Williamson Fluid Research Articles

Dynamics of Williamson Hybrid Nanofluid Over an Extending Surface with Non-Linear Convection and Shape Factors

Combined effects of the magnetic field, heat source/sink, and homogeneous–heterogeneous chemical reaction on the three-dimensional fluid flow over a stretching sheet have been examined in this paper. For originality and practicality, the influence of non-linear convection on hybridised nanoparticles of titanium dioxide (TiO2) and silver (Ag) in the non-Newtonian engine oil (EO) are introduced into the governing equations, which are then dimension-free by utilizing appropriate transformations. Williamson fluid model has been employed to determine the rheological features of the considered fluid mixture. MATLAB inbuilt bvp4c solver and Keller box method are proposed for the numerical solution of current fluid theories. Physical elaboration of the graphs is given to recognize the influence on fluid flow and heat transport mechanism in different rising conditions. Based on results, the implication of magnetic field and Williamson parameters restrict the fluid flow for both nanofluid (TiO2/EO) and hybrid nanofluid (TiO2 + Ag/EO). Special case studies of the shape factor effect show more enhancement in heat transfer rate for cylindrically shaped nanoparticles 25.8162% followed by brick-shaped 20.3286% and spherical-shaped 17.0583%. This study will provide better insight into applications including aircraft refrigeration, lubrication, plastic processing, engine and generator cooling, and so forth.

Investigation of Williamson nanofluid in a convectively heated peristaltic channel and magnetic field via method of moments

The study of Williamson nanofluid under peristaltic pumping is conducted in this work. The model equations are developed using the magnetic field and convection effects, and consequently, a nonlinear system of ordinary differential equations is achieved. Then, the residual method based on a linearly independent set of functions known as method of moments is implemented and portrayed as the results under the parameters’ variations. The model results revealed that the peristaltic pumping can be controlled by increasing the values of Gr and Gc; however, the dual effects of the directed magnetic field on the movement of Williamson fluid are examined. The heat transfer augmentation is observed for a stronger Brinkman number and it is higher toward the channel walls. Similarly, the thermophoretic effect and Brownian motion of the particles highly affect the concentration of Williamson nanofluid.

Impulsive motion causes time-dependent nonlinear convective Williamson nanofluid flow across a rough conical surface: Semi-similar analysis

The time-dependent nonlinear convective Williamson nanofluid flow over a rough conical surface in the presence of numerous diffusions and Arrhenius activation energy effects are the main focus of the investigation in this paper. The unsteady flow is essentially due to the impulsive mainstream flow. Two diffusive species, namely, liquid Hydrogen and liquid Nitrogen, occur in the flow under investigation. A sinusoidal waveform mathematically models the rough conical surface with small amplitude and high frequency. Thus, the surface gradients, namely skin friction, exhibit wavy effects in the boundary layer regime. In the current flow problem, the governing equations for the fluid flow are highly coupled nonlinear PDEs that depend on the proper initial and boundary conditions. Mangler's transformations are used to convert them into non-dimensional forms, and implicit finite difference approximation and quasilinearization are employed to produce numerical semi-similar solutions. The numerical results representing the boundary layer effects are displayed graphically and analyzed for parametric values. The friction experienced by the rough surface is strongly fluctuating for higher values of Williamson parameter W. The heat transfer rate Rex-1/2Nu increases approximately by 61% and 63% at ξ=0.8 when Nt decreases from Nt=0.5 to Nt=0.1, for the cases of W = 0 (Newtonian fluid) and W = 1(Williamson fluid), respectively. Additionally, there is a strong correlation between the current findings and the related results previously published in the literature.

Viscoelastic boundary layer analysis of constant surface temperature plate embedded in saturated porous media

AbstractMathematical models and numerical solutions of Williamson fluid flow under influences of various boundary conditions provide important support to experimental studies in the solar energy field. Therefore, the present study is concerned with the effects of forced convection of the viscoelastic boundary layer on a horizontal plate embedded in saturated porous media subjected to constant surface temperature. The study explores the profiles of shear stress, velocity, temperature, and heat transfer coefficient. The governing equations in nondimensional forms are obtained by using a model of Darcy–Forchheimer–Brinkman and finally are solved numerically by using bvp4c with MATLAB package. The results of the numerical solution show an insignificant rise in the distribution of the velocity boundary layer and shear stress profile as the Darcy parameter is increased, while a decrease in the temperature and Nusselt numbers are found. On the other hand, as the viscoelastic parameter is increased, the Darcy parameter shows a reverse response. Finally, insignificant increases in profiles of boundary layer velocity, temperature, shear stress, and Nusselt number are observed at high values of the Forchheimer number.

Significance of magnetized Williamson nanofluid flow for ferromagnetic nanoparticles

In recent years, nanofluids have been discussed owing to their extensive variety of applications in industry and engineering, such as the cooling process in nuclear reactors, radiators, chemical processes, heat transfer systems, energy production, heat exchangers, astronomical technology, power plants and fusion reactions. In this research work, we have inspected the impact of ferromagnetic nanoparticles on Williamson fluid. Some suitable similar transformations are exploited to achieve the non-linear ODEs. The acquired ODEs are then solved numerically by the use of an appropriate method known as the bvp4c scheme. Impacts of ferromagnetic interaction parameters, viscous dissipation, curie temperature, Weissenberg number along with thermal radiation are perceived for velocity, temperature and Concentration fields. Furthermore, velocity and thermal gradients are deliberated and scrutinized pictorially. It is observed that the temperature of the nanofluid intensifies for larger ferrohydrodynamic interaction and curie temperature while a reverse trend is detected for . Moreover, it is anticipated through the graphical analysis that nanofluid concentration declines for larger and , while it rises for greater .

Nonsimilar stagnation flow of Williamson fluid over an isothermal linearly stretched sheet

The objective of this work is to analyze the boundary layer flow in the vicinity of a stagnation point on a linearly stretched isothermal flat surface. The ambient fluid temperature is considered different than that of the sheet. The streaming fluid rheological behavior is approximated via the Williamson fluid model. The normalized partial differential equations based on the balances of mass, momentum, and energy are simulated numerically via the symbolic and numeric computing software Maple for two entirely different scenarios. In the first scenario, the outer potential flow velocity dominates the sheet velocity whilst it is the other way round for the second scenario. The plots showing the behaviors of velocity and temperature are presented at various streamwise locations. The skin friction and Nusselt number are also visualized graphically and listed in tabular forms. The analysis reveals that all quantities including velocity and temperature show a strong dependence on the streamwise co-ordinate. In general, velocity distribution and temperature rise with a gradual march along the streamwise direction. The heat transfer coefficient also elevates upon an increase in the streamwise co-ordinate. This contradicts several previously published results on the boundary layer flow of Williamson fluid where no such dependence is seen.

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.

Analytical and numerical investigation of Darcy-Forchheimer flow of a nonlinear-radiative non-Newtonian fluid over a Riga plate with entropy optimization

The effects of the Riga plate flow of Williamson fluid with a Darcy-Forchheimer medium and suction/injection are explained in this study. Convective heat and mass circumstances are considered. The energy and concentration equations are developed using Catteneo-Christov dual theory. The heat transfer attributes are analyzed via heat consumption/generation. To estimate total entropy creation, the second law of thermodynamics is applied. The governed mathematical models are transmuted into an ODE model by adopting befitting variables. The MATLAB bvp4c algorithm and the HAM scheme are used to solve these problems numerically and analytically. Novel attributes of various physical parameters are debated through graphs, charts and tables. The fluid flow speed decelerates when enlarging the Weissenberg number and porosity parameters. The fluid temperature enriches when enhancing the radiation parameter. The chemical reaction parameter leads to suppresses the fluid concentration. The higher quantity of heat consumption/generation parameter enriches the heat transfer gradient. The mass transfer gradient accelerates due to more presence of the chemical reaction parameter. We also compared numerical and analytical results and found them in good agreement. When the values of the radiation parameter, Brinkman number, and Reynolds number are increased, the entropy generation increases. The Bejan number downturns when enlarging the modified Hartmann number.

Study of peristaltic activity in non-linear blood analysis of Williamson fluid in a microchannel

The present investigation is modeled to study the effect of homogeneous and heterogeneous reactions on the peristaltic blood transportation of electrically conducting Williamson fluid in an asymmetric microchannel under velocity slip conditions. The mechanism of heat transfer is also examined in conjunction with viscous dissipation and thermal radiation. Implementation of small Reynolds number and large wavelength concepts leads to a reduction in the complexity of the system. Series solutions for velocity, temperature, stream function, and concentration fields are found using the regular perturbation technique. Using Mathematica software, Simpson’s rule was used to evaluate the pumping features such as pressure rise and frictional force. The effects of embedded parameters are portrayed and discussed by using a graphical approach. The skin friction and Nusselt number at the channel walls are established for a choice of assessments of significant parameters and which are exhibited in a tabular manner. It is observed that an enhancement in the values of Weissenberg number fluid velocity reduces at the lower channel wall whereas it increases at the channel upper wall.

Mixed convective MHD flow of Williamson fluid over a nonlinear stretching curved surface with variable thermal conductivity and activation energy

The mixed convection and electrically conducting flow of two-dimensional Williamson fluid across a nonlinear stretched curvy sheet in the presence of suction/injection, variable thermal conductivity, heat sink/source, and activation energy with convective boundary conditions are discussed in this article. A system of nonlinear PDEs is converted to a system of nonlinear ODEs using similarity transformations. Instead of focusing on the local effect of the Williamson fluid parameter this study looks at the global impact. Using graphs, we examine how suction/injection, variable thermal conductivity, heat sink/source, and activation energy affect the resulting velocity, temperature, pressure, and concentration profiles. Physical quantities of interest to engineers are tabulated as well, including the skin friction coefficient, Nusselt number, and Sherwood number. Both thermal and mass buoyancy force parameters directly correlate with thermal and concentration profiles. This study plays an imperative role in biological and chemical engineering.

Multiple convected conditions in Williamson nanofluidic flow with variable thermal conductivity: Revised bioconvection model

The importance of bioconvection into the application of nanoparticles has had a significant impact on fundamental technological and industrial functions in recent years. These discussions are being carried forward by the bioconvection appearance on that flow by attracting nanoparticles into additional features on thermal radiation and activation energy. The investigation had been proposed on the appealing features of the mass and thermal convective boundary constraints. The high desirable subclass on rate-type fluid, especially Williamson fluid, was used to anticipate the absolute rheological parameters. The designated partial differential system was modified along with nonlinear ordinary differential equations applying enhance being related conversion, the designated partial differential system was modified along nonlinear ordinary differential equations. The governing equations are interpreted into ordinary differential equations, and in the following, shooting process was obeyed to build up the mathematical classification on the convert dimensionless flow problem. This value of physical restraint was displayed on the table and plots tests. This noted theoretical imitation could be highly successful in improving the solar energy systems and thermal extrusion processes. The outcomes reported that the rise in Weissenberg number and Hartmann number decreased the nanoparticles velocity distribution. The progressing temperature distribution was observed to develop radiation parameter and thermal conductivity parameter. That was further noted to modify bioconvection Lewis number and Peclet number that were reduced into motile microorganism distribution effectively.

Finite Element Study of Electrical MHD Williamson Nanofluid Flow under the Effects of Frictional Heating in the View of Viscous Dissipation

This study addresses heat and mass transfer of electrical magnetohydrodynamics (MHD) Williamson fluid flow over the moving sheet. The mathematical model for the considered flow phenomenon is expressed in a set of partial differential equations. Later, linear and nonlinear ordinary differential equations (ODEs) are obtained. The finite element method tackles a reduced system of ODEs with boundary conditions. Galerkin weighted residuals and constructs of weak formulations constitute the basis of this method. An iterative procedure is considered for handling nonlinear terms in a given system of ODEs. Some results acquired using the finite element method are compared with those reported in previous research via the Matlab solver bvp4c in order to validate the obtained solutions of ODEs. It is seen that the velocity profile is decayed by enhancing the Wiesenberg number. The finite element method also converges to an accurate solution by increasing the number of elements, whereas Matlab solver bvp4c produces accurate results on small grid points. Our intention is for this paper to serve as a guide for academics in the future who will be tasked with addressing pressing issues in the field of industrial and engineering enclosures.

Electro-osmotic transport of a Williamson fluid within a ciliated microchannel with heat transfer analysis

A novel theoretical model is devised for electro osmotic flow of Williamson fluid model by incorporating heat transfer phenomena in a micro ciliated channel. The physical fluid model is designed by exploiting the renowned Debye–Huckel, long wavelength small Reynolds number approximation. The exact expression for Poisson–Boltzmann equation is obtained to find the analytical solution for axial velocity, pressure gradient, temperature and stream functions comprehensively by using perturbation technique. Whereas, transverse velocity and pressure rise profile are explored numerically through the MATHEMATICA software infrastructure. The variations of paramount significant parameters on the velocity distribution, temperature, pressure gradient and pressure rise per wavelength are demonstrated graphically. It has been investigated that axial velocity profiles escalates with enhancing Weissenberg, electro-osmotic, mobility of medium parameter, while dual behavior is recorded for the case of traverse component of velocity. Cilia plays a crucial role in ductus efferentes and assumed to transfer sperm through the rete testis to the epididymis. Besides above mentioned application cilia like actuators serve in micro-mixers to regulate the flow in bio-sensors and in various drug-delivery mechanism.

Stratification flow and variable heat transfer over different non-Newtonian fluids under the consideration of magnetic dipole

Non-Newtonian fluids have industrial and technical applications. Several liquids in nature do not have Newtonian viscosities. These fluids include applesauce, polymer mixtures, colloidal and fermented mixtures, clay glazes, paints, lubricants, cement, slush, shampoos, mud, foodstuffs, paper paste, aqueous froths, etc. This study considers stratified flow and variable heat transmission across a stretched surface. The magnetic hydrodynamics and slips’ impacts are illustrated. On the basis of flow assumptions, the mathematical model was created using the Navier–Stokes equation. The boundary layer approximation approach is provided PDEs by working on the Navier–Stokes equation under flow assumptions. This system is converted into ODEs through similarity transformations. Dimensionless system is elucidated by means of RKF-45 technique. The concerning physical parameter effects are elaborated numerically as well as graphically. Based on the findings of the comparison, it was determined that Williamson fluid had superior performance in terms of fluid velocity compared to Maxwell fluid. Furthermore, the temperature of the fluid is greater for booming values of both [Formula: see text] and [Formula: see text] parameters.

A numerical study of boundary layer flow of Williamson nanofluid in the presence of viscous dissipation, bioconvection, and activation energy

Due to dynamical applications of nanoparticles in various engineering and biomedical applications, our work focuses on examining and exploring the numerical study of bioconvected unsteady Williamson fluid flow at a heated permeable stretched sheet in a porous medium, along with the existence of particular Cattaneo–Christov heat and mass flux, viscous dissipation, activation energy, Brownian and thermophoresis motion. A mathematical model has been developed by considering the effects of the aforementioned terminologies on the flow field which are expected to be similar to the physical behavior and already published work. By using suitable similarity transformations, the system of the flow field is transformed from partial differential equations to ordinary differential equations. The developed differential system is then solved numerically through bvp4c in the computational software MATLAB. The tabular and graphical analysis have been presented against velocity, temperature, concentration, and density profiles that imply the impact of physical parameters. The skin friction coefficient, rate of heat, and mass transfer are also examined. The results coincide very well to previous published work for limiting cases that authenticate the validity of the current work. It was observed that upon increasing magnetic field (M) and porosity (Kp) parameters, the velocity profile decelerates but the opposite behavior was seen for motile density, concentration, and temperature profiles. The temperature and concentration of Williamson nanofluid reduced by enhancing the significant thermal and mass stratification. The concentration profile declines for rising values of Schmidt number (Sc), the chemical reaction rate (σ), and temperature difference (δ) parameters but accelerates for higher values of Activation energy (Ea). Also, by increasing Peclet number (Pe), bioconvection Lewis number (Lb), and microorganism concentration difference parameter Ω motile density profile decreases.

Significance of gyrotactic microorganism and bioconvection analysis for radiative Williamson fluid flow with ferromagnetic nanoparticles

Research on nanotechnology took interest of scientists as well as researchers because of its vast range of applications like curing cancer, medicines, aircraft manufacturing industry, use of nano-robot technology, bio-nano, heat exchanger instruments, used as coolants in engines of vehicles, microelectronics, water distillation, pharmaceutical procedures and rubber materials. Major purpose of this inspection is to examine the usefulness of radiation phenomena with magnetic effects micro-polar nanofluid by use of impermeable surface. The concept of microorganism’s notion is used to make suspended nano-particles stable by using effect of bioconvection influenced by synchronizing deliberation of suitable magnetic field. Since bioconvection is also an appealing research field for bioengineering and biotechnology, in recent year’s variety of bio-convection models are studied for production of microorganisms. The determination of current exploration is to compute the 2-dimensional flow of Williamson ferrofluid under the influence of magnetic dipole. Characteristics of Brownian motion parameter and thermophoresis diffusion for Williamson ferrofluid model apprehending the properties of convective boundary conditions, thermal motile as well as thermal gradients are considered. The system of nonlinear PDEs is transformed in form of ODEs with the help of apt transformations; additionally obtained ODEs are then solved with the help of bvp4c numerical scheme. Impacts of some important physical parameters are expressed pictorially. Results perceived that fluids temperature increases by increasing thermal radiation as well as thermophoresis parameter moreover shows declining behavior in case of Prandtl number. Moment of motile microorganism rises for larger δ1 and Pe whereas microorganism have opposite trend againstLb.

The Peristaltic Flow of Williamson Fluid through a Flexible Channel

The purpose of this study is to investigate the effect of an elastic wall on the peristaltic flow of Williamson fluid between two concentric cylinders, where the inner tube is cylindrical with an inelastic wall and the outer wall is a regular elastic sine wave. For this problem, cylindrical coordinates are used with a short wavelength relative to channel width for its length, as well as the governing equations of Williamson fluid in the Navier-Stokes equations. The results evaluated using the Mathematica software program. The Mathematica program used by entering the various data for the parameters, where the program shows the graphs, then the effect of these parameters became clear and the results mentioned in the conclusion. Williamson fluid peristaltic flow through an elastic conduit is the subject of this investigation. For a number of significant elements, such as velocity distribution, stress and wave frame streamlines, graphic findings are supplied at the end of the article.

A brief flow analysis of Williamson fluid near a radiated irregular vertical surface with binary chemical reaction

This analysis deals with the effect of mixed convection and thermal radiation on steady three-dimensional (3D) flow of Williamson fluid near an irregular surface. The phenomenon is examined in semi-infinite domain and the flow is produced by means of non-linear stretching. The mass transfer analysis is carried out by means of activation energy and binary chemical reaction. The governing equations are initially reformed into ODES by applying applicable variables and then solutions are calculated for the flow field, mass transfer rate, skin frictions, temperature, heat transfer rate and concentration via shooting. New characteristics of dimensionless variables are illustrated by means of graphs and tables. The detailed analysis anticipates that velocity declines by the elevation of Weissenberg number and accelerates with the increase of mixed convection parameters. Further, the temperature enhances with the increase of temperature ratio and radiation parameters and behaved oppositely analogous to development in Prandtl number.

A three dimensional frictional flow study of Williamson fluid with chemical reaction

This analysis deals with the incompressible, steady, three-dimensional (3D) viscously dissipated Williamson fluid flow near an irregular surface. It has many applications such as synthesis of polymer solutions, plastic manufacturing, food processing, paper production, adhesives, exotic lubricants, suspension solutions etc. The phenomenon is examined in semi-infinite domain and the flow is produced by means of non-linear stretching. An irreversible process is taken by means of fluid particles stress which converts the energy into heat. The most noticeable procedure of this process is the internal friction between the layers of fluid particles which causes heat generation. The governing equations are initially reformed into ODES by applying applicable variables and then numerical solutions are computed via the shooting technique. Newly characteristics of dimensionless variables are illustrated by means of graphs and tables. The detail analysis anticipates that velocity declines by the elevation of Weissenberg number and wall thickness parameters. Further, the temperature enhances with the increase of Eckert number and heat generation parameter and behaved oppositely analogous to development in Prandtl number.

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.