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.

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 study investigates the flow of a Newtonian Cu O nanofluid through a non-Darcy porous medium with radially varying viscosity, which is crucial for various industries such as pharmaceuticals, chemicals, nuclear, solar, and solar technologies. The peristaltic motion of the nanofluid is studied with thermal radiation and chemical reaction effects, and the viscosity varies with both radius and axial coordinates. The study assumes low Reynolds and long wavelength assumptions and uses the homotopy perturbation technique to obtain a semi-analytical solution of velocity, temperature, nanoparticle concentration, and skin friction. The results show that axial velocity increases with the increase of slip velocity and viscosity parameters, while wave amplitude and chemical reaction parameters increase while nanoparticle concentration decreases. High viscosity parameters allow fluid nanoparticles to gain more active energy and move more freely, which is the main idea behind crude oil refinement. This physical modeling is essential for physiological flows, such as stomach juice flow during endoscope insertion.

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.

Through heating processes, electrical conductivity plays a crucial role in the food industry. The effects of Joule heating and temperature-dependent electrical conductivity on the boundary layer flow of micropolar fluid were the main topics of this paper. Considerations include thermal radiation, activation energy, and microstructural/multiple slips effects. The resulting partial differential equations system (PDEs) is transformed into a nonlinear ordinary differential equations model using the proper similarity variables (ODEs). The shooting technique, a highly reliable/accurate technique, is used to obtain semi-analytical results. In Mathematica13.1.1, apply the generalised differential transform method (GDTM), Dawar 2021 newly published results are used to approve/confirm the accuracy of the acquired results. Findings demonstrate that the parameter of temperature-dependent electrical conductivity enhances fluid temperature and increases energy gain in the heating operation system, which is important for the design of Ohmic heaters (food industry processes).

This article discusses the effects of entropy generation as well as slip velocity condition on MHD Jeffery nanofluid flow through a porous medium in a channel with peristalsis. We take the effects of mixed convection, heat source, double diffusion and chemical reaction into consideration. Using the assumption of low-Reynolds number and long-wavelength, series solutions of the governing equations are obtained via homotopy perturbation method. Results will be discussed at various parameters of the problem and drawn graphically. Physically, our model is consistent with the motion of digestive juice in the bowel whenever we are going to insert an endoscopy through it. It is noticed that the axial velocity magnifies with an increase in the values of both first and second slip parameters. Meanwhile, the value of the axial velocity reduces with the elevation in the values of both Grashoff and Darcy numbers. On the other hand, the elevation in the value of thermal radiation leads to a reduction in the value of fluid temperature. Furthermore, increasing in the value of order of chemical reaction parameter makes an enhancement in the value of the solutal concentration. It is noticed also that the entropy generation enhances with the increment in the value of Eckert number. The current study has many accomplishments in several scientific areas like engineering industry, medicine, and others. Therefore, it represents the gastric juice motion depiction in the human body when an endoscope is inserted through it.

Abstract In this paper, non-Newtonian nanofluid flow with heat transfer through a non-Darcy porous medium has been studied, in the presence of effects. Moreover, The heat source, viscous and Ohmic dissipation, chemical reaction, elctromagnetic field, and biot number effects are taken into consideration. Suitable similarity transformations simplify the system of non-linear equations which govern the flow. Then, the Rung-Kutta-Merson method in a shooting and matching technique is used to obtain the numerical solutions of the velocity, temperature, and nanoparticles concentration as functions of the physical parameters of the problem. Moreover, the effects of these parameters on these solutions are discussed numerically and depicted graphically. It is found that both tangential and normal velocities increase or decrease as the Biot number increases. While as both the pressure gradient and radiation parameters increase, the temperature increases or decreases, and both Schmidt numbers and magnetic field parameter lead to increase the nanoparticles concentration.

The purpose of this paper is to investogate the ectromagnetic and micropolar properties on biviscosity fluid flow with heat and mass transfer through a non-Darcy porous medium. Morever, The heat source, viscous dissipation, thermal diffusion and chemical reaction are taken into consideration. The system of non linear equations which govern the motion is transformed into ordinary differential equations by using a suitable similarity transformations. These equations are solved by making use of Rung–Kutta–Merson method in a shooting and matching technique. The numerical solutions of the velocity, microtation velocity, temperature and concentration are obtained as a functions of the physical parameters of the problem. Moreover the effects of these parameters on these solutions are discussed numerically and depicted graphically. It is found that the microtation velocity increases or deceases as the electric parameter, Hartman parameter and the microrotation parameter increase. Morever, the temperature increases as Forschheimer number, Eckert number increase.

An analysis is carried out to study the problem of unsteady squeezing flow of a non-Newtonian nanofluid through a porous medium between two parallel plates. The effects of Hall currents and heat source are taken into consideration. The governing partial differential equations are transformed into a set of nonlinear ordinary differential equations by using similarity transformations. A homotopy perturbation method is performed to obtain analytical solutions for that system of equations. The behaviors of the tangential velocity, normal velocity, temperature, and nanoparticles concentrations distributions are discussed analytically and graphically under the effect of different entering parameters. Physically, our model corresponds to squeezing problems in tunnelling such as study the relation between rock types and its depths in squeezing cases and time dependent stress induced problem in sandstone. This problem provides interesting results which may have many applications in chemistry, biology, and medicine.

Numerical solutions are obtained for the problem which involves both the heat and mass transfer in a hydromagnetic flow of a micropolar fluid past a stretching surface with Ohmic heating and viscous dissipation using Chebyshev finite difference method (ChFD). A similarity transformation was employed to change the governing momentum, angular momentum, energy, and concentration partial differential equations into ordinary ones. Numerical calculations have been carried out for various values of magnetic field parameter, material parameter, Prandtl number, Eckert number, Schmidt number, couple stress at the surface, local Nusselt number and Sherwood number. The numerical results indicate that the temperature and the concentration increase, while the velocities, the Nusselt number and the Sherwood number decrease with increasing magnetic field parameter. In all of the above results, the material parameter has the opposite effect of magnetic field parameter. The temperature increases with increasing Eckert number, and decreases with increasing Prandtl number. An increase in the Schmidt number gives an increase in the Sherwood number, or a decrease in the concentration.

The effect of radiation on MHD steady asymmetric flow of an electrically conducting fluid past a stretching porous sheet in the presence of radiation has been analyzed. Exact solutions for the velocity and temperature fields have been derived and the effects of radiation, magnetic, Prandtl number, wall temperature and suction (or injection) parameters have been studied with the help of graphs.