with no dimensions. The Keller‐box technique, a second‐order finite difference method for solving second‐order equations, is used to solve them numerically. On the other hand, the effects of different non‐Newtonian flow parameters, such as the couple stress fluid parameter, the magnetic parameter, the variable fluid viscosity, the variable thermal conductivity parameters, the Brinkman number, the nanofluid and buoyancy parameters, and the rate of chemical reaction parameter, are carefully studied. The velocity, temperature, and concentration fields are calculated over a wide range of possible values for the relevant parameters. [ABSTRACT FROM AUTHOR]

A theoretical model is developed to stimulate electro-kinetic transfer through peristaltic movement in a micro-channel. The effect of variable viscosity and wall properties are considered. The long wavelength and small Reynolds number approximations are supposed to simplify the governing formulas. Debye-Huckel linearization is also utilized. The perturbation technique is utilized to solve the governing non-linear equations. The graphical outcomes are presented for velocity and streamlines. [ABSTRACT FROM AUTHOR]

The present investigation emphasizes a new attempt at the peristaltic mechanism of Eyring Powell fluid through a non-uniform channel. The flow is analyzed in the presence of wall properties under variable liquid properties, and the mathematical problem for the flow is developed. The channel walls are subjected to slip conditions with low Reynolds number, and long wavelength approximations are employed to simplify the nonlinear governing equations. The nonlinear governing equations are normalized using relevant nondimensional parameters, and the solutions are obtained with the help of the regular perturbation technique. The influence of pertinent physical parameters of interest (velocity, temperature, concentration, and streamlines) are represented graphically. The investigations reveal that the material parameters and elastic parameters of the Eyring Powell fluid model strongly affect the velocity and temperature profiles. The model shows the opposite behaviour in the material parameters A and B in velocity and temperature profiles. [ABSTRACT FROM AUTHOR]