Brownian Motion Parameter Research Articles

The influence of lymphatic vessels on nanoparticle distribution and heat transfer within tissue

AbstractThis study analytically investigates the dynamics of nanoparticle transport within a three‐dimensional porous cylinder simulating a lymphatic vessel, without external heat sources. The governing equations and boundary conditions are transformed to yield a system of ordinary differential equations, which are solved numerically using MATLAB built‐in function, bvp4c. Key parameters are visually examined and physically interpreted in relation to temperature, velocity, concentration, and Nusselt number profiles. The study reveals that the distribution of temperature and Nusselt number are maximized by increasing the heat transfer coefficient, whereas NP concentration is increased by decreasing it. Furthermore, the Brownian motion parameter enhances both heat transmission and NP concentration. It is also observed that simpler extravasation into lymphatics decreases tissue nanoparticle levels and heat conduction. Ultimately, optimal intra‐lymphatic nanoparticle distribution pathways are achieved by specifically varying heat transfer and interstitial mass flux patterns. By simulating biological barriers and lymphatic drainage, this model enhances our understanding of the underlying transport mechanisms controlling nanoparticle mobilization.

Computational study with neural networks to double diffusion in Prandtl thermal nanofluid flow adjacent to a stretching surface design with numerical treatment

The study focuses on the implementation of neural networks in analyzing the behavior of Prandtl nanofluid near a extending surface in the existence of dual diffusion. The research investigates the merged consequence of thermal and concentration gradients on the fluid flow and heat transfer characteristics using advanced computational techniques. The investigation delves into the phenomenon of double diffusion in the flow of Prandtl nanofluid near a stretching surface (DD-PNSS), employing the Levenberg-Marquardt scheme with Artificial Neural Networks (LMS-ANNs). The application of similarity variables converts the non-linear partial differential equations into non-linear ordinary differential equations. Through the application of the Lobatto IIIa formula in a three-stage process, various data sets are generated for the LMS-ANNs by varying parameters such as the Prandtl fluid parameter ([Formula: see text]), Prandtl number (Pr), Brownian motion parameter (Nb), thermophoresis parameter (Nt), and Dufour-solutal Lewis number (Ld). The range of parameter α is from 2 to 3.5, parameter β from 0.1 to 0.9, Nb is from 0.1 to 0.4, Nt is from 0.1 to 0.7, Le is from 1 to 3 and Ld is from 0.1 to 0.5. The intrinsic behavior of embedded parameters on dimensionless velocity, temperature, solutal concentration, and nanoparticle concentration profiles is graphically evaluated. The proposed LMS-ANNs model is meticulously tested, validated, and trained using a multi-stage approach, and its performance is compared to established references to ensure its reliability. The effectiveness of the suggested LMS-ANNs model is further affirmed through regression analysis, Mean Squared Error (MSE) evaluation, and histogram studies, showcasing an exceptional accuracy level ranging from 10−08 to 10−10, setting it apart from alternative approaches and reference models.

Exploring concentration-dependent transport properties on an unsteady Riga plate by incorporating thermal radiation with activation energy and gyrotactic microorganisms

Abstract The aim of this study is to examine the entropy generation (EG) associated with the transfer of mass and heat in a concentration-dependent fluid with thermal radiation and activation energy, specifically in the context of an unsteady Riga Plate with gyrotactic microorganism. It is important to solve the ordinary differential equations generated from the controlling partial differential equations using Lie symmetry scaling to verify their quality and reliability. The system’s anticipated physical behavior is compared to Mathematica’s Runge–Kutta–Fehlberg numerical solution. Source parameters are essential for validation since they offer accurate results. Methodically change these values as a percentage to determine how they affect the unsteady fluid’s density, mass, and heat transfer over the Riga plate. Velocity, temperature, nanoparticle concentration and microorganism concentration profiles decrease with varying values of the unsteadiness parameter. EG increases with increasing values of concentration difference, thermal radiation, and Reynold number parameters. The Nusselt number experiences a 26.11% rise as a result of radiation when the unsteadiness parameter is A = − 0.25 A=-0.25 , in comparison with the scenario without radiation. Mass transfer upsurges with increasing values of the Brownian motion parameter and reduces with increasing values of thermophoresis parameter. To verify our conclusions, we compare calculated data, specifically the skin friction factor, to theoretical predictions. Tabular and graphical data can show how physical limits affect flow characteristics.

Optimization of thermal performance in hybrid nanofluids for parabolic trough solar collectors using Adams–Bashforth–Moulton method

Solar energy is an environment-friendly renewable energy source that fulfills the energy consumption requirements of the world economy. Concentrated solar power is the most advanced technology that efficiently absorbs concentrated solar energy. This article investigates the solar energy storage and entropy generation in concentrated parabolic trough solar collectors for hybrid nanofluid flow due to a spinning tube inserted at the receiver's center. The effect of copper nanoparticles and multi-walled carbon nanotube mixture is studied using water-based fluid. Also, the influence of an external magnetic field is investigated with thermophoresis and Brownian motion of nanoparticles. The governing equations for the nanofluid flow are derived using the conservation principles of mass, momentum, energy, and concentration with boundary layer assumptions and no-slip boundary conditions. The governing equations are numerically solved using Adam Bashforth and Adam Moulten's fourth-order predictor-corrector numerical scheme along with the shooting approach. The numerical outcomes for the fluid velocity, temperature, Nusselt number, and entropy formation against various influential physical parameters have been discussed using graphs. It is observed that the augmenting Eckert number, thermophoretic diffusion parameter, and Brownian motion parameter escalates the thermal profiles. Also, an escalation of the radiation parameter and Lewis number enhances the Nusselt number. Thermal energy storage in solar collectors utilizing different terminologies is crucial for improving the efficiency and performance of solar thermal collectors.

Effects of exponentially stretching sheet for MHD Williamson nanofluid with chemical reaction and thermal radiative

This paper explores the combined effects of heat radiation, viscous dissipation, and chemical reactions on the steady flow of Williamson nanofluid over an exponentially stretched sheet. The Governing non-linear Partial Differential Equations (PDE's), converted to couple nonlinear Ordinary ODE's by using similarity transformation, which are solved numerically using the Runge-Kutta-Fehlberg method along with the shooting technique. The study shows detailed analysis of the behaviour of Williamson nanofluid under the influence of thermal radiation and magnetic fields, having relevant industrial applications in cooling technologies and polymer processing. The results show that increasing the magnetic field parameter reduces the fluid velocity, while higher thermal radiation and Brownian motion parameters significantly enhance heat transfer rate withing the boundary region.

Reversible esterification process in Casson nanofluids: A numerical analysis of non-newtonian hydromagnetic flow

A computational mechanism has been formulated to scientifically analyze the phenomenon of combined convection in the occurrence of magnetohydrodynamic flow behavior of Casson nanofluid. This study emphasizes the trajectory of the nanofluid along a stretching sheet with nonlinear permeability, while considering additional physical effects such as reversible chemical reaction, thermal radiation, energy source/sink, suction and viscous dissipation. In this study, we have additionally integrated the nanofluid paradigm proposed by Buongiorno, which encompasses the repercussion of thermophoresis along with Brownian motion. The utilization of appropriate similarity renovations serves the purpose of recasting the dominant multivariate differential equations to a collection of nonlinear differential equations in single variable. The Runge–Kutta shooting mechanism is implemented for the intention of numerically determining the unknown boundary conditions. The solution to the dominant equations was obtained by employing the fourth-order Runge–Kutta technique and to ensure the dependability of the outcomes, the bvp4c method was employed. The graphical and tabulated observations are presented herein to facilitate a comprehensive analysis of the underlying physical characteristics inherent in the problem at hand. The utilization of the Casson parameter has been found to be advantageous in the reduction of shear stress rate, along with the enhancement of mass and energy transfer rates. Additionally, the application of suction has been observed to be beneficial in the enhancement of Sherwood number and energy transfer rate. Within the scope of the context of the esterification process, the purpose of this proposal is to evaluate the impact that numerous arithmetical values exert on the temperature field, the velocity profile and the volumetric concentration. An in-depth graphical analysis that takes into account the relevant physical consequences is used to evaluate the most important factors that relate to the physical quantities that describe the contours of temperature, velocity and concentration. In addition to being accompanied by their respective explanations, the tabular portrayal of the local Sherwood number, shear stress rate along with local Nusselt number all feature in this paper. There is a clear distinction that can be made between irreversible and reversible flows in the evaluation of the local Sherwood number, rate of shear stress and local Nusselt number. This differentiation is brought about by taking into analysis thermophoresis parameter, Brownian motion parameter and suction parameter. The results that were produced from the theoretical simulations have significant repercussions for a variety of fields that are related to energy engineering. The findings derived from the analysis indicate a negative correlation between the Brownian motion parameter and both irreversible and reversible flow in terms of rate of energy transfer and shear stress rate. It is imperative to highlight that reversible flow holds greater significance in comparison to irreversible flow.

Radiative MHD Casson Non-Newtonian Nanofluid Slip Flow Induced by Stretching Cylinder: A Numerical Approach

Objectives: This article investigates the continuous magnetohydrodynamics slip flow across an extending cylinder, including heat radiation and free stream velocity. The proposed model incorporated the Brownian motion parameter and thermophoresis. Methods: Applying the similarity transformation to a system of partial differential equations yields an ordinary differential equation of first order. Since, there is the nonlinear nature of the modified equations, these ordinary differential equations are addressed by employing mathematical modeling. The shooting process has been embraced to solve changed equations by implementing the following Runge-Kutta Fehlberg method. Findings: Graphical representations are used to show how several fluid factors, such as Casson fluid parameter, free stream velocity, thermophoresis, magnetic parameter, Brownian motion parameter, heat generation parameter, Lewis number, radiation parameter, chemical reaction and curvature parameter affect concentration, temperature and velocity. Results for physical quantity of interest are also computed and reported in tabular form. The study's main findings showed that nanoparticle temperatures rise with greater Brownian motion parameter values, whereas nanoparticle concentration falls with higher heat radiation parameter values. Additionally, it is found that with rise in Lewis number rises as 0.1, 0.4, 0.7, 1.0, 1.3, heat transfer rate falls down by 21.19%. The outcomes are calculated using the MATLAB software. Novelty: This technique's validity is defended by comparing its most recent findings to previously published results and successfully meeting the convergence criteria. The present work emphasizes the analysis of free stream flow in the cylindrical area, specifically in the existence of partial slip and heat radiation, under convective circumstances. This study has significant implications for electronic devices such as processors as well as many businesses and the field of biological and medical sciences. The present investigation aims to support production businesses in achieving the desired level of quality of their products by effectively managing the transport phenomena. Keywords: Stretching cylinder, Heat radiation, Brownian motion, Thermophoresis, Non-Newtonian nanofluid, Shooting technique

Significance of magnetic field and Darcy–Forchheimer law on dynamics of non-Newtonian hybrid nanofluid flow over a spinning disc with Arrhenius activation energy and shape factor

Purpose The purpose of the study is to explore the three-dimensional heat and mass transport dynamics of the magneto-hydrodynamic non-Newtonian (Casson fluid) hybrid nanofluid flow comprised of − as nanoparticles suspended in base liquid water as it passes through a flexible spinning disc. The influence of a magnetic field, rotation parameter, porosity, Darcy−Forchheimer, Arrhenius’s activation energy, chemical reaction, Schmidt number and nanoparticle shape effects are substantial physical features of the investigation. Furthermore, the influence of hybrid nanofluid on Brownian motion and thermophoresis features has been represented using the Buongiorno model. The novelty of the work is intended to contribute to a better understanding of Casson non-Newtonian fluid boundary layer flow. Design/methodology/approach The governing mathematical equations that explain the flow and heat and mass transport phenomena for fluid domains include the Navier−Stokes equation, the thermal energy equation and the solutal concentration equations. The governing equations are expressed as partial differential equations, which are then converted into a suitable set of non-linear ordinary differential equations by using the necessary similarity variables. The ordinary differential equations are computed by combining the shooting operation with the three-stage Lobatto BVP4c technique. Findings Graphs and tables are used in the process of analysing the characteristics of velocity distributions, temperature profiles and solutal curves at varying values of the parameters, along with friction drag, heat transfer rate and Sherwood number. It has been revealed that the radial and axial velocities decrease when the Casson parameter value increases and that the rate of heat transmission is higher in hybrid nanofluids with nanoparticles in the shape of a blade. The increase in Brownian motion and thermophoresis parameters causes a rise in the temperature profile. Also, an increase in the activation energy parameter improves the solutal curve. The use of nanoparticles was shown to improve extrusion properties, the rotary heat process and biofuel generation. Originality/value All results are presented graphically and all physical quantities are computed and tabulated. The current results are compared to previous investigations and found to agree significantly with them.

A computation analysis with heat and mass transfer for micropolar nanofluid in ciliated microchannel: With application in the ductus efferentes

Inherited heat enhancement capabilities and their significance in the field of medical sciences and industry make nanofluids the focus of research nowadays. Furthermore, due to the remarkable advancements in bionanotechnology and its significance in biomedical fields such as drug delivery systems, cancer tumor therapy, bioimaging, and many others, it has emerged as a key research area. Contribution of cilia for the flow in ductus efferentes of human male reproductive tract is elaborated. A novel mathematical scheme is presented for the heat and mass transfer of MHD micropolar nanofluid transport in an asymmetric channel lined with cilia. The pertinent equations of nanofluid transport are exposed to lubrication approximation theory and solution for the physical problem is examined with efficient bvp4c technique in MATLAB. Fluid rheology is explored with the variations of different transport parameters like Hartmann number, Grashof number, Brownian motion, buoyancy, thermophoresis and Darcy number. It is reported that nanofluid transport is affected with rise in the Lorentz force and show reverse behavior with rising permeability. The temperature of the nanofluid in ciliated microchannel is raised with enhanced value of Hartmann number, Grashof number, Prandtl number, and Darcy number while diffusion phenomenon of nanofluid is slowed down with these parameters. Spinning motion of the nanofluid is enhanced with Grashof number and slow down with nanoparticle Grashof number and different behavior is recorded for Darcy and viscosity parameters in different flow regime. Reported investigation presents crucial findings for ciliary transport of micropolar nanofluid and tackled with appropriate selection of micropolar parameter, Brownian motion parameter, thermophoresis and Grashof number. Moreover, this investigation will be handful for cilia-based actuators which work as micro-mixers in controlling the flow in minute bio-sensors and may prove their worth in micro-pumps employed in various drug-delivery systems.

Exploring convective entropy optimization and activation energy impact on magneto-nanofluid flow over a vertical stretched plate with Hall current and nonlinear thermal radiation using SQLM

This paper investigates the profound impact of entropy generation and activation energy on the dynamics of hydromagnetic nanofluids, focusing on nonlinear thermal radiation, viscous and Ohmic dissipation, and Hall current effects over a linear stretching sheet. Various nanoparticles are incorporated into the nanofluid formulation using the thermophoresis and Brownian motion model. Through similarity transformation, the system of nonlinear equations is solved with high precision using the Spectral Quasilinearization Method (SQLM). Comprehensive analyses of velocity, cross-flow velocity, temperature, concentration, and entropy generation profiles are conducted for numerous physical parameters. Results indicate that velocity and cross-flow velocity increase with the Hall parameter while temperature and concentration profiles decrease. Both the velocity and cross-flow velocity profiles enhance for mixed convection parameters closer to the sheet, whereas the temperature and concentration profiles exhibit the contrary tendency. Prandtl number diminishes the profiles of horizontal velocity, cross-flow velocity and concentration distributions. Temperature distribution profile hikes for both the Brownian motion parameter and thermophoresis parameter. The activation energy parameter enhances the cross-flow velocity, with a corresponding decline in temperature distribution and a similar trend is observed in the concentration profile. Further, entropy generation profiles increase with higher Brinkman and Reynolds numbers while exhibiting mixed tendencies with the Schmidt number. These findings reveal that Hall current introduces complex interactions within the nanofluid flow, significantly influencing thermal, concentration, and entropy generation characteristics, particularly in magnetic fields and activation energy.

Non-similar approach for enhanced heat and mass transfer in nanofluid using Keller box algorithm

The nanofluids provide various benefits over pure fluids in heat and mass transport applications; hence, their research is crucial. For instance, they can increase heat transfer rate by enhancing the fluid’s thermal conductivity and may enhance mass transfer rate by changing the surface characteristics. Furthermore, nanofluids are being demonstrated to effectively diminish pressure drops in exchangers for heat, which can lower energy consumption and operating expenses. In the existing literature, the majority of the theoretical studies considered self-similar flows. However, there are certain actual flow situations that do not allow for a self-similar solution. The current study considers such of those situations where the non-similarity of the transport phenomena is unavoidable. The non-similarity of the present problem is caused by the consideration of thermophoretic diffusion or the contribution of viscous dissipation when the wall temperature follows a power-law form. For a pure fluid, the same problem admits a self-similar solution in the absence of viscous dissipation effects. In this problem, the non-similarity is caused by the nature of the thermal transport process and not because of the momentum transport. Therefore, the consideration of viscous dissipation in the boundary layer of nanofluid is an interesting aspect to explore the behavior of thermal and mass transport phenomena. Moreover, the current analysis intends to investigate the transport enhancement in a non-similar flow of a nanofluid by utilizing the Buongiorno model. In the current nonsimilar modeling, possibilities for the existence of a self-similar solution are also highlighted. An implicit finite-difference numerical scheme, the Keller-Box method, is utilized. The problem involves several physical parameters of interest, such as the Eckert number, Lewis number, Brownian motion parameter, and thermophoresis parameter, whose potential impact on the non-similar nature of the problem and on thermal enhancement is analyzed and quantified.

Effect of thin film thickness of ferrofluid on inclined bioconvective flow

This research examines the effect of variable thin film thickness on the bioconvective ferrofluid flow through a rotating sloped surface when a magnetic field (dipole) is present. Similarity transformation is used to standardize the current model's governing equations. By using a finite element method, the normalized nonlinear differential equations are numerically solved. Variable thickness of ferrofluid thin film and bioconvective parameters (bioconvective Lewis number, bioconvective Peclet number, and micro-organism concentration difference) yield the following results: velocity profiles (radial, tangential, and axial), gravity flow (drainage velocity and induced velocity), temperature profile, concentration profile and microorganism profile. In addition, this investigation examines the density of moving microorganisms as well as local heat and mass transport. The temperature, concentration, radial, axial, drainage, induced, and motile microbe velocity are all improved with increasing film thickness. Variable thickness increases local heat transfer whereas increasing Brownian motion and thermophoresis parameters decreases it. This study could be helpful for self-sterilizing applications and biomedical engineering.

Multilayer deep-learning intelligent computing for the numerical analysis of unsteady heat and mass transfer in MHD Carreau Nanofluid model

The objective of this article is to investigate the mechanism of unsteady heat and mass transfer (HMT) in a magnetohydrodynamics Carreau nanofluid flow (MHD-CNFF). To accomplish this, we utilized a novel artificial intelligence-based (AI) method, deep learning predictive technique combined with Levenberg-Marquardt scheme (DLPT-LMS). The similarity transformation is applied to convert the partial differential equations (PDEs) into a set of non-linear ordinary differential equations (ODEs). We numerically solved these resulting ODEs using the Adam numerical approach in sophisticated “Mathematica” software. The influence of Brownian motion parameter, thermophoresis parameters, Prandtl number, Lewis number, and mass transfer parameters on the temperature, velocity, and concentration profile is analyzed using a synthetic dataset. This evaluation is conducted across different variation of MHD-CNFF by leveraging DLPT-LMS. The absolute error (AE) across various iteration of MHD-CNFF demonstrated a progressive drop, indicating the accuracy of DLPT-LMS. The outcomes of this investigation revealed that the AE ranged from 10-3 to 10-8 which shows a minimum error between actual and predicted value. Additionally, the MSE confirmed the accuracy of proposed DLPT-LMS in predicting the behavior of velocity, temperature, and concentration profiles, with lower values showing better predictions. The model accuracy was reinforced by performance results, including regression analysis and error histograms. Error values gradually decreased during training, validation, and testing phases, exhibiting a robust convergence and indicating the highly reliability of AI-based algorithm for investigating intricate fluid dynamics in MHD-CNFF systems.

Integrated neural network based simulation of thermo solutal radiative double-diffusive convection of ternary hybrid nanofluid flow in an inclined annulus with thermophoretic particle deposition

Numerical simulation of magnetohydrodynamic radiative double-diffusive convective heat and mass transfer of a ternary hybrid nanofluid with thermophoretic particle deposition in an inclined annulus is studied. Both sides of cylinders are preserved at uniform temperatures, while the remaining sides are thermally insulated. The coupled nonlinear partial differential equations are solved using a finite difference approach. The detailed computational results of heat and mass transfer rate, temperature, concentration and flow fields are presented and discussed for a distinct range of significant physical parameters. The results demonstrated that increasing the angle of the inclination factor increases fluid flow. In light of buoyancy, when the annular cavity is set downward, the enhanced shear velocity is transported upwards, where it reaches its optimal temperature. The higher temperature difference leads to augmented dynamic fluid motion, particularly in the radial direction, as the system seeks to balance the thermal energy through convective transfer. The Brownian motion parameter has abrupt mobility of nanoparticles in liquid, which promotes particle collisions with liquid molecules, yielding kinetic energy. Increased values of thermophoretic parameters augment the thermophoresis force. Thermophoretic particle deposition increases the concentration of nanoparticles in an annulus due to the migration of particles from hot to cold regions under the influence of temperature gradient. The heat and mass transfer characteristics of ternary hybrid nanofluid are forecasted through an artificial neural network-based Levenberg–Marquardt backpropagated algorithm. The built model shows the heat and mass transfer rate root mean squared values through the Levenberg–Marquardt algorithm as one and mean squared error values as 1e-07 and 1e-08 respectively.

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 mathematical model of Casson nanofluid flow over a vertically stretched porous surface along with bioconvection, Joule heating and thermal Robin conditions

The current analysis aims is to investigate the steady-state visco-plastic Casson nanofluid flow over an electrically conducting stretching porous surface. Thermophoresis and Brownian motion parameters are utilized for modeling and analysis. Also, Joule heating, thermal radiation, thermal robin condition, thermo-solutal stratifications, and viscous dissipation are considered for energy and nanoparticle concentration. Using appropriate similarity transformation, the partial differential equations (PDEs) system is altered into ordinary differential equatons (ODEs). The Homotopy analysis method (HAM) is used for solving governing equations. The effect of distinct physical parameters on the velocity, concentration, temperature, and microorganism’s density is revealed graphically and discussed tabularly. Additionally, numerical analysis is conducted on designed Nusselt number, Sherwood number, skin friction, and motile microorganism’s density. The major finding of the study is that the fluid velocity decreases as both the magnetic parameter and Casson fluid parameter increases. Instead, increasing the values of the Deborah number and activation energy results in an increase in fluid temperature. The current study is useful for coating deposition of magnetic nanomaterials at comparatively higher temperatures.

Numerical modeling of thermophoresis and Brownian with heat transfer in shear-rate-dependent fluid: The finite element simulations

This article discusses the simultaneous influence of thermophoresis, Brownian motion, and the dispersion of nanoparticles on thermal enhancement in non-Newtonian fluid existing over a surface stretching with non-uniform velocity. The modeled problems describing the transport of heat by the fluid are boundary value problems and are solved by the finite element method (FEM). The mesh-free analysis is done and accuracy is checked. The numerical solutions are computed and used for depicting flow field behaviors. It is visualized that Cu− Prandtl fluid and Cu−Al2O3− Prandtl fluid flow are affected in opposing ways by Prandtl and elastic factors. As a result, momentum in the Newtonian fluid does not penetrate as quickly as that does in Prandtl fluid. The Brownian motion parameter is responsible for a decrease in the Nusselt number whereas the thermophoresis parameter causes a decrease in the Sherwood number. Thus, it is essential to note that the wall heat transfer rate in the fluid can be enhanced by making arrangements to reduce Brownian motion. Similarly, wall mass flux can be controlled through the thermophoresis parameter. Nusselt and Sherwood number has shown an increasing tendency when the Prandtl parameter is increased. Thus, fluids with higher Prandtl fluid parameters are suitable for higher wall heat and mass fluxes. The temperature of mono and hybrid nano-Prandtl fluids is increased by caused by thermophoresis and Brownian motion.

Comparative numerical study featuring magnetized nanofluids configured by elongating sheet with thermophoresis and Brownian motion

This study investigates the heat and mass transfer characteristics of MHD rotating Fe₃O₄-Al₂O₃/H₂O hybrid nanofluid flow over a three-dimensional stretching surface. Comparative analysis was conducted among the base fluid H₂O, Al₂O₃-H₂O nanofluid, and Fe₃O₄-Al₂O₃/H₂O hybrid nanofluid, focusing on velocity, temperature, and concentration distributions influenced by thermophoresis, Brownian motion, Hall current, temperature ratio, magnetic parameter, rotation, and thermal radiation. The governing nonlinear partial differential equations were transformed into ordinary differential equations using similarity adaptations and solved numerically with the BVP-5C method in MATLAB. Results indicate that increasing the thermophoresis and Brownian motion parameters elevates the temperature profile while affecting the concentration distribution differently. The hybrid nanofluid exhibited a higher temperature distribution compared to the nanofluid and base fluid, whereas the base fluid showed a greater concentration gradient.

Buongiorno’s radiative Prandtl-Eyring nanofluid flow through porous medium over a stretching surface with cross-diffusion effects

The main focus of the current analysis is to describe the thermo-magnetic flow, heat and mass transport features of two-dimensional dissipative Prandtl-Eyring nanofluid (PE-NF) flow over a stretching sheet under the influence of porous medium and magnetic Ohmic dissipation numerically. An innovative Buongiorno’s nanofluid model in terms of Brownian motion and thermophoresis is deployed to accurately simulate the nano behavior in Prandtl-Eyring within the boundary layer regime. The thermal radiation and heat source/sink effects are also included to describe the thermal transport process. In addition to this, the thermo-diffusion and diffusion-thermo effect are included to demonstrate the temperature and concentration diffusion mechanism under the presence of chemical reaction process. The emerged coupled nonlinear two-dimensional time-independent partial differential equations are rendered to their dimensionless form through appropriate similarity transformations and solved by deploying Matlab-based BVP4C technique. The graphical visualization showed that, the increasing magnetic number diminished the flow field and enhanced the temperature and concentration profiles in the flow regime. Rising porous parameter decayed the Prandtl-Eyring nanofluid velocity. Increasing radiation and Eckert numbers enhance the temperature field in the flow regime. Magnifying Prandtl-Eyring parameter suppressed the velocity diffusion. Increasing Brownian motion and thermophoresis parameters increases the temperature profile. Amplifying Soret parameter upsurges the concentration profile. Skin-friction coefficient amplified with enhanced magnetic and porous numbers. Heat transfer rate acts as increasing function of thermophoresis and Brownian motion parameters. The main objective of this study is the addition of magnetic Ohmic dissipation, radiation, porous medium, thermal source/sink, Soret and Dufour effects and Buongiorno nanofluid model and this consideration generalizes former studies and gives a new re-defined mathematical formulation of heat and mass transport features of Prandtl-Eyring nanofluid flow over a stretching sheet. Finally, the numerical accuracy of the current similarity results is validated with available solutions and noticed a good agreement.

Diffusion-thermo and thermo-diffusion impacts on MHD natural convection flow of maxwell nanofluids over a stretching sheet

The present study carried out significant importance in its magnetic field and crosswise diffusion influenced the Maxwell nanofluid flow past a nonlinear stretching sheet. This investigation aimed to shed light on the behavior of critical parameters, particularly in the presence of thermophoresis and Brownian motion. The primary aim is to investigate the impact of thermal diffusion, diffusion-thermo, and various influencing factors on a Maxwell nanofluid near a stretching sheet in the magnetic field, and the impact of three distinct slip conditions (velocity, thermal, and solutal). The partial differential equations by the nonlinear coefficients are utilized in obtaining the most important equations. These equations are distorting to beneficial nonlinear ordinary differential equations making use of the appropriate transformations variables and transformation coefficients. To investigating the computational solutions for the reducing sets of the nonlinear ordinary differential equations, these were developing and utilized the Keller box methodology. The simulations are carried out the nanofluids velocity, temperature, concentration, skin friction coefficients, the rate of temperature transport, in addition to the rate of mass transportation, amongst previous variables. The validations of this methodology are displayed via the comparison of the present outputs through the preceding judgments into the literatures. The major conclusions drawn from this study are the concentration profiles exhibited opposing behaviours as concentration slip parameter increased. However, the temperature profile increases for Brownian motion parameter and thermophoresis parameter parameters. Secondly, concentration displayed an increasing behavior as the Soret number increased.