Williamson Nanofluid Flow Research Articles

MHD Williamson nanofluid flow past a permeable stretching sheet with thermal radiation and chemical reaction

ABSTRACT Heat and mass transmission of non-Newtonian fluids get considerable attention due to their complexity and high nonlinearity in rheology. Among the various fluid models, Williamson fluid model very well describes the low as well as high-viscosity situations. With this perspective, the present work deals with heat and mass transfer of MHD Williamson nanofluid flow past a porous stretching surface with thermal radiation and chemical reaction. Highly nonlinear governing equations are transformed into ordinary ones by employing similarity invariants. The reduced systems of ODEs are numerically treated with R-K’s fourth-order method along with the shooting technique. Using MATLAB the associated nondimensional parameters are graphically interpreted and found to be in good agreement with the literature. For the higher values of magnetic and Williamson parameters, fluid motion becomes a decreasing function whereas the temperature profile is enhanced for the magnetic, Williamson, and radiation parameters. The investigation will serve in the process involving fluids such as food processing, glass manufacturing, oil extraction, etc.

Bio-convection effects on Williamson nanofluid flow with exponential heat source and motile microorganism over a stretching sheet

This article studies the bio-convection impacts on Williamson nanofluid flow and covers the nonlinear thermal radiation and chemical reaction effects on stretching sheet. The fundamental focus is to enhance heat transfer. Nanofluids are the most important source of effective heat source, having many applications in scientific and technological processes. Nanomaterials with superior thermal characteristics offer a wide range of uses in medicine, energy generation, heat exchange, and electronic cooling systems, among others. The present physical problem involving this flow is contained the nonlinear partial differential equations (PDEs). An appropriate transformation is used to convert the partial differential equations (PDEs) to ordinary differential equations (ODEs), which are then numerically settled utilizing bvp4c method in MATLAB. The physical features of nanofluids such as fluid velocity, volumetric concentration, temperature, and profiles of motile organisms are studied in relation to various factors. Additionally, the skin friction coefficient, Nusselt number, Sherwood number as well as motile microorganism number are calculated numerically using tables. It is found that the velocity profile decreases for the boosted values of Walliamson fluid parameter, magnetic parameter, angle of inclination and buoyancy ratio parameter. The temperature grows by increasing the values of thermophoresis parameter, exponential space and thermally based heat source/sink parameter. A survey of the available literature corroborates the aforementioned results.

Temperature Distribution in the Flow of a Viscous Incompressible Non-Newtonian Williamson Nanofluid Saturated by Gyrotactic Microorganisms

The heat and mass transfer in magnetized non-Newtonian Williamson nanofluid flow, saturated by gyrotactic microorganisms due to a stretched sheet, is debated here. The rough sheet is subjected to uniform heat flux, and its velocity is proportional to its distance from the slit. Nanofluid viscosity and thermal conductivity are temperature-dependent, but microbe diffusivity and Brownian motion are concentration-dependent. Through similarity transformation, the system of modeled equations is reduced to dimensionless differential equations. We employed the shooting approach in conjunction with the Runge–Kutta scheme to obtain a solution for the physical model. For various combinations of the controlling parameters, some numerical results are found. When the generated results are compared to the existing literature, the highest settlement is found. According to numerical results, the skin-friction coefficient rises as the magnetic field and thermal conductivity parameters rise, while the opposite tendency is observed for both the slip velocity and viscosity parameters.

Impact of radiative and dissipative heat on the Williamson nanofluid flow within a parallel channel due to thermal buoyancy

The present investigation reveals the non-Newtonian flow characteristics for the Williamson nanofluid through a parallel channel due to the conjunction of thermal buoyancy. As a good conductor of heat, the metal like Copper is treated as the nanoparticles submerged into the base fluids water and kerosene to perform the flow phenomena within the channel embedding with the porous medium. For the involvement of the applied magnetic field and permeability it is not wise to neglect the impact of dissipative heat energy. Therefore, both the Joule and the Darcy dissipations are also considered those are affecting the thermal properties. The model is developed considering the Mintsa model thermophysical properties of conductivity and the Gharesim model viscosity for the enhancement of heat transport properties. In various industrial as well as engineering applications nanofluids are used as a best coolant. The use of suitable similarity variables and stream function helps to transform the governing nonlinear differential equations into nonlinear ordinary. Further, an approximate analytical approach such as Adomian Decomposition Method is used to handle those transformed equations. The current outcomes obtained from the behavior of various flow characteristics are presented via graphs and table to validate the results. The observation shows that with an augmentation in the particle concentration, fluid velocity retards however the retardation in case of water-based nanofluid overrides the case of kerosene-based nanofluid. Further, particle concentration enriches the nanofluid temperature greatly in comparison to pure fluid.

Thermophoresis and Brownian motion effects on Williamson nanofluid flow past a stretching surface with thermal radiation and chemical reaction

AbstractThe heat transfer mechanism of nanofluids has numerous industrial applications owing to the non‐Newtonian behavior and has been exercised as a thermophysical phenomena in presence of thermal radiation. The present paper deals with the thermal transfer characteristics of time‐independent magnetohydrodynamics Williamson fluid past a stretching surface in presence of the reaction of chemical equilibrium is dealt. The flow constitutive nonlinear partial differential coupled equations are transmitted into ordinary differential equalities by employing relevant similarity transmutations. These deduced equations are determined by using the Runge–Kutta numerical technique with a shooting approach with the aid of MATLAB software. Influences of distinct pertinent flow parameters like an inclined uniform magnetic field, Soret number, heat generation/absorption, and Schmidt number constrained to convective boundary condition is displayed through graphs with relevant physical interpretations. Computed numerical values for the friction factor coefficient, local Nusselt parameter, and Sherwood number are tabulated.

Viscous Dissipation and Joule Heating Effects on 3D Magnetohydrodynamics Flow of Williamson Nanofluid in a Porous Medium Over a Stretching Surface With Melting Condition

Abstract The aim of the current article is to demonstrate heat transfer characteristics of Williamson nanofluid flow through a stretching surface with a porous medium in two lateral directions. Heat generation, nonlinear thermal radiation, viscous dissipation, Joule heating, and chemical reaction are also considered in time-independent boundary layer equations of heat and concentration. One more significant boundary condition is the melting condition which is introduced in this study for the purpose of more heat generation and suitable transformations by the satisfied continuity equation are selected, These are used to translate the coupled time-independent partial differential equations into a coupled nonlinear system of ordinary differential equations. The translated equations are computed as numerical solutions by utilizing the Runge–Kutta–Fehlberg (R–K–F) fourth-order algorithm with the help of a shooting procedure in matlab (bvp4) programming. The significance of physical emerging nondimensional parameters is predicted through graphs and discussed numerically in detail on mass of conservation, temperature, and concentration. The numerical values of the coefficient of the skin friction are displayed through a table with large enhanced values of nondimensional parameters and heat transfer rate explained in detail through graphs.

Performance of activation energy and variable thermal conductivity on bioconvection heat transfer of Williamson nanofluid undergoing binarychemical reaction with multiple slip

In this paper, we have examined the influence of activation energy and binary chemical reaction on the magneto-hydrodynamic bioconvection of Williamson nanofluid flow over a stretching sheet in the presence of variable thickness and variable thermal conductivity considering nonlinear thermal radiation under multiple slip conditions. The necessary similarity transformations are applied to the governing partial differential equations to reduce them to a set of nonlinear ordinary differential equations. These sets of ordinary differential equations with boundary conditions are solved numerically. The significant result of the present work is that the velocity profile reduces by enhancing the values of Williamson fluid parameter . Temperature profile decreases by increasing the temperature slip parameter values, whereas it increases by increasing the values of velocity power index parameter m. The density of the microorganisms profile decreases by increasing the density of microorganisms slip parameter values and the Williamson fluid parameter. Also, by increasing the Lewis number and activation energy parameter values, the rate of mass transfer increases. The rate of heat transfer retards by increasing the thermal conductivity parameter and thermal radiation parameter values.

Swimming of Gyrotactic Microorganism in MHD Williamson nanofluid flow between rotating circular plates embedded in porous medium: Application of thermal energy storage

Purpose: The presence of thermal energy storage devices in concentrated solar power plants is advantageous for controlling power and energy demand. The capacity of materials used in total thermal energy storage is thought to improve their performance. As a result, we investigate the unsteady flow confined by parallel rotating circular plates in a porous media filled with Williamson nanofluid in the current study. The importance of fluid flow over circular plates is owing to the variety of physical mechanisms they contain. Technically, such flows are important in lubrication, rotating machinery, crystal formation processes, and viscometry. Nanoparticles and motile gyrotactic microorganisms are included in the Williamson fluid model. The inclusion of an extrinsic magnetic field, which causes the production of an induced magnetic field between two circular plates, influences the flow. The impact of magnetic fields on lubrication drew attention because of the critical functions they play in a variety of industrial applications. For instance, the increased utilization of liquid metal lubricants in high-temperature bearings. Design/methodology/approach: A numerical methodology known as the differential transform method is used to solve nonlinear differential equations. Computational software is utilized to handle coupled nonlinear problems utilizing the proposed technique. The Padé approximation is also employed with the suggested technique to improve the convergence rate. Findings: The tabular and graphical approaches are used to discuss the simultaneous impact of various characteristics. On the axial and tangential velocity profiles, the rotational Reynold number shows a reverse trend. The magnetic field in both axial and tangential direction decreases as the magnetic Reynold number is increased. The effects of Prandtl number cause the temperature distribution to decline; similar occurrences are found at larger values of squeezed Reynolds number. Squeezing Reynolds number values increase nanoparticle concentration and motile microorganism profile. Brownian motion and thermophoresis parameters indicate opposing patterns for nanoparticle concentration. The motile microorganism profile is reduced when the Peclet number is increased, whereas the microorganism profile is increased when the bioconvection Schmidt number is increased. Originality/value: The acquired results for the proposed mathematical modeling with DTM-Padé are new to the literature and are reported here for the first time.

Entropy analysis of unsteady MHD three‐dimensional flow of Williamson nanofluid over a convectively heated stretching sheet

AbstractThis article addresses an investigation of the entropy analysis of Williamson nanofluid flow in the presence of gyrotactic microorganisms by considering variable viscosity and thermal conductivity over a convectively heated bidirectionally stretchable surface. Heat and mass transfer phenomena have been incorporated by taking into account the thermal radiation, heat source or sink, viscous dissipation, Brownian motion, and thermophoretic effects. The representing equations are nonlinear coupled partial differential equations and these equations are shaped into a set of ordinary differential equations via a suitable similarity transformation. The arising set of ordinary differential equations was then worked out by adopting a well‐known scheme, namely the shooting method along with the Runge‐Kutta‐Felberge integration technique. The effects of flow and heat transfer controlling parameters on the solution variables are depicted and analyzed through the graphical presentation. The survey finds that magnifying viscosity parameter, Weissenberg number representing the non‐Newtonian Williamson parameter cause to retard the velocity field in both the directions and thermal conductivity parameter causes to reduce fluid temperature. The study also recognizes that enhancing magnetic parameters and thermal conductivity parameters slow down the heat transfer rate. The entropy production of the system is estimated through the Bejan number. It is noticeable that the Bejan number is eminently dependent on the heat generation parameter, thermal radiation parameter, viscosity parameter, thermal conductivity parameter, and Biot number. The skillful accomplishment of the present heat and mass transfer system is achieved through the exteriorized choice of the pertinent parameters.

Entropy optimization and heat transfer analysis in MHD Williamson nanofluid flow over a vertical Riga plate with nonlinear thermal radiation

The entropy generation for a reactive Williamson nanofluid flow past a vertical Riga system is the subject of this article. The effects of MHD, thermophoresis, nonlinear heat radiation and varying heat conductivity are modeled into the heat equation in the established model. Suitable similarity transformations are examined to bring down the partial differential equations into ordinary differential equations. The Homotopy analysis approach is used to solve the dimensionless transport equations analytically. The graphic information of the various parameters that emerged from the model is effectively collected and deliberated. The temperature field expands with thermophoresis, Brownian motion and temperature ratio parameters as the modified Hartmann number forces an increase in velocity, according to the findings of this analysis. With the increase in the fluid material terms, the entropy generation and Bejan number increase. Riga plate has numerous applications in improving the thermo-physics features of a fluid, the value of magnetic field embraces an important role in fluid mechanics. An external electric field can be used to control flow in weak electrically conductive fluids. The Riga plate is one of the devices used in this regard. It’s a device that creates electromagnetic fields. They produce the Lorentz force which is a force that directs fluid flow. The authors have discussed the entropy optimization for a reactive Williamson nanofluid flow past a vertical Riga plate is addressed. This is the first investigation on mass and heat transfer flow that the authors are aware of, and no similar work has yet been published in the literature. A thorough mathematical examination is also required to demonstrate the model’s regularity. The authors believe that the results acquired are novel and have not been plagiarized from any other sources.

MHD Williamson Nanofluid Flow over a Slender Elastic Sheet of Irregular Thickness in the Presence of Bioconvection.

Bioconvection phenomena for MHD Williamson nanofluid flow over an extending sheet of irregular thickness are investigated theoretically, and non-uniform viscosity and thermal conductivity depending on temperature are taken into account. The magnetic field of uniform strength creates a magnetohydrodynamics effect. The basic formulation of the model developed in partial differential equations which are later transmuted into ordinary differential equations by employing similarity variables. To elucidate the influences of controlling parameters on dependent quantities of physical significance, a computational procedure based on the Runge–Kutta method along shooting technique is coded in MATLAB platform. This is a widely used procedure for the solution of such problems because it is efficient with fifth-order accuracy and cost-effectiveness. The enumeration of the results reveals that Williamson fluid parameter , variable viscosity parameter and wall thickness parameter impart reciprocally decreasing effect on fluid velocity whereas these parameters directly enhance the fluid temperature. The fluid temperature is also improved with Brownian motion parameter and thermophoresis parameter . The boosted value of Brownian motion and Lewis number reduce the concentration of nanoparticles. The higher inputs of Peclet number and bioconvection Lewis number decline the bioconvection distribution. The velocity of non-Newtonian (Williamson nanofluid) is less than the viscous nanofluid but temperature behaves oppositely.

MHD Williamson Nanofluid Flow over a Stretching Sheet through a Porous Medium under Effects of Joule Heating, Nonlinear Thermal Radiation, Heat Generation/Absorption, and Chemical Reaction

In this article, the effect of electromagnetic force with the effect of thermal radiation on the Williamson nanofluid on a stretching surface through a porous medium was studied considering the effect of both heat generation/absorption and Joule heating. On the other hand, the effect of Brownian motion and thermophoresis coefficients was considered. The system of nonlinear partial differential equations governing the study of fluid flow has transformed into a system of ordinary differential equations using similarity transformations and nondimensional variables which were subsequently solved numerically by using the Rung-Kutta fourth-order method with shooting technique. Moreover, the effect of the resulting physical parameters on the distributions of velocity, temperature, and concentration of nanoparticles has been studied by using graphical forms with an interest in providing physical meanings to each parameter. Finally, special diagrams were made to explain the study of the effect of some physical parameters on the skin friction coefficient and the local Nusselt number; these results led to reinforcement in the values of the skin friction coefficient for the increased values of the magnetic field and the Darcy number while the effect on the local Nusselt number by thermal radiation as well as the heat generation/absorption coefficients became negative.

Numerical Simulation of Heat Mass Transfer Effects on MHD Flow of Williamson Nanofluid by a Stretching Surface with Thermal Conductivity and Variable Thickness

The current analysis deals with radiative aspects of magnetohydrodynamic boundary layer flow with heat mass transfer features on electrically conductive Williamson nanofluid by a stretching surface. The impact of variable thickness and thermal conductivity characteristics in view of melting heat flow are examined. The mathematical formulation of Williamson nanofluid flow is based on boundary layer theory pioneered by Prandtl. The boundary layer nanofluid flow idea yields a constitutive flow laws of partial differential equations (PDEs) are made dimensionless and then reduce to ordinary nonlinear differential equations (ODEs) versus transformation technique. A built-in numerical algorithm bvp4c in Mathematica software is employed for nonlinear systems computation. Considerable features of dimensionless parameters are reviewed via graphical description. A comparison with another homotopic approach (HAM) as a limiting case and an excellent agreement perceived.

Nonlinear mixed convective Williamson nanofluid flow with the suspension of gyrotactic microorganisms

This investigation aims to present the thermally developed bioconvection flow of Williamson nanoliquid over an inclined stretching cylinder in presence of linear mixed convection and nonuniform heat source/sink. The activation energy and suspension of gyrotactic microorganisms are accounted with applications of bioconvection phenomenon. Appropriate nondimensional variables are opted to attain the dimensionless form of flow equations. The resulting momentum, energy, concentration and motile density equations are abridged to highly coupled and nonlinear in nature. The numerical treatment is followed for the solution procedure by employing the shooting method. The influence of some relevant dimensionless parameters is discoursed graphically along with physical justifications. Moreover, the impact of several dimensionless parameters on skin friction and Nusselt number is obtained and listed in tables. It is observed that the velocity of fluid shows a decreasing variation for Williamson fluid parameter. The change in unsteadiness parameter and heat source parameter enhanced the nanofluid temperature. The motile microorganisms profile declines with bioconvection constant and bio-convection Lewis number.

Numerical investigation of magnetohydrodynamics Williamson nanofluid flow over an exponentially stretching surface

This research work describes the investigation of a magnetohydrodynamic flow of Williamson nanofluid over an exponentially porous stretching surface considering two cases of heat transfer i.e., prescribed exponential order surface temperature (PEST), and prescribed exponential order heat flux (PEHF). As a result of this infestation, a mathematical model of the problem based on conservation of linear momentum and law of conservation of mass and energy is developed. Whereas governing nonlinear partial differential equations (PDEs) are converted to nonlinear ordinary differential equations (ODEs). Subsequently, the velocity, concentration, and temperature profiles are developed by using the method of similarity transformation. Furthermore, the effects of various physical parameters of engineering interests are demonstrated graphically. It is highlighted that both the magnetic parameter [Formula: see text] and Williamson parameter [Formula: see text] causes to reduce the boundary layer thickness.

A three-dimensional bioconvection Williamson nanofluid flow over bidirectional accelerated surface with activation energy and heat generation

The main focus of this research is to explore the consequences of motile gyrotactic microorganisms for unsteady Williamson nanofluid induced by bidirectional periodically accelerated surface. The combined features of magnetic and buoyancy forces with association of nanoparticles and swimming microorganisms developed the nanofluid bioconvection. Thermal radiation and heat generation aspects are considered to analyze the heat transportation phenomenon. The consequences of activation energy and chemical reaction are further explored for physical relevance. Appropriate transformations have been employed to transmute the formulated nonlinear equations into dimensionless form, and then analytically elucidated by homotopic technique. The effect of diverse dominant parameters on velocities, concentration, temperature, motile microorganisms as well as skin friction coefficients are deliberated through various graphs while the deviation in local Sherwood, Nusselt and motile density numbers have been deliberated by numerical data in tabular form. It is noticed that both velocity components periodically drop for augmentation in Williamson parameter. Current investigation accentuated that higher reaction rate leads to decay in concentration distribution, but impact of activation energy parameter is rather conflicting. Furthermore, the profile of motile microorganism leads to be intensified for higher magnetic parameter, while opposite trend is perceived for bioconvected Peclet and Lewis numbers.

Heat and mass transfer in MHD Williamson nanofluid flow over an exponentially porous stretching surface

The present study investigates the rate of heat and mass transfer in MHD Williamson nanofluid flow over an exponentially porous stretching surface subject to the heat generation/absorption and mass suction. The analysis has been carried out for the two different conditions of heat transfer stated as prescribed exponential order surface temperature (PEST) and prescribed exponential order heat flux (PEHF). Moreover, an exterior magnetic field is applied with an inclined angle along the stretched surface. Mathematically, the existing flow problem has been configured in accordance with the fundamental laws of motion and heat transfer. The similarity transformations have been used to transform the governing equations into the nonlinear ordinary differential equations (ODEs). The numerical solution to the resulting nonlinear ODEs with the associated boundary conditions have been obtained with the utilization of bvp4c package in MATLAB. The behavior of the resulting equations of the problem is checked graphically under the influence of various flow parameters which ensures that the rate of heat transfer decreases with the increase of Brownian motion parameter as well as it increases with the increase of thermophoresis parameter. Moreover, the Sherwood number increases with the rising values of the Prandtl number and Lewis number.

Features of 3D magneto-convective nonlinear radiative Williamson nanofluid flow with activation energy, multiple slips and Hall effect

In this article, the impacts of Hall current and Arrhenius activation energy on three-dimensional hydromagnetic Williamson nanofluid flow past a slendering stretching sheet in the presence of multiple slips, viscous dissipation, Joule heating and binary chemical reaction is analyzed. The presence of nonlinear thermal radiation and nonlinear mixed convection is also taken into consideration. The dimensional governing equations are transformed into non-dimensional ordinary differential equations by using some suitable similarity transformation. The resulting coupled and highly nonlinear boundary value problem is then solved numerically by shooting technique based on Runge-Kutta-Fehlberg method. The behaviors of concentration, temperature and velocity distributions w.r.t. the various controlling parameters are illustrated graphically. However, the numerical values of local skin-friction coefficients, local heat and mass transfer rates are explained and presented in tabular form. Furthermore, a result validation is performed to check the accuracy and correctness of the obtained results by comparing the results with previously published results for some limited case of the present problem and an excellent agreement is found between the results.

Bidirectional Williamson nanofluid flow towards stretchable surface with modified Darcy’s law

Bidirectional flows of Williamson nanomaterial in porous space is discussed. Nonlinear model contains thermophoresis and Brownian motion. Bidirectional non-linear and time-dependent stretching sheet velocity is considered. Nanoparticles zero mass flux condition is accounted. Modified Darcy’s law is invoked. Resulting nonlinear systems are computed by optimal homotopy analysis method (OHAM). Numerical values of velocity gradient coefficients and Nusselt and Sherwood numbers via involved pertinent variables are computed and addressed. Plots and tabulated values lead to physical interpretation. By increasing Williamson parameter and porosity parameter, bidirectional velcities slow down. While temperature is an increasing function of thermophoresis parameter and space and temperature dependent heat sources. Skin friction coefficients and Nusselt number are increasing functions of porosity parameter and Prandtl number while Sherwood number decreases for Brownian motion.

Numerical Simulation of Heat Transfer Flow Subject to MHD of Williamson Nanofluid with Thermal Radiation

In this paper, heat transfer and entropy of steady Williamson nanofluid flow based on the fundamental symmetry is studied. The fluid is positioned over a stretched flat surface moving non-uniformly. Nanofluid is analyzed for its flow and thermal transport properties by consigning it to a convectively heated slippery surface. Thermal conductivity is assumed to be varied with temperature impacted by thermal radiation along with axisymmetric magnetohydrodynamics (MHD). Boundary layer approximations lead to partial differential equations, which are transformed into ordinary differential equations in light of a single phase model accounting for Cu-water and TiO2-water nanofluids. The resulting ODEs are solved via a finite difference based Keller box scheme. Various formidable physical parameters affecting fluid movement, difference in temperature, system entropy, skin friction and Nusselt number around the boundary are presented graphically and numerically discussed. It has also been observed that the nanofluid based on Cu-water is identified as a superior thermal conductor rather than TiO2-water based nanofluid.