Impacts of binary chemical reaction with activation energy on unsteady flow of magneto-Williamson nanofluid

Exploring the impact of Joule heating and Brownian motion on assisting and opposing flows in Eyring-Prandtl fluid

Motivation and Objectives

The basic aim of this investigation is to explore the energy transfer impact on Eyring-Prandtl fluid, a topic that has not been previously examined, thereby paving the way for future researchers. The present literature is crucial for advancing thermal management in engineering applications. This study aims to numerically investigate the thermophoretic effects and Brownian motion of non-Newtonian nanofluid relying on Eyring-Prandtl fluid model across the stretching sheet. The sheet is along the vertical direction under applied magnetic field. Energy and mass transfer rate is explored by considering Joule heating, thermal radiations and chemical reaction effects.

Significance

The increasing potential of Eyring-Prandtl fluid lies in its applications in heat and mass transfer. The current analysis holds significant promise, particularly in scenarios where non-Newtonian working fluids are utilized. This research aids in optimizing industrial processes, designing of efficient cooling systems in electronic devices, and in polymer and food processing.

Methodology

The similarity transformations are utilized to turn a set of partial differential equations (PDEs) into a system of ordinary differential equation (ODE). The resulting system is modified and effectively solved by mean of numerical method known as the Runge Kutta method with bvp4c in MATLAB.

Outcomes

Graphical results show the behavior of several physical parameters across boundary layers of buoyancy assisting and buoyancy opposing region. The magnetic field enhances the thermal conductance of the fluid flow that give rise to flow rate at the surface as well as within the boundary layers. The existing outcomes in the study are attained as a special case of current study. Eyring-Prandtl fluids, with their unique rheological properties can improve the design and efficiency of microfluidic systems used in various applications such as chemical synthesis, drug delivery, and biomedical diagnostics.

Energy transfer through third-grade fluid flow across an inclined stretching sheet subject to thermal radiation and Lorentz force

The heat and mass transfer through the third grade fluid (TGF) flow over an inclined elongating sheet with the consequences of magnetic field and chemical reaction is reported. The impact of activation energy, heat source/sink, and thermal radiation is considered on the TGF flow. Fluid that demonstrate non-Newtonian (NN) properties such as shear thickening, shear thinning, and normal stresses despite the fact that the boundary is inflexible is known as TGF. It also has viscous elastic fluid properties. In the proposed model, the TGF model is designed in form of nonlinear coupled partial differential equations (PDEs). Before employing the numerical package bvp4c, the system of coupled equations are reduced into non-dimensional form. The finite-difference code bvp4c, in particular, executes the Lobatto three-stage IIIa formula. The impacts of flow constraints on velocity field, energy profile, Nusselt number and skin friction are displayed through Tables and Figures. For validity of the results, the numerical comparison with the published study is performed through Table. From graphical results, it can be perceived that the fluid velocity enriches with the variation of TGF factor and Richardson number. The heat source parameter operational as a heating mediator for the flow system, its influence enhances the fluid temperature.

Unsteady hybrid nanofluid ([Formula: see text], MWCNTs/blood) flow between two rotating stretchable disks with chemical reaction and activation energy under the influence of convective boundaries

Hybrid nanofluids are extensively analyzed in recent studies due to their better performance in numerous areas such as heat and mass transfer enhancement, biological fluid movement, medical equipment, heat exchangers, electronic cooling and automotive industry. In current study the nanoparticle concentration utilized is much important in biomedical industry. Major applications include drug delivery, radio-pharmaceuticals, centrifuging blood to obtain red blood cells and plasma, medical implants, onco therapeutics and photo thermal cancer therapy. In this regard, the primary focus of this study is to simulate a blood based unsteady hybrid nanofluid flow between two rotating, stretching disks and convective boundaries. The two nanoparticles in this study are uranium dioxide [Formula: see text] and multi-walled carbon nanotubes MWCNTs. The hybrid nanofluid is under the influence of magnetohydrodynamic effects and chemical reaction with activation energy. The governing partial differential equations (PDEs) are transformed into ordinary differential equations (ODEs) using suitable similarity transform. Homotopy analysis method is used to solve the non-linear system of ODEs and [Formula: see text]-curves are plotted to find suitable region of [Formula: see text] for convergent series solution. Velocity profile is examined for axial, radial and tangential direction against various fluid parameters. Temperature and concentration profiles are analyzed for both convective and non-convective cases. It is observed that convective boundaries result in elevated temperature when compared with non-convective case. Moreover, skin friction, heat and mass transfer rates are also examined with respect to changing volume fraction [Formula: see text].The results revealed that skin friction and rate of heat transfer increases with increase in volume fraction of both nanoparticles [Formula: see text] and MWCNTs while the mass transfer rate depicts contrasting behavior.

Heat Transport Phenomena for the Darcy–Forchheimer Flow of Casson Fluid over Stretching Sheets with Electro-Osmosis Forces and Newtonian Heating

In this study, an investigation has been carried out to analyze the impact of electro-osmotic effects on the Darcy–Forchheimer flow of Casson nanofluid past a stretching sheet. The energy equation was modelled with the inclusion of electro-osmotic effects with viscous and Joule dissipations. The governing system of partial differential equations were transformed by using the suitable similarity transformations to a system of ordinary differential equations and then numerically solved by using the Runge–Kutta–Fehlberg method with a shooting scheme. The effects of various parameters of interest on dimensionless velocity and temperature distributions, as well as skin friction and heat transfer coefficient, have been adequately delineated via graphs and tables. A comparison with previous published results was performed, and good agreement was found. The results suggested that the electric and Forchheimer parameters have the tendency to enhance the fluid velocity as well as momentum boundary layer thickness. Enhancements in temperature distribution were observed for growing values of Eckert number. It was also observed that higher values of electric field parameter diminished the wall shear stress and local Nusselt number.

Darcy–Brinkman–Forchheimer Model for Nano-Bioconvection Stratified MHD Flow through an Elastic Surface: A Successive Relaxation Approach

The present study deals with the Darcy–Brinkman–Forchheimer model for bioconvection-stratified nanofluid flow through a porous elastic surface. The mathematical modeling for MHD nanofluid flow with motile gyrotactic microorganisms is formulated under the influence of an inclined magnetic field, Brownian motion, thermophoresis, viscous dissipation, Joule heating, and stratifi-cation. In addition, the momentum equation is formulated using the Darcy–Brinkman–Forchheimer model. Using similarity transforms, governing partial differential equations are reconstructed into ordinary differential equations. The spectral relaxation method (SRM) is used to solve the nonlinear coupled differential equations. The SRM is a straightforward technique to develop, because it is based on decoupling the system of equations and then integrating the coupled system using the Chebyshev pseudo-spectral method to obtain the required results. The numerical interpretation of SRM is admirable because it establishes a system of equations that sequentially solve by providing the results of the first equation into the next equation. The numerical results of temperature, velocity, concentration, and motile microorganism density profiles are presented with graphical curves and tables for all the governing parametric quantities. A numerical comparison of the SRM with the previously investigated work is also shown in tables, which demonstrate excellent agreement.

Chemical reaction and thermal radiation impact on a nanofluid flow in a rotating channel with Hall current

The objective of the present exploration is to examine the nanoliquid flow amid two horizontal infinite plates. The lower plate is stretchable and permeable. The uniqueness of the flow model is assimilated with the Hall effect, variable thermal conductivity, thermal radiation, and irregular heat source/sink. Transmission of mass is enhanced with the impression of chemical reaction incorporated with activation energy. Appropriate similarity transformation is applied to transform the formulated problem into ordinary differential equations (ODEs). The numerical solution is obtained by employing MATLAB software function bvp4c. The dimensionless parameters are graphically illustrated and discussed for the involved profiles. An increasing behavior is exhibited by the temperature field on escalating the Brownian motion, thermophoresis parameter, variable thermal conductivity, and radiation parameter. For larger values of Schmidt number and chemical reaction parameter, the concentration profile deteriorates, while a reverse trend is seen for activation energy. The rate of heat transfer is strengthened at the lower wall on amplifying the Prandtl number. A comparative analysis of the present investigation with already published work is also added to substantiate the envisioned problem.

Analyzing the impact of induced magnetic flux and Fourier's and Fick's theories on the Carreau-Yasuda nanofluid flow

The current study analyzes the effects of modified Fourier and Fick's theories on the Carreau-Yasuda nanofluid flow over a stretched surface accompanying activation energy with binary chemical reaction. Mechanism of heat transfer is observed in the occurrence of heat source/sink and Newtonian heating. The induced magnetic field is incorporated to boost the electric conductivity of nanofluid. The formulation of the model consists of nonlinear coupled partial differential equations that are transmuted into coupled ordinary differential equations with high nonlinearity by applying boundary layer approximation. The numerical solution of this coupled system is carried out by implementing the MATLAB solver bvp4c package. Also, to verify the accuracy of the numerical scheme grid-free analysis for the Nusselt number is presented. The influence of different parameters, for example, reciprocal magnetic Prandtl number, stretching ratio parameter, Brownian motion, thermophoresis, and Schmidt number on the physical quantities like velocity, temperature distribution, and concentration distribution are addressed with graphs. The Skin friction coefficient and local Nusselt number for different parameters are estimated through Tables. The analysis shows that the concentration of nanoparticles increases on increasing the chemical reaction with activation energy and also Brownian motion efficiency and thermophoresis parameter increases the nanoparticle concentration. Opposite behavior of velocity profile and the Skin friction coefficient is observed for increasing the stretching ratio parameter. In order to validate the present results, a comparison with previously published results is presented. Also, Factors of thermal and solutal relaxation time effectively contribute to optimizing the process of stretchable surface chilling, which is important in many industrial applications.

Consequences of Soret–Dufour Effects, Thermal Radiation, and Binary Chemical Reaction on Darcy Forchheimer Flow of Nanofluids

This research article aims to investigate the consequences of binary chemical reaction, thermal radiation, and Soret–Dufour effects on a steady incompressible Darcy–Forchheimer flow of nanofluids. Stretching surface is assumed to drive the fluid along positive horizontal direction. Brownian motion, and the Thermophoresis are accounted in particular. The governing highly nonlinear system of problems which are advanced version of Navier–Stokes equations are transformed into ordinary differential equations (ODEs) using appropriately adjusted transformations invoking symmetric property of the independent variables. The numerical approach using RK45 in connection with shooting technique is adopted to solve the final equations. Graphical approach is used to interpret the results and the values of important physical quantities are given in tabular data form. Velocity field, temperature distribution and concentration distribution are graphically analyzed for variation in respective fluid parameters. Furthermore, density graphs and stream lines are sketched for the present model. The outputs indicate a rise of temperature field in connection with thermal radiation parameter. A clear decline is noticed in velocity field for elevated values of Forchheimer number and porosity factor. The Dufour effect anticipates a rising factor for temperature distribution and the same is noticed for concentration distribution in lieu of Soret effect. Thermal radiation and binary chemical reaction has strong impact on heat transport mechanism. The results for physical quantities such as skin friction, heat and mass flux rates are given in tabular data form in last section of this study.

Characterization of Marangoni Forced Convection in Casson Nanoliquid Flow with Joule Heating and Irreversibility

The Marangoni forced convective inclined magnetohydrodynamic flow is examined. Marangoni forced convection depends on the differences in surface pressure computed by magnetic field, temperature, and concentration gradient. Casson nanoliquid flow by an infinite disk is considered. Viscous dissipation, heat flux, and Joule heating are addressed in energy expressions. Thermophoresis and Brownian motion are also examined. Entropy generation is computed. The physical characteristics of entropy optimization with Arrhenius activation energy are discussed. Nonlinear PDE's are reduced to highly nonlinear ordinary systems with appropriate transformations. A nonlinear system is numerically computed by the NDSolve technique. The salient characteristics of velocity, temperature, concentration, entropy generation, and Bejan number are explained. The computational results of the heat-transfer rate and concentration gradient are examined through tables. Velocity and temperature have reverse effects for the higher approximation of the Marangoni number. Velocity is a decreasing function of the Casson fluid parameter. Temperature is enhanced for higher radiation during reverse hold for concentration against the Marangoni number. The Bejan number and entropy generation have similar effects for Casson fluid and radiation parameters. For a higher estimation of the Brinkman number, the entropy optimization is augmented.