The present analysis is motivated by the need to elucidate with more accuracy and sophisticaion the motion of Williamson nanofluid with activation energy and modified darcy law through porous medium over a stretching riga sheet. The problem is modulated mathematically by using the momentum,energy and concentration equations. The nonlinear partial differential equations describe the motion is transformed to nonlinear ordinary dfferential equations by using a suitable transformations. The obtained system of equations with boundary conditions inside the boundary layer are solved semi analytically by using homotopy perturbation method. The velocity, temperature and the concentration of the fluid as well skin-frication, Nusselt and Sherwood numbers are obtained as a functions of the physical parameters of the problem. The effects of these parameters on the solutions are discussed numerically and illustrated graphically through some figures. It is found that the parameters play a dramatic role to control the solutions. For example the velocity increases with increeasing Williamson parameter, permiability parameter and modified Hermann number. On the other hand the fluid temperature increases with increasing both of Brownian parameter and Eckert number. In addition, increasing the activation energy and thermophoresis parameter increases the fluid concentration.

Including mobile microorganisms aids in stabilizing suspension of nanoparticles formed by the combined action of the magnetic field and buoyancy force. We have established activation energy using the Arrhenius function, and thermal conductivity of the physiological fluids utilized varies linearly with temperature in peristaltic flow of non-Newtonian nanofluid through microchannels. Relative importance of electric and magnetized forces, as well as quadratic thermal radiation and viscous dissipation are analyzed. Optimization of system entropy under the influence of all these variables is investigated. Wolfram program (Mathematica) then uses a built-in algorithm (ND-Solve function) to solve system of nonlinear simultaneous differential equations that it has created. Numerical data and images emphasize significance of diverse physiological traits of flow volumes. Additionally, use of contour visualizations and circulatory bolus highlights one of the most notable peristaltic motion phenomena, trapping phenomenon. Results indicate that maximizing the Brinkman number leads to more advantageous characteristics of the heat transfer rate. It is possible to comprehend and use the peristaltic and electroosmosis processes in the development of complex lab-on-a-chip devices and microfluidic systems. This innovation boosts productivity and usefulness in fields that require accurate regulation of fluids at microscale, such as chemical detection and biomedical engineering.

The magneto -hydrodynamic (MHD) flow of non -Newtonian nanofluid with variable thermal conductivity past a moving surface of variable thickness has been investigated in the present work. The flow in this discussion obeys Casson model through a porous medium. Moreover, the effects of thermal radiation, heat generation, Ohmic heating, viscous dissipation and chemical reaction are taken into account. The governing non-linear partial differential equations (PDEs) which describe the velocity, temperature and nanoparticle concentration are converted to a non-linear system of ordinary differential equations (ODEs) using similarities transformation. The obtained system of equations is solved by using a numerical technique with the help of shooting method. The impacts of various parameters on the fluid behaviour are discussed and illustrated graphically via a set of figures. It is found that the velocity increases with increasing of the magnetic field parameter. Also, the temperature increases as the thermal radiation parameter rises. Moreover, an increment in the Brownian motion parameter causes a reduction in nanoparticle concentration.

The main purpose of this study is to investigate the influence of the chemical reaction and activation energy on peristaltic flow of MHD Jeffery nanofluid through a non-Darcy porous medium in the gap between two coaxial tubes inclined at an angle alpha alpha. Couple stresses, radiation, heat generation/absorption, magnetic field, viscous dissipation, and thermal diffusion and diffusion thermo effects are taken into account. The long wavelength and low Reynolds number approximations are used to simplify the non-linear equations governing the flow. Then, a semi-analytical method called the homotopy perturbation method (HPM) is employed to solve the non-linear equations. Graphs for velocity, temperature, and nanoparticle concentration distributions are plotted. Graphical representations of skin friction coefficient, heat transfer coefficient, Nusselt number, and Sherwood number are sketched. Physical explanations for the results are provided. Findings revealed that the increase of the ratio of relaxation to retardation times of Jeffery nanofluid lambda 1 lambda 1 and the couple stress coefficient eta ' decreases the velocity profile, while the couple stress parameter gamma(1) increases it. Also, the velocity has a dual behavior under the infuence of Darcy number Da and Hartman number MM. Moreover, the temperature decreases with an increase of the radiation parameter RR, but an opposite reaction observes by increasing Hartman number MM and the thermophoresis parameter Nt. Furthermore, a reduction in the nanoparticle concentration profile occurs by increasing xi, rho(1), and E. The motion of gastric juice when an endoscope is inserted through a small intestine is a famous example that describes the model of this study.

The primary aim of this study was to examine the peristaltic flow of an unsteady non-Newtonian TiO2 nanofluid through a uniformly symmetric channel under the influence of electro-osmosis. The fluid behavior was modeled by the Sutterby model. Furthermore, the flow took place through a porous medium, following a modified form of Darcy’s law. Additionally, the impacts of Dufour and Soret effects, chemical reaction, activation energy, viscous dissipation, heat generation, and thermal radiation were considered. A wave transformation was used to simplify the governing equations describing the velocity, temperature, and nanoparticle concentration. These simplified equations were then solved analytically using the homotopy perturbation method. Additionally, set figures were employed to illustrate and discuss the impact of the physical parameters involved in the problem on the obtained solutions. It is found that the presence of a modified Darcy’s medium in the Navier–Stokes equation results in a porous term that is dependent on the index of the Sutterby model. Furthermore, it is found that as the thermophoresis parameter increases, the nanoparticles are more concentrated, and their flow from the hot region to the cold region is more effective. Additionally, it is observed that in the presence of thermal radiation, the activation energy and the Brownian motion parameter have similar effects on the concentration profile.

In this theoretical paper, an analysis is undertaken to explore the peristaltic transition of a non-Newtonian Bingham nanofluid within a non-uniform microchannel oriented horizontally. This inquiry investigates the entropy generation arising from the flow of magnetohydrodynamic (MHD) and the accompanying heat transport. This theoretical investigation addresses the behavior of an electrically conductive fluid influenced by electroosmotic flow, incorporating the effects of couple stresses and Darcy law with a heat generation scheme. To bolster the robustness of the study, an activation energy term is incorporated into the nanoparticle concentration using both a modified Arrhenius model and a Buongiorno-type approach. The assumptions of long wavelengths and low Reynolds numbers are applied to change the complex equations that describe fluid motion into ordinary ones. The homotopy perturbation mechanism is utilized to solve the derived neutralized equations. The findings reveal that the critical velocity escalates with an augmentation in both the electroosmotic parameter and the regularization parameter. Moreover, the elevation of the heat absorption parameter and thermophoresis contributes to the augmentation of the temperature profile. Additionally, it is noted that an augmentation in the activation energy parameter has a positive impact on the concentration approach. This consideration recognizes broad applicability in both clinical and industrial settings. This research is beneficial in micro-fabrication mechanisms, reservoir engineering, and the chemical industry, where electro-osmotic energy and mass exchanges play a crucial role.

This study investigates the impact of electroosmosis on the peristaltic flow of unsteady micropolar nanofluid with heat transfer. The findings could enhance the design of peristaltic pumps, potentially improving drug delivery systems, simulations of blood flow in medical devices, and cancer treatments. The fluid under investigation adheres to a micropolar model and flows through a microchannel that exhibits peristalsis along its walls. Moreover, the system is subjected to various external effects, including a uniform magnetic field, the electroosmotic phenomenon, heat absorption, and a chemical reaction with activation energy. Consequently, the problem is mathematically modulated by a system of nonlinear partial differential equations governing the velocity, temperature, and nanoparticle concentration. By employing wave transformation, these governing equations are reduced to ordinary differential equations (ODEs). The reduced equations were solved both analytically, using the homotopy perturbation method, and numerically, using the Runge–Kutta–Merson method. A comparison was made between the solutions, which were found to be closely aligned. Furthermore, a series of figures were employed to provide visual representation and discussion of the implications of the physical properties. The calculations reveal that the electroosmotic flow (EOF) enhances the axial flow of the micropolar fluid along the direction of the applied electric field. It is also observed that the increase in the activation energy (which indicates a low reaction rate) increases the concentration profile whereas the increase in the reaction rate parameter reduces the concentration profile. Additionally, the spin velocity of the particles is diminished by either an increase in the magnetic parameter or the coupling parameter.

Non-Newtonian nanofluids are widely utilized in medical and engineering fields, such as in cooling of microchips, lubrications, cancer therapy, drug delivery etc. In the present article, we focused on the electro-osmotic effect on the peristaltic transport of a non-Newtonian nanofluid inside a horizontal micro-channel. The fluid obeys Williamson model, flowing through a porous medium with modified Darcy's law. In addition, the effects of a chemical reaction with the contribution of activation energy are taken in consideration. Furthermore, in the case of modified Darcy's law, the apparent viscosity of the fluid is used in the governing equations. Furthermore, when temperature of the hot wall tube is less than three times that of the cold wall, the term of the activation energy is simplified by using Taylor expansion. The governing equations that illustrate the velocity, temperature, and concentration of nanoparticles distributions are considered and simplified under the assumptions of a long wavelength and low Reynolds number. The homotopy perturbation method is used as semi-analytical solution for the governing equations. Moreover, some figures are used to illustrate and discuss the role of physical parameters entering the problem on the obtained solutions. Since, most of non-Newtonian fluids are viscoelastic materials, it is important to discuss the effect of Weissenberg number that represents product of strain rate and relaxation time. It is found that Weissenberg number has dual effects on the axial velocity as well as the temperature and the concentration distributions. In addition, according to Fick's law of diffusion; the temperature and concentration distributions should have opposite effects, however, it is found that the increases in the thermophoresis parameter increases both temperature and concentration distributions. This means the nanoparticles are more concentrated when migrates from one side of the tube to the other side. Furthermore, the graphs illustrate the dissimilar effect of the activation energy and the rate of the chemical reaction on the concentration of nanoparticles.

The present study investigates the impact of an unsteady internal flow of a particulate nanofluid within a porous material on the heat and mass transfer along a circular horizontal conduit. It is assumed that both the carrier nanofluid and the dust particles have a high viscosity and are hence incompressible. To kick off this two-phase flow, a constant pressure gradient is applied along the axial direction of the circular pipe. The porous medium’s drag is explained by Darcy’s law and the energy calculations account for the Darcy limit of porous dissipation. A set of nonlinear partial differential equations (PDEs) is used to characterize the nanofluid and dust particle phases, as well as the concentration of suspended nanoparticles. These PDEs were numerically solved using the methodology of finite differences. Coefficients of skin friction and flow rates regarding both phases were also calculated. The novelty lies in the ability of numerical simulation to capture the intricate interplay between Brownian motion, thermophoretic diffusion, and fluid flow within nanofluids. This approach allows for detailed analysis of the complex phenomena involved, which may not be easily achieved through experimental investigations alone. These profiles are formed as a result of the regulating physical factors. Graphs and tabular data are utilized to visually represent the impact of different parameters on solutions. Ultimately, an evaluation of the current solutions for some special cases with previously published findings demonstrates the precision and reliability of the present results.

In this theoretical paper, an investigation is conducted into the peristaltic transition of a hyperbolic tangent nanofluid that contains mobile gyrotactic microorganisms. This study examines the entropy generation resulting from magnetohydrodynamic (MHD) flow and heat transport. The analysis encompasses an anisotropically stenosed endoscope, which is influenced by Ion-slip, activation energy, viscous dissipation, Hall efficacy, Joule heating and entropy generation. The impacts of nonlinear thermal radiation and chemical processes with Soret and Dufour schemes are studied. The porous medium is described using a modified form of Darcy's principle involving a Forchheimer framework. The assumptions involve the extended wavelength besdes reduced Reynolds numeral. The homotopy perturbation strategy is employed to solve the resulting equations. The results show that the critical velocity rises as the local temperature Grashof numeral increases. Moreover, the study offers insights into the movement of digestive gastric fluid within the small intestine as the endoscope moves through.

The research covers important information in fluid dynamics because it has many important applications in different fields. It also has important results that are considered an addition to the field of fluid dynamics. I accept it

The present analytical study exposed the impact of Cattaneo - Christov heat and mass fluxes on the peristaltic blood influx. The impacts of Hall and ion slip currents are imposed. The Sisko micropolar nanofluid through porous midst is also presumed. The influences of heat generation absorption, thermal radiation, and chemical reaction are presupposed. The slip constraint for both velocity and temperature are postulated. The convective restrictions for nanofluid volume fraction and concentration are examined. The coupled differential systems of equations yield Soret and Dufour feature. The supposition of the long wavelength as well as low Reynolds number is applied to convert the system of partial differential equations into an unpretentious formula (ordinary differential ones). Over and above, the resultant analytical solutions of these equations are tackled essentially by employing both procedures of the conventional perturbation and the homotopy perturbation method (HPM). The diverse physical variables impact on the resultant allocations are calculated numerically and elucidated graphically through a group of graphs. It is recorded that the axial velocity dwindles with an escalating in the magnitudes of Hartman number. Meanwhile, it elevates with rising in Sisko parameter. The spin velocity decays with the elevating in the microrotation parameter. The enriching in heat relaxation causes a dwindling influence on the temperature. Further, escalating the nano Biot number causes a declination in nanoparticles volume fraction. This study is very helpful and has prosperous significant in diverse medical implementations as gold nanoparticles are utilized in the remedy of cancer tumor. (c) 2024 L&H Scientific Publishing, LLC. All rights reserved.

The main objective of this study was to investigate the peristaltic flow of an unsteady non-Newtonian nanofluid through a uniformly symmetric vertical duct. The investigation was conducted considering the presence of external electric and magnetic fields, which led to the occurrence of both electroosmosis and induced magnetic field phenomena. The nonNewtonian fluid obeys the third-order model. Furthermore, the flow is through a porous medium which follows the modified form of Darcy's law. The study also considered the influences of mixed convection, Dufour and Soret, chemical reaction, activation energy, viscous dissipation, and heat generation in the system. To simplify the governing equations that describe velocity, temperature, and nanoparticle concentration, wave transformation techniques were employed. The resulting simplified equations were then analytically solved using the homotopy perturbation method (HPM). Furthermore, a set of figures were utilized to visually illustrate and discuss the influence of the various physical parameters involved in the problem on the solutions obtained. The investigation provided a clearer understanding of the relationships and effects of the parameters on the system's behavior. It is found that the modified Darcy term significantly extends the impact of permeability in the porous medium (near the walls) to the core flow (middle of the tube). As a result, the axial velocity is enhanced in the flow direction. Moreover, the investigation reveals a clear correlation between the permeability parameter and the electro-osmotic parameter. This relationship exists due to the inverse proportionality between the electro-osmotic parameter and the length of the electric double layer (EDL) that is formed adjacent to the walls of the tube (high porous region). Furthermore, it is found that as the activation energy increases the rate of the chemical reaction is reduced which in turn reduces the concentration of nanoparticles. Additionally, it is found that as the external magnetic field strength increases the nanoparticles are more concentrated which helps in many biological applications such as drug delivery. Conversely, as induced electric field strength increases the nanoparticles disperse through the fluid.

In this study, we focused on the heat transfer through a uniformly inclined rectangular duct caused by the electro-osmotic peristaltic flow of an unsteady non-Newtonian nanofluid. With couple stress, the fluid obeys the Papanastasiou model. The flow is through a porous medium that follows Darcy’s law in a modified form. In addition, Dufour and Soret effects, mixed convection, the impacts of a chemical reaction, and the effects of viscous couple stress dissipation are all considered. The governing equations that explain the velocity, temperature, and concentration of nanoparticles are simplified when wave transformation is used. The homotopy perturbation method was used to solve these equations analytically. Additionally, a collection of figures is used to discuss and visually illustrate the consequences of the physical characteristics. In fact, the modified Darcy’s law makes the velocity gradient appear in the momentum equation, which increases the contribution of the velocity gradient to the velocity profile. In addition, the electro-osmotic parameter and Helmholtz-Smoluchowski velocity have a significant impact on the velocity gradient’s direction, as well as the velocity gradient’s ability to be either positive or negative, depending on their values. In addition, in the case of forced convection, the values of the Nusselt number and the Sherwood number are highly affected by the value of Helmholtz–Smoluchowski velocity. The current findings have applications in biology and medicine, particularly in cancer therapy, which involves peristaltic blood pumps(arteries) and suspended gold nanoparticles (nanofluid). According to our knowledge, no prior studies have merged the couple stress Papanastasiou model and the modified Darcy’s law.

The theme of this study is to investigate the influence of the chemical reaction and activation energy on MHD peristaltic flow of Jeffery nanofluids in an inclined symmetric channel through a porous medium. Joule heating, radiation, viscous dissipation, heat generation/absorption, activation energy, and thermal diffusion and diffusion thermo effects are involved. The long wavelength and low Reynolds number approximations are used to simplify the non-linear equations that govern the flow. Then, the simplified equations are solved by using the homotopy perturbation method (HPM). We have depicted the velocity, temperature, solute concentration, and nanoparticles volume friction graphically. Physical explanations for the results are provided. The influence of interest parameters on entropy generation is also observed. Numerical results for the heat transfer coefficient, Nusselt number, and Sherwood number are presented. The results revealed that an increase in the value of the ratio of relaxation to retardation times of Jeffery nanofluid enhances the velocity distribution, while a reduction in the solute concentration distribution occurs by increasing the activation energy parameter and the temperature difference parameter . We also discovered that an increase of the chemical reaction parameter increases the temperature profile and decreases the velocity and solute concentration profiles. Furthermore, the velocity becomes lower along the normal axis y and ends up with the minimum value near the upper wall of the channel. Also, the maximum and minimum values of the velocity increase with an increase of the second order slip parameter , while they decrease as Darcy number increases

The main objective of this work is to present a comprehensive study that scrutinize the influence of DD convection and induced magnetic field on peristaltic pumping of Boron Nitride-Ethylene Glycol nanofluid flow through a vertical complex irregular microchannel. Experimental study showed that the nanofluid created by suspending Boron Nitride particles in a combination of Ethylene Glycol exhibited non-Newtonian characteristics. Further, the Carreau's fluid model provides accurate predictions about the rheological properties of BN-EG nanofluid. In order to imitate complicated peristaltic wave propagation conditions, sophisticated waveforms are forced at the walls. The essential properties of Brownian motion and thermophoresis phenomena are also included in simulating of heat equation as well as viscous dissipation. Mathematical simulation is performed by utilizing the lubrication approach. The resulting nonlinear coupled differential equation system is solved numerically using the built-in command (ND Solve function) in the Mathematica program. Numerical and pictorial evidence is used to illustrate the importance of various physiological features of flow quantities. The major findings demonstrated that the thermal resistance is observed to rise as the Soret and Dufour numbers increase, while the dissolvent concentration and nanoparticles volume fraction have the opposite effect.