Eyring-Powell Fluid Research Articles

Numerical simulation for nonlinear radiated Eyring-Powell nanofluid considering magnetic dipole and activation energy

Abstract The boundary-driven magnetized flow of non-Newtonian nanofluids have several applications in the processing and manufacturing of electronic devices, medicine and medical equipments, glass fiber, paper production, polymer sheets and filaments. Due to all such potential implications, we characterized the Powell-Eyring fluid over a stretching surface in the regime of magnetic dipole. Rheological flows with heat transfer have superficial roles in the modern industries. We evaluated the transportation of heat under nonlinear thermal radiation. Convective heat condition is taken into account. Furthermore, the Brownian and thermophoresis aspects of nanofluid with activation energy are explored. Appropriate transformations are implemented to convert the nonlinear system of partial differential expressions into system of ordinary differential ones. The governing dimensionless equations are solved by shooting scheme. The outcomes of sundry variables are demonstrated through graphs and numerical benchmarks.

Non-similar Solution of Eyring–Powell Fluid Flow and Heat Transfer with Convective Boundary Condition: Homotopy Analysis Method

The study presents the mixed convective boundary layer flow of Eyring–Powell fluid over a vertical plate with variable velocity and temperature distribution taking convective boundary condition into account. The transformed non-dimensional governing equations in non-similar nature are solved by employing hybrid technique: local non-similarity method in conjunction with homotopy analysis method. The convergence of homotopy series solution is obtained and presented for various order of approximations. The series solutions have been validated by comparing the results available in the literature and found good agreement. The obtained results are shown properly by graphs and discussed for various values of thermo-physical parameters. It is found that the Eyring–Powell fluid shows higher velocity than Newtonian fluid whereas lower temperature than Newtonian fluid. Furthermore as increase in fluid parameter, ratio of relaxation and retardation parameter, skin friction coefficient decreased and heat transfer coefficient increased. The study finds wide applications in the field of design of heat exchangers, process of cooling of metallic plate, extrusion of plastic sheets, in polymer and glass industries etc.

Analysis of Convective Transport of Temperature-Dependent Viscosity for Non-Newtonian Erying Powell Fluid: A Numerical Approach

Non-Newtonian is a type of fluid that does not comply with the viscosity under the Law of Newton and is being widely used in industrial applications. These include those related to chemical industries, cosmetics manufacturing, pharmaceutical field, food processing, as well as oil and gas activities. The inability of the conventional equations of Navier–Stokes to accurately depict rheological behavior for certain fluids led to an emergence study for non-Newtonian fluids’ models. In line with this, a mathematical model of forced convective flow on non-Newtonian Eyring Powell fluid under temperature-dependent viscosity (TDV) circumstance is formulated. The fluid model is embedded with the Newtonian heating (NH) boundary condition as a heating circumstance and is assumed to move over a stretching sheet acting vertically. Using appropriate similarity variables, the respective model was converted into ordinary differential equations (ODE), which was later solved utilizing the Keller box approach. The present model is validated by comparing the existing output in literature at certain special limiting cases, where the validation results display a firm agreement. The current outputs for the proposed model are shown in tabular and graphical form for variation of skin friction plus Nusselt number, velocity and temperature distribution, respectively.

Mixed Convection of Non-Newtonian Erying Powell Fluid with Temperature-Dependent Viscosity over a Vertically Stretched Surface

The viscosity of a substance or material is intensely influenced by the temperature, especially in the field of lubricant engineering where the changeable temperature is well executed. In this paper, the problem of temperature-dependent viscosity on mixed convection flow of Eyring Powell fluid was studied together with Newtonian heating thermal boundary condition. The flow was assumed to move over a vertical stretching sheet. The model of the problem, which is in partial differential equations, was first transformed to ordinary differential equations using appropriate transformations. This approach was considered to reduce the complexity of the equations. Then, the transformed equations were solved using the Keller box method under the finite difference scheme approach. The validation process of the results was performed, and it was found to be in an excellent agreement. The results on the present computation are shown in tabular form and also graphical illustration. The major finding was observed where the skin friction and Nusselt number were boosted in the strong viscosity.

Homotopy solution for MHD mixed convective unsteady flow of a Powell-Eyring fluid in a vertical porous space with oscillating wall temperature

In this paper, unsteady magnetohydrodynamic (MHD) flow of Powell-Eyring fluid in a vertical channel with diffusion thermo and thermal diffusion effects in the presence of heat source have been studied. The governing nonlinear, coupled partial differential equations are reduced to ODEs using oscillating parameter and then solved by homotopy analysis method (HAM). The influence of emerging parameters on heat and mass transfer characteristics of the flow are studied. It is found that the velocity of a Non-Newtonian fluid is found to decrease in comparison with Newtonian fluid. Also, it is observed that thermal parameters and Soret number are lead to promote the temperature of the fluid significantly. Increasing magnetic parameter tends to produce oscillating behaviour on volume flow rate whereas uniform depreciation can be noticed with increasing Schmidt number.

Homotopy solution for MHD mixed convective unsteady flow of a Powell-Eyring fluid in a vertical porous space with oscillating wall temperature

In this paper, unsteady magnetohydrodynamic (MHD) flow of Powell-Eyring fluid in a vertical channel with diffusion thermo and thermal diffusion effects in the presence of heat source have been studied. The governing nonlinear, coupled partial differential equations are reduced to ODEs using oscillating parameter and then solved by homotopy analysis method (HAM). The influence of emerging parameters on heat and mass transfer characteristics of the flow are studied. It is found that the velocity of a Non-Newtonian fluid is found to decrease in comparison with Newtonian fluid. Also, it is observed that thermal parameters and Soret number are lead to promote the temperature of the fluid significantly. Increasing magnetic parameter tends to produce oscillating behaviour on volume flow rate whereas uniform depreciation can be noticed with increasing Schmidt number.

Thermal analysis of an Eyring-Powell fluid flow-through a constricted channel

This paper is aimed to investigate the entropy generation in a MHD convective flow of Eyring-Powell fluid through a mildly constricted channel. The constriction is assumed to be of regular or irregular shape and is presented inside the channel wall. Mathematical model is developed using the basic laws of conservation of mass, momentum, and energy. The governing equations are normalized using appropriate set of dimensionless variables and solutions are obtained by regular perturbation technique. The solutions are further used to calculate the entropy expression associated with the Second law of thermodynamics. The heat transfer characteristics, like, temperature, isotherms, entropy generation number entropy lines and the Bejan number are analyzed for the variation in magnetic field, shape parameter, and material constants. It is observed that entropy production is maximum in the narrow part of the channel. Moreover, entropy generation rate is higher for the regular parabolic shape as compared to irregular shapes of constriction.

Mathematical model for blood flow through the stenosed channel

In this paper, we investigate the blood flow through a stenoised channel. In current study Cartesian coordinates are contemplated for flow in the channel and in an axisymmetric tube with transfer of heat having cosine shape stenosis. Blood is supposed as Eyring–Powell fluid which is independent of time. Thermal conductivity is determined by temperature. After assimilating these deliberations, dimensional equations are transformed into non-dimensional system of differential equations with the use of similarity transformations and are then solved numerically. A parametric study is executed to depict the impact of various parameters on the velocity and temperature fields of fluid. Heat transfer coefficient and skin friction are also explained through graphs and discussed in tabular form for distinct values of dimensionless parameters. The current investigation tells that velocity field significantly increases by rising the value of M and δ. Temperature field increases for extended value of δ, M, K, B, A and Pr. Nusselt number curve increases due to increase in Pr.

The impacts of varying magnetic field and free convection heat transfer on an Eyring–Powell fluid flow with peristalsis: VIM solution

A mathematical model of a non-Newtonian fluid (Eyring–Powell fluid) flow with peristalsis under the effect of varying magnetic field and free convection heat transfer has been discussed. Most of the previous attempts of peristaltic flow problems for a non-Newtonian fluid have been solved by using the perturbation technique for a small non-Newtonian parameter, which gives some limits for the results. To avoid such restriction, the variational iteration method (VIM) is applied to solve the current model. A code is established by using the symbolic software MATHEMATICA to get the successive solutions. Semi-analytical solutions are found by VIM for the velocity, heat transfer, pressure gradient and stream function, which include Eyring–Powell fluid parameters. Moreover, a comparison between VIM and numerical solutions is discussed. The obtained results show that the variation of the heat transfer for the Newtonian fluid is large compared with the Eyring–Powell fluid. In addition, it is noteworthy that the peristaltic transport overcomes on Lorentz force nearby the peristaltic walls.

Influence of heat generation on magnetohydrodynamic (MHD) flow using a theory of kinetics for liquids

In the present article, the influence of heat generation on the magnetohydrodynamic (MHD) flow of an Eyring–Powell fluid along a permeable plate has been explored. The influence of heat generation or absorption on a steady flow of non-Newtonian fluid over a surface is investigated. The governing equations obtained from Eyring–Powell fluid model are transubstantiated into ordinary differential equations using suitable transformations. Along with the Runge–Kutta method, we attained a numerical solution of the present problem by explicating the shooting technique. Influences of distinct parameters on temperature and the velocity field profiles are highlighted in graphs and tables. The acceleration in the value of γ, velocity profile shows decreasing behavior, but recovery occurs with an increase in M. The streamlines and three-dimensional results have been shown graphically for a selection of different parameters. Numerical results of the present work have been discussed with the support of tables.

Heat transfer analysis of magneto-Eyring–Powell fluid over a nonlinear stretching surface with multiple slip effects: Application of Roseland’s heat flux

Non-Newtonian fluid model is intricate, nonlinear, and interesting to study because of the presence of rheological flow parameters and viscoelastic properties, which tend to emerge and make industrial flows considerably more complex to explain accurately. Improvement of industrial applications, such as glass fabrication, is an important consequence of this study. In this manuscript, we have explored the combined impact of the higher order slip with variable transverse magnetic field flow and thermal transport using Roseland’s heat flux of the Eyring–Powell fluid with assumption of boundary layer, on nonlinear stretching sheet, in which fluid is considered electrically conducting. The transformed ordinary differential equations are solved by three-stage Lobatto IIIa collocation finite difference scheme using MATLAB. The impact of pertinent flow parameters on dimensionless velocity and temperature profiles is presented graphically and discussed in detail. Obtained results confirm that excellent agreement is achieved for the limiting case with those from the available literature. It is found that skin friction increases in the presence of slip parameters, whereas the opposite behaviour is noted in the Nusselt number.

Eyring–Powell nanofluid flow with nonlinear mixed convection: Entropy generation minimization

Background: Entropy is the amount of energy which is lost during any irreversible process. Here our main focus is that how can we reduce this energy loss to enhance the capability of our system. Blood is an example of Eyring–Powell fluid. Many strategies are used to rise the capacity of heat transport. Heat transport can be enhanced by intensifying the materials thermal conductivity through nanoparticles. Thermal conductivity of the material can be enhanced by adding nanoparticles in base fluid. The objective of this work is to discuss entropy generation in MHD Eyring–Powell nanofluid flow. The flow is generated by a linear stretchable surface. Current analysis includes the effects of viscous dissipation, nonlinear mixed convection and Joule heating. Nanoparticles analyzed the consequences of Brownian motion and thermophoresis effects.Method: The boundary layer flow equations are solved for series solutions by applying homotopic technique.Results and conclusion: Graphical results of involved quantities like entropy generation, velocity, concentration and thermal fields are presented. Skin friction, Sherwood and Nusselt number are numerically scrutinized.

MHD non-Newtonian thin film fluid flow due to an unsteady stretching sheet under thermocapillarity phenomenon

This theoretical work explores the effect of the magnetic field on the liquid thin film flow of a non-Newtonian Powell–Eyring fluid. The thermocapillarity phenomenon in association with the effect of slip velocity is studied. In our research, we cannot ignore the important role of the numerical shooting method which employed to get the solution for our problem. This method helped us to sketch both the dimensionless velocity and the dimensionless temperature for several parameters. Furthermore, the authentication on the correctness and effectiveness for our method is checked by performing a comparison between this problem in the absence of some parameters and the previously published work, which confirms the robustness for the shooting method. Finally, an overview of the effect of the emerging parameters on the velocity and temperature profiles as well as the local skin-friction coefficient and the local Nusselt number is done.

Numerical solution for flow of a Eyring–Powell fluid in a pipe with prescribed surface temperature

In the current study, the flow and heat transfer of MHD Eyring–Powell fluid in a circular infinite pipe is discussed. The rheology of fluid is described by constitutive equation of Eyring–Powell fluid. The solution is constructed for both constant and variable viscosity cases. For variable viscosity case, the viscosity function is defined by Reynolds and Vogel’s models. The solution of each case is calculated numerically with the help of eminent iterative numerical technique. The effects of thermo-fluidic parameters on flow and heat transfer phenomenon are highlighted through graphs. The velocity and temperature profiles diminish against magnetic parameter $$(M_{e} )$$ and material parameter (M) in all cases, whereas both velocity and temperature profiles rise via magnitude of the pressure gradient and material parameter Y. The validity of our numerical results due to shooting method is presented by comparing them with the numerical results produced by pseudo-spectral collocation method. Relative absolute errors are plotted, and achieved accuracies are of the order four and five in w and $$\theta$$, respectively. The outcomes of current investigation may be useful in thin film, catalytic reactors, polymer solutions and paper production, etc.

Powell–Eyring fluid flow towards an isothermal sphere in a non-Darcy porous medium

Non-Newtonian viscoelastic fluid flow past an isothermal sphere embedded in non-Darcy porous medium is examined numerically in this work. To be specific, the non-Newtonian Powell–Eyring fluid in the presence of both the heat and mass characteristics is mathematically modelled in terms of differential system. A non-Darcy drag force model is employed to simulate the effects of linear porous media drag and second-order Forchheimer drag. The surface of the sphere is maintained at a constant temperature and concentration. The numerical solution of the resultant system is reported via the Keller box method. Both tabular and graphical forms are adopted to identify the variations in Powell–Eyring fluid velocity, Powell–Eyring fluid temperature, and Powell–Eyring fluid concentration. In addition, the surface physical quantities, namely, skin friction and heat and mass transfer rates, are explored. The obtained observations are validated with earlier Newtonian studies. We found an excellent match in this regard. It is found that the velocity is reduced with increasing fluid parameter (ε), Forchheimer parameter (Λ), and tangential coordinate (ξ). In contrast, the temperature and concentration are increasing with increasing value of ε. A very slight increase in velocity is seen with an increase in the local non-Newtonian parameter, δ. But the temperature and concentration decrease slightly with an increase in δ. An increase in Darcy parameter enhances velocity but reduces both temperature and concentration. The present study finds an extensive array of applications in modern nuclear engineering, mineral and chemical process engineering, nuclear waste in geomaterial repositories, petroleum product filtration, and insulation systems.

Dufour and Soret effects on unsteady heat and mass transfer for Powell-Eyring fluid flow over an expanding permeable sheet

In the present analysis, the Dufour and Soret effects on unsteady heat-mass transfer of a viscous incompressible Powell-Eyring fluids flow past an expanding/shrinking permeable sheet are reported. The fluid boundary layer develops over the variable sheet with suction/injection to the non-uniform free stream velocity. Under the symmetry group of transformations, the governing equations along with three independent variables, are converted into a system of PDEs with two independent variables. Finally, by employing the order-reduction technique the PDEs are transformed into ODEs, which are then solved numerically. The results are presented graphically and analyzed. The main advantage of this technique is that without any prior knowledge, one can easily find the scaling transformations, expanding velocity, suction/injection velocity, and free-stream velocity. From computed numerical results many important findings are obtained. Most importantly, thermal and concentration overshoots are found for larger values of Dufour and Soret numbers, respectively. Also, thermal and concentration crossing over found for different values of Soret and Dufour numbers, respectively.

Numerical solutions for the problem of the boundary layer flow of a Powell–Eyring fluid over an exponential sheet using the spectral relaxation method

The spectral relaxation method is a very powerful tool which was applied in this paper to get the numerical solution for the system of nonlinear ordinary differential equations which describe the problem of fluid flow of a Powell–Eyring model past an exponentially shrinking sheet with the presence of magnetic field and thermal radiation. The introduced method is based on the spectral relaxation method, which is successfully used to solve this type of equations. Also, this method is developed from the Gauss–Seidel idea of reducing the governing nonlinear system of ordinary differential equations into smaller systems of linear equations. Likewise, the influences of the governing parameters on the velocity and temperature profiles are studied graphically. Results of this study shed light on the accuracy and efficiency of the proposed method in solving this type of the nonlinear boundary layer equations.

Second law analysis of Powell–Eyring fluid flow through an inclined microchannel with thermal radiation

The present paper investigated the Eyring–Powell fluid flow through an inclined microchannel in the presence of radiation and convective heating effects. The energy efficiency has been analyzed via entropy generation of the system. The governing differential equations are converted by using dimensionless parameters into a set of non-dimensionalzed differential equations. The set of these converted equations are solved by using the finite element method. The various pertinent non dimensional parameters on the flow are illustrated graphically and discussed in detail. The thermal performance can be improved through the effects of radiation, viscous heating and convective condition. It is found that, with an increase in Reynolds number, entropy generation decreases near the lower plate but the reverse trend is observed near the upper plate.

On magnetized non-Newtonian rotatory fluid flow field

The current pagination is devoted to offering the untapped features of non-Newtonian rotatory magnetized fluid flow over the solid disk. The said non-Newtonian fluid model is a Powell–Eyring fluid model. The flow field is further carried with suspended nanoparticles with velocity slip effects. The strength of the article is a complex mathematical modeling subject to physical effects mentioned before, and the computational results are provided through the self-coded algorithm rather than to move on with the usual built-in scheme. To make the implementation possible, the obtained flow-narrating system is converted into a system having fewer independents. The key involved parameters are Powell–Eyring fluid, magnetic field, velocity slip, thermophoresis, and Brownian motion parameters. The dependent quantities namely axial, tangential velocities, temperature, and concentration are examined against flow-controlling parameters. The obtained outcomes in this direction are offered by means of graphical trends. It is noticed that both axial and radial velocities possess direct relation with Power–Eyring parameter ( M). The Powell–Eyring fluid temperature is an increasing function of the thermophoresis parameter. Furthermore, the Powell–Eyring concentration enhances significantly toward the higher values of the Brownian motion parameter.

A study on magneto hydrodynamics Jeffery-Hamel flow with heat transfer problem in Eyring-Powell fluid using Differential Transform Method

A study on magneto hydrodynamics Jeffery-Hamel flow with heat transfer problem in Eyring-Powell fluid using Differential Transform Method