non-Newtonian Williamson Fluid Research Articles

Numerical heat and mass transfer in magnetized Williamson liquid motion over a sensor wall engulfed in a micro-cantilever system: An application to thin-film fluidic cells

Central focus of this numerical analysis is to investigate the influence of magnetic body force and thermal radiation on the time-dependent electrically conducting two-dimensional viscous incompressible boundary layer flow of non-Newtonian Williamson fluid over a microcantilever sensor surface suspended in a squeezed regime numerically. A novel heat source/sink and Soret effects are included in the respective governing equations. The constructed time-dependent nonlinear coupled partial differential equations are solved by using a bobust RK-4 technique. Increasing magnetic number increases the velocity distribution and decreases the temperature and concentration profiles in the flow regime.Enhancing Soret number increases the mass diffusion profile. Increasing magnetic number suppress the skin-friction coefficient. Heat transport rate booted with rising radiation number and Sherwood number decreased with enlarged Schmidt number in the channel regime. Finally, the numerical accuracy of the present similarity solutions and used numerical method is validated with existing results and observed a remarkable agreement.

Entropy analysis for two-dimensional double-diffusive mixed convective flow of a Williamson nanofluid through a porous medium

The problem of double-diffusive convection is investigated by considering the MHD effect on non-Newtonian Williamson fluid flowing over a porous medium. The nature of fluid flow and the amount of heat and mass transfer are studied by the variation of MHD and porous parameters. The flow equations are coupled having more than one independent variable which can be transformed into a single independent variable by introducing similarity variables and solved numerically with the utilization of builtin MATLAB bvp4c package. The Brownian motion and thermophoresis effects on flow equations are studied graphically and the irreversibility of flow is considered. The presence of the Prandtl number in the momentum equation and its effect on physical parameters are taken into account. The variation of Williamson parameter on velocity, temperature, nanoparticle concentration, and concentration profiles are analyzed. The primary innovation of our research is shown in tables that contrast the acquired outcomes with the earlier conclusions found in the literature. The behavior of energy and concentration profiles are shown through graphs by differing numerical values of physical parameters.

Thermal analysis of AA7075-AA7072/methanol via Williamson hybrid nanofluid model past thin needle: Effects of Lorentz force and irregular heat rise/fall

Hybrid nanofluids have received remarkable attention due their promising thermal performance compared to conventional nanofluids. The use of hybrid nanofluids is widely found in the pumping power, solar collector, electronic components, coolants in nano devices, and engine applications etc. Such types of applications grabbed the attentionof researchers and scientistswith the aim to understand in depththe problems involving the hybrid nanofluids. Therefore, the primary objective of the present investigationis to investigatethe thermal performance of hybrid nanofluid consisting of asuspension of aluminum alloys (AA7075-AA7072) in methanol-base fluid. The non-Newtonian Williamson fluid flow model under Lorentz force, and irregular heat rise/fall impact past incessantly moving thinneedleis considered. The governingflow equations are solved by bvp4c solver. Results are computed for governing flow parameters such as magnetic field parameter, needle thickness parameter, Weissenberg number, volume fractions, and irregular heat rise/fall constants. Graphs confirm that augmenting values of magnetic field parameter, needle thickness parameter, and Weissenberg number lead to downfall of velocity field but reverse behavior is noticed for increasing nanoparticles volume fraction. A rise in temperature field has been noticed by increasing the magnitude of magnetic field, irregular heat rise/fallparameter, and nanoparticles volume fraction but a decline in fluid temperature occurswithraising theneedle thickness parameter. Detailed discussion about the observed variation in physical properties under pertinent parameters effects is presented. The proposed model is validated by comparison with previouslypublished results.

Analytical solution of non-Newtonian Williamson fluid under the effect of magnetohydrodynamics

In this paper, inscribed non-Newtonian Williamson fluid relaxation and contraction phenomena due to the effect of magnetohydrodynamics (MHD) is taken into account. This issue is modeled, and precise solutions are handled using a low Reynolds number and long wavelength approximation. Graphical depiction of the consequences of various parameters on temperature and velocity are provided. It becomes clear that the temperature reactions to increases in Biot numbers are decreased. Considering a cylindrical coordinate system, the impact of various physical parameters on the temperature distribution, velocity, the pressure gradient, and frictional force are secured from the flow for non-Newtonian Williamson fluid exposed from MATLAB. Additionally, it has been discovered that the velocity profile at the tube’s center increases for shear-thinning a fluid and decreases for thickening a fluid. Furthermore, the peristaltic walls show the opposite behavior.

Activation energy and convective heat transfer effects on the radiative Williamson nanofluid flow over a radially stretching surface containing Joule heating and viscous dissipation

This article recognizes the time-dependent axisymmetric flow of a non-Newtonian Williamson fluid caused by a radially stretching surface in the presence of nanoparticles in the porous medium. The combined impacts of Joule heating and viscous dissipation on the flow profiles are also discussed. Chemical reaction at the surface is implemented. The convective heat transfer model and Brownian motion are also studied for the electrically conducting nanofluid flow. The Williamson nanofluid flow has been modeled using a set of partial differential equations based on the fundamental conservation laws of mechanics. By using nondimensional quantities, these equations are first transformed into ordinary differential equations. The Galerkin weighted residual method is performed to resolve these equations numerically. Visual displays and detailed descriptions of the impacts of relevant variables on the thermal performance, concentration field, and velocity field are provided. It is noticed that the thermal profile enhances as the values of the Brownian motion parameter and temperature ratio parameter increase while declining when the values of the velocity slip parameter increase. The Biot number, activation energy, and unsteadiness parameters have proportional effects on the concentration profile, but the reaction parameter has inversely proportional effects on the concentration profile. Heat transfer rate increases with increasing the Weissenberg number and velocity slip parameter, drops with increasing the thermophoresis and unsteadiness parameters, and the Arrhenius activation energy. Finally, a comparison of the obtained numerical solution for the porous and nonporous medium are also done graphically and discussed in details.

Analytical Solutions of Peristalsis Flow of Non-Newtonian Williamson Fluid in a Curved Micro-Channel under the Effects of Electro-Osmotic and Entropy Generation

In the current effort, the effects of entropy generation and electro-osmotic driven peristaltic flow of non-Newtonian Williamson liquid in a curved micro-channel is investigated. Formulation of the problem is conducted in a wave frame of reference. Due to the complexity of non-Newtonian fluid, the analytical solutions of non-linear coupled equations are not easy to obtain and are very rarely found in the literature. For analytical solutions, the governing equations are reduced in the form of the Bessel function. The electric double layer is employed as a result of a zeta potential of about 25 mV. The low Reynolds number and long wavelength approximations are taken into account. Graphical analysis has been carried out for velocity, temperature and entropy for physical parameters. It is noted that the Brinkmann number enhances the temperature. The results of this model will be extremely helpful in designing electro-peristaltic pumps for thermal systems.

Influence of chemical reaction and variable mass diffusivity on non-Newtonian fluid flow due to a rough stretching sheet with magnetic field and Cattaneo-Christov fluxes

A non-Newtonian Williamson fluid flow due to a stretching sheet with radiation, magnetic field, and viscous dissipation effects is described using variable conductivity and variable diffusivity. The Cattaneo-Christov model is used to correctly compute the physical properties of a heat and mass flux model. Both the chemical reaction phenomenon and the slip velocity have an impact on the heat and mass mechanism. The physical problem is represented mathematically as a nonlinear coupled differential system. After that, the shooting method is used to solve the mathematical model numerically. To gain a better understanding of the behavior of governing emergent factors on dimensionless velocity, concentration, and temperature profiles, physical interpretations are created and discussed utilizing graphical and tabular representations. The results show that the Sherwood number and the Nusselt number are both decreased by the magnetic, viscosity, and slip velocity parameters. Also, according to the findings it has been observed that the concentration outlines enhances for the magnetic number, the viscosity parameter, and the slip velocity parameter, but they dwindle for expanding reaction rate values. Finally, after confirmation of our numerical results, the theoretical results show good agreement with previously published work.

Impact of an MHD Cattaneo-Christov model for a Williamson fluid flow across a wedge with a convective boundary condition: Homotopy Analysis Method

The present study aims to scrutinise the influence of the Cattaneo-Christov (CC) heat flux model on magnetohydrodynamic (MHD) laminar boundary-layer flow through a wedge in a non-Newtonian Williamson fluid along with convective boundary condition embedded in a porous medium. Significantly, the presence of the CC model explores the heat transfer characteristics which forecast the effect of thermal relaxation time on the boundary-layer phenomenon. The governing equations are formulated and modified into non-linear, coupled ODEs by utilising similarity transformations and then tackled by Homotopy Analysis Method (HAM). The obtained results are discussed and presented graphically for various values of emerging parameters on velocity and temperature distributions. The results reveal that the velocity is an enhancing function of the magnetic parameter, permeability parameter and Hartree pressure gradient parameter whereas decreasing with larger values of the Williamson fluid parameter. It is evident that the temperature upsurges due to the Biot number and decays with the relaxation parameter. The numerical values of skin-friction and Nusselt number are tabulated. Comparative reviews between the formerly published literature and the current data are made for specific cases, which are inspected to be in tremendous agreement. Abbreviations: BLF: Boundary layer flow; MHD Magnetohydrodynamic; CC model: Cattaneo-Christov model; NNF: non-Newtonian fluid; ODEs: Ordinary differential equations; PDEs: Partial differential equations

Ramification of Hall and Mixed Convective Radiative Flow towards a Stagnation Point into the Motion of Water Conveying Alumina Nanoparticles Past a Flat Vertical Plate with a Convective Boundary Condition: The Case of Non-Newtonian Williamson Fluid

Heat transfer technologies are experiencing rapid expansion as a result of the demand for efficient heating and cooling systems in the automotive, chemical, and aerospace industries. Therefore, the current study peruses an inspection of mixed convective radiative Williamson flow close to a stagnation point aggravated by a single nanoparticle (alumina) from a vertical flat plate with the impact of Hall. The convective heating of water conveying alumina (Al2O3) nanoparticles, as appropriate in engineering or industry, is investigated. Using pertinent similarity variables, the dominating equations are non-dimensionalized, and after that, via the bvp4c solver, they are numerically solved. We extensively explore the effects of many relevant parameters on axial velocity, transverse velocity, temperature profile, heat transfer, and drag force. In the opposing flow, there are two solutions seen; in the aiding flow, just one solution is found. In addition, the results designate that, due to nanofluid, the thickness of the velocity boundary layer decreases, and the thermal boundary layer width upsurges. The gradients for the branch of stable outcome escalate due to a higher Weissenberg parameter, while they decline for the branch of lower outcomes. Moreover, a magnetic field can be used to influence the flow and the properties of heat transfer.

Bioconvection peristaltic transport of Williamson hybrid nanofluid with motile microorganism, Ohmic heating, and entropy generation through an endoscope

On account of the significance of entropy generation and bioconvection in biomedical and bioengineering, valuable contributions have been made by scientists in the present decade. The current study explores the impact of entropy generation, bioconvection of microorganisms, and Ohmic heating on the peristaltic transport of Williamson fluid containing molybdenum disulfide and silver nanoparticles through an endoscope with a long wavelength and low Reynolds number assumptions. The second law of thermodynamics is used to examine the entropy generation, and also Ohmic heating effect is used in the system. Between two coaxial tubes, a non-Newtonian Williamson fluid with molybdenum disulfide and silver nanoparticles is considered. The Homotopy perturbation method (HPM) is applied to describe the nonlinear partial differential equations. We were able to arrive at analytical solutions for velocity, nanoparticle concentration, microbes’ density, and temperature. In the end, the impact of distinct physical parameters on temperature, nanoparticle concentration, velocity, microorganism density, entropy generation, Bejan number, and the heat transfer rate was graphically depicted. The significant outcome of the present study is that the impact of the Peclet number enhances the velocity profile. But Peclet number and bioconvection constantly decline the density of motile microorganisms. One more significant outcome is that the Brinkman number declines the entropy generation near the inner tube and in the rest of the part, enhances the entropy generation. Brinkman number enhances the heat transfer rate. These findings have applications in biological sciences, engineering, geothermal energy, and industry, including the construction of microbial fuel cells and bio-convection nanotechnology devices. Microorganisms are beneficial in the degradation of biomaterials, resulting in the production of oxygen and the preservation of human health.

Effective Similarity Variables for the Computations of MHD Flow of Williamson Nanofluid over a Non-Linear Stretching Surface

The present study concerns investigating the two-dimensional Magnetohydrodynamics (MHD) boundary layer flow of Williamson nanofluid over a non-linear stretching sheet. The focus of this study is based on the global influence of the non-Newtonian Williamson fluid parameter (λ) rather than the local one that exists in the literature for linear and non-linear stretching cases. The mathematical model of the problem is based on the law of conservation of mass, momentum, and energy. The derived partial differential equations are transformed into ordinary differential equations by applying an appropriate similarity transformation. The subsequent equations are solved numerically by using the Shooting method. The physical quantities Skin friction coefficient, as well as the Sherwood and Nusselt numbers are computed locally. To validate the implemented shooting method, a comparison is made with the results obtained by Matlab function bvp4c, and good agreement is found. The Prandtl number, Pr, has an increasing impact of 25.14% on the wall temperature gradient. The impact of various physical parameters are presented through graphs and tables.

Impact of activation energy and MHD on Williamson fluid flow in the presence of bioconvection

The main purpose of the current study is to invetigate the influence of Brownian motion and thermophoresis diffusion in non-Newtonian Williamson fluid flow through exponentially stretching sheet with the effects of thermal radiation and the bioconvection of microorganisms. For this purpose, similarity functions are involved to transmute partial differential equations to corresponding ordinary differential equations. Then Runge–Kutta method with shooting technique is hired to evaluate the desired findings with utilization of MATLAB script. The fluid velocity becomes slow against strength of magnetic parameter and it boosts with mixed convection. The temperature rises with parameter of Brownian motion and thermophoresis. The bioconvection Lewis number diminishes the velocity field. Compared with the existing literature, the results show satisfactory congruence’s.

Dissipative Williamson fluid flow with double diffusive Cattaneo-Christov model due to a slippery stretching sheet embedded in a porous medium

<abstract><p>A numerical analysis of the incompressible two-dimensional flow of a non-Newtonian Williamson fluid is offered by expanding the sheet embedded in a porous medium and combining it with the Cattaneo-Christov model. Additionally, it is considered that the thermal conductivity and fluid viscosity both change as a linear function of temperature and an exponential function, respectively. The velocity, temperature and concentration field are all affected by thermal radiation, viscous dissipation, fluid variable properties, chemical reactions, and the slip velocity phenomenon. When the appropriate variables are employed, a system of non-linear, non-dimensional parameters emerges. The shooting method is used to numerically address this system. To better comprehend the impact of dimensionless parameters on dimensionless velocity, concentration, and temperature profiles, physical descriptions are prepared and justified using graphical representations. The values of the local skin-friction coefficient, the rate of heat transfer, and the rate of mass transfer are also investigated using tables. The behavior of changing fluid properties, on the other hand, establishes the link between Williamson fluid flow and the rate of heat mass transfer. According to the results, increasing the slip velocity and viscosity factors lowers both the Nusselt number and the Sherwood number. Also, due to an increase in Deborah number and the chemical reaction parameter, the temperature profiles decrease.</p></abstract>

Analytical simulation of time dependent electromagneto-hydrodynamic flow of Williamson fluid due to oscillatory curved convectively heated Riga surface with variable thermal conductivity and diffusivity

The main objective of the present article is to provide an analytical simulation for time dependent boundary layer flow of non-Newtonian Williamson fluid due to stretchable curved oscillatory Riga surface. Also the characteristics of heat and mass transport are studied under the influence of variable thermal conductivity and diffusivity along with convective heat and mass boundary conditions. Additionally, energy equation is also characterized with the impact of heat production. Curvilinear coordinate scheme is followed to attain the boundary layer expressions for the flow model. The governing nonlinear partial differential equations are solved analytically via homotopy analysis method (HAM). Graphs are plotted to examine comprehensively the consequences of various concerned parameters like modified magnetic parameter and radius of curvature, Williamson fluid parameter, relation of the surface's oscillating frequency to its stretching rate constant, Prandtl number, variable conductivity and heat production parameters, Schmidt number and variable diffusivity parameter on concentration, temperature, pressure and velocity profile. Also the outcomes of afore said variables on surface drag force, rate of temperature and mass transmission (Nusselt and Sherwood numbers) are shown in tabular form. The liquid velocity amplitude is enhanced with modified magnetic parameter and shows opposite behavior for Williamson fluid parameter.

Insights into the dynamics of blood conveying gold nanoparticles on a curved surface when suction, thermal radiation, and Lorentz force are significant: The case of Non-Newtonian Williamson fluid

The motion of blood conveying gold nanoparticles on a curved surface when suction, thermal radiation, and Lorentz force are significant is explored in this report with the aim to announce the increasing effects of Williamson fluid parameter, volume fraction, radius of curvature, thermal radiation, and Lorentz force on such a transport phenomenon. This report was designed to explore the upper and lower solutions of the model suitable to study the enhancement of the aforementioned variables. The similarity solution of the dimensional governing equation was sought using the appropriate similarity variables. These dimensionless forms of ODEs are numerically solved using the 3-stage Lobatto formula, also known as bvp4c. The validation of the numerical scheme was considered. The drag force decelerates and then upsurges owing to the volume fraction of nanoparticles in the corresponding UBS and reduces in LBS, while the rate of heat transfer drastically decreases. The temperature and velocity gradient escalate and decelerate, respectively for both branches of results owing to the effect of higher curvature parameter. The temperature distribution decelerates in both outcomes due to the strength of mass suction while the velocity is​ weakened in the lower branch solution (LBS) and augments in the upper branch solution (UBS).

Entropy generation analysis of radiative Williamson fluid flow in an inclined microchannel with multiple slip and convective heating boundary effects

The main theme of the current work is to investigate the flow and heat transport characteristics of non-Newtonian Williamson fluid in an inclined micro-channel along with entropy generation analysis. The significance of the thermal radiation, convective boundary condition, and multiple slip effects is explored. The entropy generation of the system has been analyzed by adopting the 2nd law of thermodynamics. The rheological expressions of the Williamson fluid model are also taken into account. The nonlinear system is tackled by using the finite element method. An appropriate comparison has been made with previously published results in the literature as a limiting case of the considered problem. The comparison confirmed an excellent agreement. Detailed discussion of the significance of effective parameters on Bejan number, entropy generation rate, temperature and velocity is presented through graphs. The numerical results portray that the entropy generation and Bejan number have escalating behavior to the higher value of angle of inclination. Furthermore, the Bejan number changing its behavior at two points for different values of Reynolds’ number.

Entropy analysis for radiative inclined MHD slip flow with heat source in porous medium for two different fluids

The motive of the current investigation is to present a comparative study of entropy generation on Newtonian and Non-Newtonian fluids. Heat transfer of the slip flow over a melting expending surface, is investigated with an imposed heat source and non-uniform radiation. Uniform inclined magnetic field is also applied and medium is considered porous. A further non-linear chemical reaction is also studied. Non-Newtonian Williamson fluid is taken and compared with viscous Newtonian fluid. The developed dimensionless governing equations by using proper similarity transforms are solved with Runge-Kutta method of order four with shooting technique and numerical outcomes are described for various non-dimensional physical parameters by the graphs. From the results after comparing with available literature, it is concluded that the entropy generation can be increased with higher magnetic field parameter, parameter of porosity and inclination angle α of magnetic field and opposite behavior is seen with decreasing values of slip parameter for both fluids. With increasing the melting surface parameter, the thickness of the temperature profile get cut down.

An Analytic Solution for Electrical Magneto-Hydrodynamics Darcy–Forchheimer Three Dimensional Non-Newtonian Nanofluid Flow with Convective Boundary Conditions

In this article, the treatment of three-dimensional non-Newtonian Williamson fluid has been carried out under examination. Using the standard transformation, the governing equations are converted into universal similarity equations which have been solved by the optimal homotopy asymptotic method. We observed that the method is effective, reliable, consistent and efficient in solving strongly nonlinear differential equations. The influence of embedded parameters on the fluid flow has discovered graphically and using table. The velocity profile in thex-direction is increased with magnetic and electric field parameters and decreased with the increased stretching parameter, coefficient of inertia, velocity slip parameterL1and porosity parameters. The velocity profile in they-direction is increased with magnetic and electric field parameters, the distended stretching parameter, while reduced with the velocity slip parameterL2, coefficient of inertia, and porosity parameters. The temperature profile is increased with the radiation, thermophoresis and Brownian motion parameters, and Biot number. The profile of concentration is rising with the enlarged Biot numbers and thermophoresis parameter, while reduced with the Brownian motion parameter.

Flow of Electrically Conducting Williamson Fluid with Cattaneo-Christov heat flux due to Permeable Sheet

An analysis is presented for the flow of non-Newtonian Williamson fluid due to permeable sheet. The recent modification of Fourier’s law of heat conduction, i.e. Model of Cattaneo-Christov heat flux is studied in present article to analysis the heat flux. The permeable sheet undergoes suction and the effect of Soret and Dufour is also investigated The governing boundary layer equations are transformed into a non-dimensional form using appropriate set of transformation and the resulting non-linear coupled system of ordinary differential equations are solved using robust Homotopy Analysis method. The influence of physical parameter affecting the velocity of fluid, heat and mass transfer are discussed and outputs are expressed in figures and tables. Some interesting results are found from the study that the velocity profile is decelerating with increase in magnetic parameter. Increasing Darcy number accelerates the flow due to a corresponding rise in permeability of the regime and concomitant decrease in Darcian impedance.

Peristaltic transport of conducting Williamson fluid in a porous channel

In physiology, peristalsis is used to transport the biofluid from a region of lower pressure to higher pressure in the living body. Most of the biofluids (such as blood) are classified as non-Newtonian fluids. In some pathological conditions, the distribution of fatty cholesterol and artery clogging blood clots in the lumen of coronary artery can be modeled as fluid flow in a porous tube. In view of this, the peristaltic flow of a conducting non-Newtonian Williamson fluid in a porous channel with flexible walls under the effects of radiation is investigated. The problem is solved applying perturbation method. Velocity distribution and pressure flow characteristics are calculated and the effects of various emerging parameters on the flow characteristics are discussed in detail.