Williamson Nanofluid Flow Research Articles

An investigation on non-Darcian Williamson nanofluid flow stimulated by activation energy resulting from a slick elastic sheet encased in a porous medium

An investigation on non-Darcian Williamson nanofluid flow stimulated by activation energy resulting from a slick elastic sheet encased in a porous medium

Entropy generation of Williamson hydromagnetic non-linear radiative nanofluid flow near a stagnation point over a porous stretching sheet

Purpose This study aims to analyze the multi-slip effects of entropy generation in steady non-linear magnetohydrodynamics thermal radiation with Williamson nanofluid flow across a porous stretched sheet near a stagnation point. Also, the qualities of viscous dissipation, Cattaneo–Christove heat flux and Arrhenius activation energy are taken into account. Thermophoresis, Brownian motion and Joule heating are also considered. Design/methodology/approach The Navier–Stokes equation, the thermal energy equation and the Solutal concentration equations are the governing mathematical equations that describe the flow and heat and mass transfer phenomena for fluid domains. By using the proper similarity transformations, a set of ordinary differential equationss are retrieved from boundary flow equations. The classical Runge–Kutta fifth-order algorithm along with the shooting technique is implemented to solve the obtained first order differential equations. Findings The study concludes that the temperature distribution boosting for thermal radiation, magnetic field and Eckert number where as the velocity and entropy generation escalate for the Williamson parameter, diffusion parameter and Brinkman number. The skin-friction and heat and mass transfer rate increases with the fluid injection. In addition, tabulated values of friction drag and rate of heat and mass transfer for various values of constraints are provided. Originality/value The comparison of the present results is carried out with the published results and noted a good agreement.

Two branches solutions for mixed convection flow of thermally Williamson nanofluid flow with heat transfer due to magnetized shrinking sheet

AbstractThe study of magnetohydrodynamics (MHD) and thermal radiation over‐stretching and shrinking sheets has significant applications in a wide range of fields, from chemical manufacturing to transport engine cooling systems, electronic chip cooling, plasma, the nuclear‐powered sector, saltwater, etc. The present study aims to numerically and theoretically analyze the movement of thermally magnetized Williamson nanofluid owing to an extended/contracting sheet. The regulating flow equations are converted to self‐similar equations through similarity transformation, and then numerically solved by bvp4c using MATLAB software. A comparison of the present numerical study with the published study is quite impressive. The investigation demonstrates that the self‐similar equations disclose the two branches for the limited shrinking factor range. For the stretching case, only one solution exists. As a result, the most fundamentally feasible solution has been determined by the linear assessment of temporal stability. For the aim of stability analysis, the lowest eigenvalue sign indicates the stability or instability of a solution. Through stability analysis, it is witnessed that the first solution (first branch) is stable. Due to the presence of the Lorentz force effect, it is perceived that the velocity curves decline in the whole channel. The point to be noted here is that the velocity of the lower branch compared to the upper branch is higher. The reduced Skin Friction is increased in the first branch and declines in the second branch for the two different values of magnetic factor.

Irreversibility analysis of CNT‐enhanced Williamson nanofluid flow in a stretching cylinder

AbstractThis study presents a novel exploration into the intricate interplay of slanted magnetohydrodynamic and radiative fluxes within a Williamson fluid incorporating single‐walled carbon nanotubes (SWCNTs) and multi‐walled carbon nanotubes (MWCNTs) in a water‐based system. Utilizing an exponentially stretching cylinder model, the research holistically integrates entropy production, encompassing thermal radiation, porosity, buoyant forces, and heat source/sink constraints within the governing equations. To solve the resulting governing equations with boundary conditions, the shooting technique is employed to convert them into initial value problems. Subsequently, the Runge–Kutta–Fehlberg 4–5th order method is used to obtain numerical solutions. Unveiling unprecedented insights, the investigation reveals distinctive parameter dependencies governing fluid behavior. It delineates how variations in different factors distinctly impact fluid velocity, thermal profiles, entropy generation, Bejan number, drag force, and heat transfer rates across different nanofluid compositions. Furthermore, the study highlights the transformative impact of nanocomposites on altering the thermal properties of the fluid and orchestrating nanofluid mobility. The results show that MWCNTs have an enhanced entropy generation rate when compared to SWCNTs. These findings bear substantial promise for real‐world applications involving water‐based nanofluids, shedding light on their manipulation and optimization in various technological domains.

Impact of thermal conductivity of a Williamson’s nanofluid flow due to a stretching sheet

This paper intends to build a mathematical model of a two-dimensional Williamson nanofluid flow due to the stretching of a sheet linearly. The flow geometry is influenced by the magnetic field that is applied externally to the system. The induced magnetic field is infinitesimal and hence neglected. However, the flow structure is incorporated with the Brownian motion and thermophoresis effects as it alter the physics of the flow. The equations that model the flow comprise the highly nonlinear coupled simultaneous system. Thus, a numerical technique namely finite difference accompanied with the Thomas algorithm is adopted to approach the flow system. The motion, temperature, and concentration of the Williamson nanofluid flow are studied for the different flow controlling parameters. The co-efficient of skin-friction, heat, and mass transfer rates is also computed. The streamlines, isotherms, and iso-concentration are plotted to picturise the flow phenomena in the complete domain. The study reveals that the temperature of the flow raises with the Brownian motion of the nanoparticles and the trend is opposite with the concentration. The strength of the streamlines, isotherms, and the concentration contour is identified to be high for the least magnitude of Weissenberg number. The Brownian motion raises the heat transfer rate and slows down the mass transfer rate.

Analysis of Brownian motion and thermophoresis effects with chemical reaction on Williamson nanofluid flow over permeable stretching sheet

This study warrants a broad analysis on the simultaneous effects of Brownian and thermophoresis on the chemically reacting Williamson nanofluid flow via a permeable expanding sheet. The analysis includes the properties of slip velocity and thermal radiation, providing a more representative picture of the physical phenomena. The differential equations governed by demonstrating the fluid flow phenomena are renewed to a set of nonlinear differential equations utilizing similarity rules. These transformed equations are subsequently handled numerically adopting the fourth-order Runge-Kutta method. The results reveal the significant control of Brownian motion together with thermophoresis and additionally, the inclusion of velocity slip and thermal radiation remarkably affect the velocity, temperature, and concentration distributions. Parametric studies show the validation of the present system to variations in the Williamson fluid parameter, slip parameter, radiative heat parameter, Brownian motion parameter, and thermophoresis parameter.

A study of mixed convection magnetohydrodynamics Williamson nanofluid flow over a nonlinear permeable elongating sheet over a porous medium with viscous dissipation

A study of mixed convection magnetohydrodynamics Williamson nanofluid flow over a nonlinear permeable elongating sheet over a porous medium with viscous dissipation

Dynamic processes of quartic autocatalysis chemical reaction in Williamson nanofluid flow over a parabolic surface

Studying the dynamic processes of quartic autocatalysis chemical reactions in Williamson nanofluid flow over a parabolic surface is significant for optimizing and enhancing the efficiency of industrial and engineering systems involving complex fluid dynamics and chemical reactions. The investigation of the type of flow channel is very important. In the present problem, the motion is investigated on an upper horizontal surface of a paraboloid of revolution. The analysis is performed about the Williamson nanofluid flow with Cattaneo–Christov (C–C) heat flux, quartic autocatalysis chemical reaction and gyrotactic microorganisms motion past an upper horizontal surface of a paraboloid of revolution (uhspr). Similarity transformations are applied to get the non-dimensional equations in differential form. Homotopy Analysis Method (HAM) is operated for computing the solution. The solution is processed to obtain the results which have been shown through the graphs which note the effects of existing parameters on profiles. The computed results have a nice agreement with the published results. The investigations are about the upper horizontal surface of a paraboloid of revolution which has leading role in science, aerodynamics like surface of a rocket, bonnet of a car and pointed surface of a vehicle and airplane.

Modeling of EMHD ternary hybrid Williamson nanofluid flow over a stretching sheet with temperature jump and magnetic induction

This study explores the heat transfer and fluid flow characteristics of an incompressible Williamson ternary hybrid nanofluid (WTHNF) over an unsteady stretching surface, influenced by external electric and magnetic fields, thermal radiation, and a porous boundary. The WTHNF consists of ZrO2, MoS2, and GO nanoparticles suspended in water. By applying suitable transformations, the fundamental equations are simplified and solved numerically using the Explicit Runge Kutta Method (ERKM). The research investigates how various physical parameters, such as electric and magnetic field strengths, thermal radiation, porous plate permeability, velocity slip, and temperature jump, impact the velocity, temperature, skin friction coefficient, and local Nusselt number. The findings offer valuable insights into the interactions between WTHNF and external factors, which can inform the design and optimization of advanced heat transfer and fluid flow systems in engineering. Additionally, this study demonstrates the potential of WTHNF to enhance heat transfer rates, making it a promising candidate for cooling systems, heat exchangers, and energy storage devices. The research contributes to developing more efficient and sustainable technologies in aerospace, biomedical engineering, and renewable energy. Moreover, the results provide a foundation for future research on the behavior of complex fluids under various external influences. This could lead to the creation of more advanced fluid flow systems, improving efficiency and performance across numerous applications.

Effects of Arrhenius Activation Energy on Thermally Radiant Williamson Nanofluid Flow Over a Permeable Stretching Sheet with Viscous Dissipation

This paper explores the role of viscous dissipation, Arrhenius activation energy, and thermal radiation of Williamson nanofluid flow over a permeable stretching sheet. The governing partial differential equations have been simplified through a transformation process, resulting in a set of non-linear differential equations. To find a solution for these equations, a numerical approach is employed, specifically the fourth order Runge-Kutta method. Additionally, a shooting technique is utilized to enhance the accuracy of the numerical solutions. Overall, the study involves reducing complex equations, solving them numerically, and refining the results through a combination of methods. The study investigates the impact of different physical parameters on key factors like velocity, temperature, skin friction coefficient, nano particle volume fraction, and rates of mass and heat transfer. This study exhibits that activation energy parameter enhances concentration profiles, whereas fitted rate constant shows opposite behavior. The activation energy into heat transfer model allows for the optimization of heat transfer systems utilizing Williamson nano fluids.

Application of Fibonacci wavelet in the analysis of unsteady MHD Williamson nanofluid flow over a permeable stretching sheet via porous medium

This research investigates the unsteady flow behavior of a magnetohydrodynamic Williamson nanofluid (WNF) over a permeable stretching sheet within a porous medium. It considers the influence of chemical reactions, Joule heating, heat generation/absorption, thermal radiation, and viscous and porous dissipation. The study on magnetohydrodynamic WNF over a permeable stretching sheet within a porous medium has gained much significance due to its numerous industrial and engineering applications. The study employs the Fibonacci wavelet series collocation method (FWSCM) for analysis. An appropriate similarity transformation transforms the governing partial differential equations (PDEs) into nonlinear coupled ordinary differential equations (ODEs). These ODEs are solved using FWSCM. The accuracy of the FWSCM is validated with some previous studies, the Mathematica NDSolve command, and the Haar wavelet collocation method (HWCM). The graphs and tables are used to discuss the physical parameter’s impact. The findings of this study reveal that the Nusselt number increases by 45.32 % with the Weissenberg number and 31.25 % with the unsteadiness parameter. In comparison, it decreases by 45.01 % with the heat generation/absorption parameter, 4.89 % with the porosity parameter, and 1.95 % with the chemical reaction parameter.

Influence of Magneto-hydrodynamic with Williamson Nanofluid Flow Control of Forcheeimer Model under Chemical Reaction

Objective: The research focused on Williamson's nonlinear governing flow on Magneto hydrodynamic incompressible, steady fluid over a porous stretching sheet in a two-dimensional direction. The permeable stretching sheet embedded by Williamson fluid is based on the flow model of non-Darcy Forchheimer law with chemical reaction. This article concentrated on an energy equation dominated by the dissipation parameter analysis. Methods: The governing mathematical partial derivative formulations are changed to a system of ordinary differential formulations with appropriate similarity transformation. The mathematical formulations are evaluated employing the numerical method of the R-K fourth-order scheme. MATLAB software bvp4c is used for computing numerical results. The numerical results and graphs were successfully demonstrated with the R-K fourth-order system. Findings: For the influence of Williamson non-Newtonian, non-fluid observed emerging dimensionless quantifiers such as Williamson number, porous, electric, thermophoresis, Brownian motion, Prandtl, and Schmidt dimensionless number respectively. The performance of non-dimensional parameters is investigated in detail. Novelty: As described in the results, Williamson's non-Newtonian nanofluid under the influence of magneto-hydrodynamics is mentioned as a new value to the existing literature. The gained results are the innovative study of the influence of chemical reaction on Williamson non-Newtonian nanofluid and magnetic strength and reported on dimensionless parameters. Keywords: Electric parameter, Williamson Nanofluid, Darcy-Forchheimer, Viscous dissipation, Chemical reaction quantifier

Radial basis kernel harmony in neural networks for the analysis of MHD Williamson nanofluid flow with thermal radiation and chemical reaction: An evolutionary approach

The current investigative exploration exemplifies the conceptualization of a novel design intelligent computing paradigm based on artificial neural networks (ANNs) by utilizing radial basis function (RBF) to analyze magnetohydrodynamic (MHD) Williamson nanofluid two-dimensional flow along a stretchable sheet under the effect of chemical reaction as well as thermal radiation in a porous medium. This newly designed technique is an amalgam of a well-known reliable global solver named genetic algorithms (GAs) and a swift convergence generated local solver named sequential quadratic programming (SQP) used in ANNs by taking RBF as a kernel function i.e. ANNs-RBF-GASQP solver. The PDEs demonstrating the current nanofluid problem flow are transformed into the system of non-linear ODEs through a relevant similarity transformation and subsequently solved using ANNs-RBF-GASQP solver to investigate thermohydraulic properties by manipulating the values of various system parameters present in the ODEs. Moreover, the simulation results show that increasing the heat source parameter leads to a significant decrease in temperature. Additionally, an increase in the porosity parameter causes a decrease in the velocity of nanofluid, as a higher value of porosity increases fluid permeability and greater resistance to flow. The efficacy of the suggested solver is scrutinized through various statistical and convergence analyses.

Modeling of magneto bioconvection Williamson nanoliquid through modified heat flux: The significance of entropy

The combination of microbes and nanofluids has noteworthy consequences for technological and engineering progress, particularly in the realm of heat transfer applications. This study explains radiative flow with chemical reactions affect the emergence of microorganisms in magnetic mixed convective Williamson nanofluid flow. The Cattaneo-Christov heat flux theory and the effects of heat source/sink have been examined about the energy equation. The prime idea of this analysis is to enhance heat and mass transport. The modelled equations have been converted to dimensionless by considering suitable alteration. The dimensionless expression is then numerically tackled using MATLAB's bvp4c approach. The graphs for different profiles—that is, momentum, temperature, concentration and concentration of microorganisms that move—are made visible for particular nondimensional factors. Furthermore, entropy generation minimization has been obtained through law of thermodynamics. The drag friction, heat and mass transfer rate, and microbe density are also computed in a tabular manner. The most important findings that are pertinent to this study are that an increase in the values of the Brownian motion, thermal radiation and thermophoresis significantly enhance heat transfer characteristics. A consistent pattern can be observed when comparing the current results with earlier research.

Numerical Analysis Study of Chemically Radiative MHD Williamson Nanofluid Flow over an Inclined Surface with Heat Source

The design and optimization of systems such as nuclear reactors, solar collectors, and thermal power plants may benefit from an understanding of the behaviour of nanofluids with chemical processes, thermal radiation, and magnetic fields over inclined surfaces with heat sources.This review looks at the magnetohydrodynamic (MHD) flow of a Williamson nanofluid over an inclinable stretched sheet and the impact of thermal radiation, heat source, and chemical processes. The outcomes of the generation of heat or absorption, as well as thermal radiation, are all factored into account in the energy equation. On the other hand, the mass transport equation also takes into account chemical interactions.The similarity substitution serves to turn the governed partial differential equations for velocity, temperature, and concentration into ordinary differential equations, which are then numerically resolved with Mathematica's NDSolve program. Changes in temperature, concentration, and dimensionless velocity as a function of various factors are graphically touched upon. The temperature diminishes while the Prandtl number accelerates as the thermal boundary layer thins and the viscosity enrichment. The temperature contour develops along with the magnetic field strength. When all the parameters were compared for a particular case, a very good association was discovered. Depending on the precise conclusions and understandings drawn from the investigation of chemically radiative MHD nanofluid flow over inclined surfaces with a heat source, the applications may range greatly. It's important to remember that such research often aids in the creation of more effective and environmentally friendly solutions in a variety of sectors.

Numerical analysis of the MHD Williamson nanofluid flow over a nonlinear stretching sheet through a Darcy porous medium: Modeling and simulation

Abstract In the current study, we delve into examining the movement of a nanofluid within a Williamson boundary layer, focusing on the analysis of heat and mass transfer (HMT) processes. This particular flow occurs over a sheet that undergoes nonlinear stretching. A significant facet of this investigation involves the incorporation of both the magnetic field and the influence of viscous dissipation within the model. The sheet is situated within a porous medium, and this medium conforms to the Darcy model. Since more precise outcomes are still required, the model assumes that both fluid conductivity and viscosity change with temperature. In this research, we encounter a system of extremely nonlinear ordinary differential equations that are treated through a numerical technique, specifically by employing the spectral collocation method. Graphical representations are used to illustrate how the relevant parameters impact the nanoparticle volume fraction, velocity, and temperature profiles. The study involves the computation and analysis of the effect of physical parameters on the local Sherwood number, skin friction coefficient, and local Nusselt number. Specific significant findings emerging from the present study highlight that the rate of mass transfer is particularly influenced by the thermophoresis factor, porous parameter, and Williamson parameter, showing heightened effects, while conversely, the Brownian motion parameter demonstrates an opposing pattern. The results were computed and subjected to a comparison with earlier research, indicating a notable degree of conformity and accord.

Sensitivity analysis and response surface methodology for entropy optimization in the exponentially stretching stratified curved sheet for Casson–Williamson nanofluid flow

The current study explains the parametric entropy optimization by using response surface methodology and sensitivity analysis. It also reveals the effects of thermal radiation and exponential heating on Casson–Williamson nanofluid flow over an exponentially stretching curved sheet. The Darcy–Forchheimer model is used and stratification, Navier slip, and suction-injection are used as the boundary constraints. The 4–5th ordered Runge–Kutta Fehlberg approach is enacted to exhibit the modeled flow. Response surface methodology is used to build the statistical design for the Weissenberg number, magnetic parameter, and Brinkmann number. The thermal stratification parameter, according to the findings, lowers temperature. Entropy grows as Brinkmann number and magnetic parameter increase. When the thermal buoyancy factor assumes the minimum value, little shear stress is seen for high Forchheimer number. The squared co-efficient is confirmed to be 99.99 %. The Pareto chart confirms that point 2.2 is the important point. Entropy surface diagrams in three dimensions demonstrate that with high magnetic parameter, high Brinkman number levels and low Weissenberg number levels, high entropy is obtained. For low and medium levels of magnetic parameter, Weissenberg number exhibits positive sensitivity, whereas for high and medium levels of magnetic parameter, it exhibits negative sensitivity.

Unfolding some numerical solutions for the magnetohydrodynamics Casson–Williamson nanofluid flow over a stretching surface

Abstract This research focuses on exploring the significance of chemical reactions and thermal radiation on the magnetohydrodynamic (MHD) flow of a Casson–Williamson nanofluid (CWNF) over a stretching sheet. The objective is to comprehend how these factors influence the flow and heat transfer. A mathematical model, comprising partial differential equations adjusted into ordinary differential equations (ODEs) via utilizing some transformation. These ODEs are then tackled by MATLAB’s BVP4C method, which is part of the finite difference technique. Results are verified by comparison with existing literature and are depicted visually and in tabular format. Additionally, the study explores the effects of external factors such as magnetic fields and the Lewis number on parameters like Nusselt number, friction factor, and Sherwood number. Furthermore, heat generation in MHD CWNF is analyzed, along with a thorough evaluation of heat transfer near a stretching sheet with a permeable layer. The findings suggest that growing Brownian motion factor (Nb) and thermophoresis coefficient (Nt) enhance the rate of heat transfer, signifying improved heat transfer rates. Similarly, higher Nt values are associated with enhanced Sherwood numbers, indicating better mass transfer. Conversely, higher Nb values lead in lower local Sherwood numbers. Physically, an increase in Brownian motion causes significant displacement of nanofluid particles, boosting their kinetic energy and thereby enhancing heat generation within the boundary layer. It is noted that the Eckert number (Ec) reflects the impact of different Ec values on temperature distribution. As Ec increases, there is a proportional increase in fluid temperature due to frictional heating, which stores heat energy within the fluid. This effect becomes more pronounced for non-linear stretching surfaces, demonstrating the response of the thermal region to viscous dissipation. Viscous dissipation has the potential to enhance convective heat transfer, leading to amplified temperature distribution and thickening of the thermal layer.

Numerical paradigm to explore the chemically reacting Williamson nanofluid flow with the influence of bioconvection effects using neural networks

This research focuses on using a type of advanced computer program called artificial neural networks (ANNs) using the Levenberg–Marquardt backpropagation technique (LMBPT-NNs) to stimulate the behavior of bioconvective effects on heat and mass transport in non-Newtonian chemically Williamson nanofluid through stretched surface (BEHMT-NNCRWNF-SS). Williamson nanofluid flow refers to specially engineered fluids with nanoparticles dispersed within them and moving when subjected to external forces. Understanding their flow behavior is crucial to effectively use them in various applications, especially in the field of heat and mass transfer and fluid dynamics. Before being solved numerically, a couple of governing partial differential equations are transformed into ordinary differential equations through suitable similarity functions. The finite difference method (FDM) (Lobatto IIIA) is applied for the solution of a nonlinear nanofluidic system by selecting different collocation points. These collocation points play a crucial role in approximating the solution and ensuring accurate results. To address various fluidic problems, it's important to use the appropriate results of FDM to create a reference dataset for the LMBPT-NNs. Statistical analysis should then be performed on the training, testing, and validation of the reference datasets to obtain the optimal scheme for different fluidic flow issues.. The precision of the LMBPT-NNs is checked through ANN tools like mean square error (MSE), regression analysis, curve fitness, and histogram error.

Effects of Hall, ion slip, viscous dissipation and nonlinear thermal radiation on MHD Williamson nanofluid flow past a stretching sheet

This work aims to explore the effects of ion slip and Hall current on the flow of MHD Williamson nanofluid over a stretching plate in the presence of chemical reaction, viscous dissipation, ohmic (Joule) heating, nonlinear thermal radiation, and heat generation/absorption. After using appropriate similarity transformations, the highly nonlinear governing partial differential equations are transformed to a system of ordinary differential equations. The subsequent non-linear problems are treated to numerical results by reducing the converted nonlinear ODE in to first order. The fifth-order Runge–Kutta method along with the shooting approach is implemented using the python programming tool to analyze the problem. Graphical representations have been used to investigate the impacts of the derived physical parameters on the temperature, velocity, and concentration distributions of nanoparticles with the goal of giving each parameter a physical interpretation. The study of the effects of various physical parameters on the skin friction coefficient, the local Nusselt number and the Sherwood number was finally explained with the help of graphs and tables. It is discovered that when the Williamson parameter increases, both the principal and secondary velocity profiles decline but the temperature and concentration profiles rise. Both the Hall parameter and ion slip effect produce similar results with increasing principal velocity profile and decreasing secondary velocity, temperature and concentration profiles. Furthermore, it is seen that the temperature and concentration profiles increase in response to an increase in the nonlinear thermal radiation parameter. The increment in Eckert number (viscous dissipation term) also showed enhancements in temperature and concentration profiles. Additionally, the primary skin friction coefficient and rate of mass transfer are accelerated by raising the magnetic field parameter, Williamson parameter, or Darcy number, but the heat transfer rates are slowed down in the boundary layer. Lastly, the obtained results were cross-referenced with earlier findings, considering specific assumptions, to establish the credibility of the results. The comparison revealed that the new results provided valuable and profound insights into the studied phenomenon.