Zero Mass Flux Research Articles

Numerical analysis of mathematical model of nanofluid flow through stagnation point involving thermal radiation, activation energy, and living organisms

In a stagnation point flow, the rate at which heat transfers in fluid containing nanoparticles across a sheet that is stretchable on a surface having pores has been investigated in this research. Magnetohydrodynamic viscous nanofluid flow is considered that is subjected to Brownian movements and the thermophoresis effect. By utilizing a numerical technique, the characteristics of heat transmission in nanofluids are investigated. The model is based on momentum, energy, and concentration equations. To explain the flow model’s physical significance, zero mass flux condition has been employed at the surface. Nonlinear partial differential equations are transformed into a collection of linked ordinary differential equations via similarity transformations. Convergent implications of nonlinear systems are produced by MATLAB software’s built-in bvp4c algorithm. To indicate the physical importance, a thorough examination of relevant characteristics, such as heat sink/source, porosity, and magnetic parameter is conducted. We have observed the behavior of profiles by fixing the numerical values of the involving parameters as 0.1 ≤ λ ≤ 2.0, 0.1 ≤ Nr ≤ 3.0, 0.1 ≤ R ≤ 0.4, 0.1 ≤ M ≤ 0.4, 0.1 ≤ Rb ≤ 1.5, and 0.1 ≤ Nb ≤ 0.7. The temperature rises yet the rate at which heat transfers at the surface declines due to the increased far-field velocity. The greater nanoparticles concentration at the far field relative to the surface is related to the zero mass flux condition.

Lie symmetry analysis on heat and mass transport aspects of rate type fluid flow with waste discharge concentration: Keller Box approach

The present analysis examines the effect of thermal radiation on the stream of Maxwell liquid past a stretchy surface in the presence of a zero-mass flux condition. The effect of waste discharge concentration, thermophoresis-Brownian motion, and porous media on the fluid motion is also considered. Investigation of the liquid flow with waste discharge concentration in stretched sheets may lead to the growth of effective methods for disposing of waste and preventing pollution. Due to their extensive applicability, the mechanisms of flow and heat transmission in the context of thermal radiation play a crucial role in research and industry. This phenomenon often occurs in spacecraft, nuclear reactor cooling, power production, aerospace technologies, combustion applications, gas turbines, hypersonic flights, and high-temperature processes. The modelled governing partial differential equations (PDEs) are converted into dimensionless ordinary differential equations (ODEs) utilizing appropriate similarity variables. Further, the Keller–Box approach is utilized to solve the resultant ODEs numerically. The influence of several parameters on the temperature, concentration and velocity profiles is shown via graphic representations. The intensification in Deborah’s number and porous parameter values declines the velocity profile. As the values of the radiation, thermophoresis, and Brownian motion parameters increase, the thermal profile increases. The concentration profile increases as the pollutant external source parameter value upsurges.

Numerical study of an electrically conducting nanofluid flow past a vertical stretching Riga plate

The heat and mass transfer through electrically conducting and mixed convective nanofluid flow across an elongating Riga plate is studied. Riga plate is an electromagnetic sheet, in which electrodes are assembled alternatively. The arrangement of Riga plate produces electromagnetic behavior in the fluid flow. In the current analysis, the influence of Arrhenius activation energy, viscous dissipation and heat source/sink over the surface of Riga sheet is considered. The heat and mass transfer are examined by convective boundary conditions and nanoparticles (NPs) zero-mass flux. The Brownian motion and thermophoretic diffusion of fluid molecules are applied via Buongiorno's approach. Von Karman's similarity approach is implemented to reset the modeled equations into the dimensionless form of ordinary differential equations (ODEs). The system of ordinary differential equations is solved numerically via PCM (parametric continuation method). The fluid velocity, temperature field, and concentration gradients are analyzed by varying various flow parameters and graphically portrayed. The numerical results are validated by comparing them with the published studies. It can be resolved form the results that the flow rate decilnes with the effect of power index m, whereas enhances with the consequence of Hartmann number. The significance of thermophoresis term augments the temperature curve of the fluid.

Active control of transonic airfoil flutter using synthetic jets through deep reinforcement learning

This paper presents a novel framework for the active control of transonic airfoil flutter using synthetic jets through deep reinforcement learning (DRL). The research, conducted in a wide range of Mach numbers and flutter velocities, involves an elastically mounted airfoil with two degrees of freedom of pitching and plunging oscillations, subjected to transonic flow conditions at varying Mach numbers. Synthetic jets with zero-mass flux are strategically placed on the airfoil's upper and lower surfaces. This fluid–structure interaction (FSI) problem is treated as the learning environment and is addressed by using the arbitrary Lagrangian–Eulerian lattice Boltzmann flux solver (ALE-LBFS) coupled with a structural solver on dynamic meshes. DRL strategies with proximal policy optimization agents are introduced and trained, based on the velocities probed around the airfoil and the dynamic responses of the structure. The results demonstrate that the pitching and plunging motions of the airfoil in the limited cycle oscillation (LCO) can be effectively alleviated across an extended range of Mach numbers and critical flutter velocities beyond the initial training conditions for control onset. Furthermore, the aerodynamic performance of the airfoil is also enhanced, with an increase in lift coefficient and a reduction in drag coefficient. Even in previously unseen environments with higher flutter velocities, the present strategy is achievable satisfactory control results, including an extended flutter boundary and a reduction in the transonic dip phenomenon. This work underscores the potential of DRL in addressing complex flow control challenges and highlights its potential to expedite the application of DRL in transonic flutter control for aeronautical applications.

A comparative analysis on the dynamics of solid-liquid interfacial layer and nanoparticle diameter of magnetohydrodynamic nanofluid flow containing spherical and cylindrical-shaped alumina nanoparticles over a stretching curved surface

In this work, a comparative analysis on magnetohydrodynamic nanofluid flow containing spherical and cylindrical-shaped alumina nanoparticles over a stretching curved surface is mainly focused. The effects of Brownian motion, Joule heating, thermophoresis, chemical reaction and activation energy are taken into consideration in this work. It is important to mention that this analysis considers a 4 % volume fraction of the alumina nanoparticles. A thermal convective and zero-mass flux conditions are imposed to scrutinize the heat transfer analysis. The leading equations are transformed into dimensionless form by using suitable similarity variables. A numerical solution is obtained using the shooting technique. The acquired outcomes depict that greater magnetic factor enhances the skin friction coefficient. The greater magnetic factor, thermal Biot number, Eckert number, and interfacial layer thickness augment the heat transfer rate, while a greater nanoparticle diameter diminishes the thermal transfer rate. A higher magnetic factor has an increasing impact on thermal distribution and a reducing impact on velocity distribution. A greater curvature factor enhances both the velocity and thermal distributions. The concentration distribution is enhanced by the higher interfacial layer thickness and activation energy factor, while it is reduced by a higher nanoparticle diameter, Brownian motion factor, and chemical reaction factor. From the comparative analysis, it is found that the velocity, thermal, and concentration distributions are higher for the cylindrical-shaped nanoparticles compared to spherical-shaped nanoparticles.

Numerical simulation of two‐phase flow towards a stagnation point in the Jeffrey nanofluid across a porous deformable disc with zero mass flux condition and Lorentz forces

AbstractThere have been a lot of claims made in the literature recently regarding the physical characteristics of nanofluids in different flow systems, especially the laminar flow regimes. The goal of this study is to investigate the two‐dimensional laminar flow of Jeffrey liquid that describes the characteristics of heat and mass transfer towards a stagnation point over a radial moving disc through the Buongiorno nanofluid model. The study also aims to investigate the impact of mass transpiration velocity, magnetic field, and zero mass flux incorporated in a Jeffrey fluid. The study reduces complicated partial differential equations to a collection of ordinary differential equations using the similarity transformation, which makes it easier to compute dual numerical solutions using the bvp4c solver. A particular value of the shrinking parameter yields dual solutions. The findings of the current research demonstrate that the suction constraint amplifies the friction factor phenomenon in the second solution, while in the first solution, an annulment tendency is noted. Additionally, the first solution exhibits a monotonic behavior whereas the second solution shows a fall in both the friction factor and the rate of heat transfer by increasing the Deborah number. Finally, the results of this analysis with the available data matched the limiting situations very well.

Unsteady Inclined MHD Powell-Eyring Fluid with Microorganisms Over an Inclined Permeable Stretching Sheet with Zero Mass Flux and Slip Condition

Unsteady Inclined MHD Powell-Eyring Fluid with Microorganisms Over an Inclined Permeable Stretching Sheet with Zero Mass Flux and Slip Condition

Enhancement of Heat and Mass Transfer in 2D-Mixed Convection Nano-Liquid Flow Over a Flexible Riga Plate with Heat Source/Sink and Chemical Reaction

This study delves into the complex dynamics of two-dimensional (2D) hydro-magnetic nano-fluidic flow over an elastic Riga plate, aiming to elucidate the interactions among thermal energy, concentration transfer, pressure gradient, and convective & zero mass flux at the boundary. Notably, the investigation incorporates concentration and temperature buoyancy forces, integrating them into the analysis with a comprehensive energy transfer equation and essential nanofluid properties in the species concentration. Further, the internal heat source/sink and rate of first order chemical reaction are considered. Employing the advanced capabilities of MATHEMATICA12 software, the study applies the Optimal Homotopy Analysis Method (OHAM), reducing the governing equations partially to ordinary ones. Furthermore, the study reveals intriguing patterns, highlighting the significant impact of the modified Hartmann number on velocity and concentration gradients, while displaying contrasting effects on thermal profiles. Moreover, the dual nature of pressure gradient behavior underscores the complexity of the studied phenomenon, offering valuable insights for further research and practical applications in nano-fluidic systems.

Numerical analysis of the flow dynamics in Maxwell hybrid nanofluid flow with gyrotactic microorganisms over a permeable stretching surface with convective and zero-mass flux conditions: A comparative analysis

This study observes the 2-D flow of a Maxwell hybrid nanofluid flow on a permeable stretching surface containing Cu and CuO nanoparticles and gyrotactic microorganisms. The thermal convective and zero-mass flux constraints are adopted by incorporating a hot working fluid with a heat transfer coefficient and zero mass flow at the permeable sheet’s surface to investigate the heat transfer rate. This study is designed to present a comparative analysis of the nanofluid (Cu–water) as well as hybrid nanofluid (Cu–CuO/water) flows on a stretching sheet. Examining activation energy in water-based hybrid nanofluid flow offers important insights into the kinetics of chemical reactions, which in turn helps to optimize the features of the nanofluid and build more effective systems that use nanofluids for a variety of applications. The problem formulated initially is converted to dimension-free notation using appropriate variables for finding the numerical solution by incorporating the bvp4c MATLAB function. From the obtained results, it is found that the higher magnetic and porosity factors have declined the velocity profiles. Also, in the absence of porous media and magnetic field effects, the velocity distribution is highly affected when compared with the existence of these effects. It is observed that the velocity profiles of both nanofluids are dominant for Newtonian fluid in comparison to non-Newtonian fluid. Also, the thermal profiles of both nanofluids are dominant for non-Newtonian fluid in comparison to Newtonian fluid. The friction force of hybrid nanofluid is significantly influenced by the magnetic factor, porosity factor, and volume fractions of the solid nanoparticles when compared to nanofluid.

A numerical investigation of the magnetized water-based hybrid nanofluid flow over an extending sheet with a convective condition: Active and passive controls of nanoparticles

Abstract This study presents a numerical investigation of a viscous and incompressible three-dimensional flow of hybrid nanofluid composed of Ag and Al2O3 nanoparticles over a convectively heated bi-directional extending sheet with a porous medium. The main equations are converted into dimensionless form by using appropriate variables. The effects of magnetic field, porosity, Brownian motion, thermophoresis, and chemical reaction are investigated. Furthermore, the mass flux and zero-mass flux constraints are used to study heat and mass transfer rates. The obtained data show that the growing magnetic factor has reduced the velocity profiles while increasing the thermal profile. The increased porosity factor has decreased the velocity profiles. The increased thermal Biot number has increased the concentration and thermal profiles. When compared to passive control of nanoparticles, the hybrid nanofluid flow profiles are strongly influenced by the embedded factor in the active control of nanoparticles.

Two-phase numerical simulation of thermal and solutal transport of zero mass flux conditions over a porous deformable disc: The extension of Jeffrey-Hamel model

In recent times, numerous assertions on the thermophysical properties of nanoliquids in various flow regimes, particularly the laminar flow regimes have been documented in the literature. With this focus, this theoretical investigation is to explore multiple solutions of the laminar two-dimensional Jeffrey fluid describing the Buongiorno nanofluid model and features of heat transport near a stagnation point across a movable radial disc. Also, the study seeks to explore the effects of zero mass flux and velocity of mass transpiration embedded within a Jeffrey fluid. With the help of the ansatz similarity transformations, the study simplifies complex partial differential equations into a set of ordinary differential equations, facilitating numerical dual solutions employing the bvp4c solver. The multiple solutions become apparent in a specific range of the shrinkable parameter. The results of the present study show that the suction parameter intensifies the phenomena of friction factor in the upper solution, whereas an annulment trend is observed in the lower solution. In addition, the shear stress and heat transfer rate decline with higher impacts of the Deborah number for the first solution while a monotonical behaviour is seen for the second solution. Besides, the absolute critical value decreases owing to the change value of the Deborah number, as a result, the separation of the boundary layer accelerates. Moreover, the heat transfer rate declined by about 0.29%, 0.37%, and 0.28% for the FBS and 0.30%, 0.32%, and 0.28% for the SBS with larger values of Nta, Nba and Sca, respectively. Lastly, the outcomes of the present examination with existing data are an excellent match for the limiting cases.

Exploring double-diffusive nanofluid flow in divergent/convergent nondarcy porous space: A machine learning numerical approach with zero mass flux

In this study, authors address the problem of analyzing the Jeffrey–Hamel nanofluid flow within a nonparallel channel under the influence of a thermally balanced non-Darcy permeable medium. Our objective is to explore the behavior of the nanofluid, employing the Buongiorno nanofluid model, and considering factors such as zero mass flux conditions, variable rheological fluid properties, and the presence of temperature jump phenomena through ANN-PSO-NNA. To tackle this intricate issue, propose a novel approach using Artificial Neural Networks (ANN) integrated with particle swarm optimization (PSO) hybrid with neural network algorithm (NNA). This combined technique is referred to as ANN-PSO-NNA. The governing flow equations based on the Jeffrey–Hamel analysis are first transformed into dimensionless forms. To establish the efficacy of our approach compare it with the widely used NDSolve method. Furthermore, the study presents the absolute error analysis for four distinct cases offering a quantitative assessment of the accuracy of ANN-PSO-NNA. The absolute error between the NDsolve and the proposed ANN-PSO-NNA is given for four different cases, ranging from 1.95E-06 to 1.18E-08. The biases and weights obtained through proposed method range from −10 to 10. This enables us to gauge the performance of the ANN-PSO-NNA minimum values of the fitness function 2.37E-08, 2.30E-08, 3.92E-08, and 1.22E-08 from multiple independent runs, which are showcased to be convergent, underscoring the robustness of the ANN-PSO-NNA approach. Employing graphical representations, explores the influence of various parameters on the velocity and temperature profiles. Our integrated approach offers a comprehensive understanding of the underlying dynamics, paving the way for optimized designs and enhanced efficiency across these diverse engineering applications.

Electrically conducting mixed convective nanofluid flow past a nonlinearly slender Riga plate subjected to viscous dissipation and activation energy

This paper reports the mass and energy transmission characteristics of an electrically conducting mixed convective nanofluid flow past a stretching Riga plate. An additional effect of viscous dissipation, Arrhenius activation energy and heat source is also studied. The energy and mass transmissions are evaluated by a zero-mass flux of nanoparticle and convective boundary conditions. Buongiorno’s relations are proposed for the Brownian motion and thermophoretic diffusion. The similarity substitutions are employed to derive the non-dimensional set of modeled equations. The obtained set of equations is numerically processed via parametric continuation method (PCM). Several flow factors affecting the velocity, energy, and mass distributions are graphically discussed. It has been perceived that the fluid velocity field declines with the influence of velocity power index (m), while improves with the upshot of modified Hartmann number (Q). The effect of Schmidt number and chemical reaction diminishes the concentration profile [Formula: see text]. Furthermore, the energy curve enhances with the effect of thermophoresis factor, Biot and Eckert number.

Distinctive approach for MHD natural bioconvection flow of Reiner–Rivlin nano-liquid due to an isothermal sphere

The analysis of heat excess through non-Newtonian fluid is noticed proper and promising arena for biomedical technological applications than Newtonian liquid. Herein, a type of non-Newtonian (Reiner–Rivlin) nanomaterial has been scrutinized with gyrotactic microorganisms around an isothermal sphere with surface of zero mass flux. Being mindful of that the model of Buongiorno’s nanofluid is utilized. Non-dimensional formulas for the basic dimensional partial differential equation system are obtained using appropriate non-similarity transformations. MATLAB function bvp4c code is adopted to get the non-similar solutions. The computations disclosed that the velocity of Reiner–Rivlin nanofluid and its gradient accelerate away from the surface of sphere to infinity and reduces in proximity to the sphere surface for higher values of Reiner–Rivlin factor K. The rate of surface density transport, rate of surface heat transport, and gradient of velocity diminish as the stream wise coordinate boosts. As the problem is subjected to special circumstances, there is a remarkable agreement between the acquired and prior numerical calculations resulting from the comparison.

Entropy generation analysis on zero mass flux effects of nonlinear mixed convective Williamson nanofluid flow with christov-Cattaneo heat flux

Entropy generation analysis on zero mass flux effects of nonlinear mixed convective Williamson nanofluid flow with christov-Cattaneo heat flux

Chemically reactive aspects of stagnation-point boundary layer flow of second-grade nanofluid over an exponentially stretching surface

Assessing the stagnation-point flow of a second-grade nanofluid with an induced magnetic field and the effects of Joule heating toward an exponentially extending surface is the leading goal of the current effort. The modeling of the thermal and solute energy equations has taken into account nonlinear thermal radiation as well as the impact of activation energy. The boundary of the sheet is subjected to the zero-mass flux and thermal slip boundary conditions. The simulated flow equations are converted into coupled nonlinear ODEs (ordinary differential equations) using similarity variables. The BVP4C MATLAB technique is used to numerically resolve these ODEs. Graphs and tabular data are used to perform the physical debate. The importance of a greater estimation of the magnetic Prandtl number and magnetic parameter is emphasized in order to obtain a better induced magnetic field profile. Additionally, the greater estimations of the second-order fluid parameter increase the rates of friction and heat transmission.

Significance of Variability in Liquid Properties on 3D MHD Maxwell Nanofluid Flows Over a Stretching Surface with Heat Generation/Absorption and Chemical Reaction

Objective of the current research investigation is linked with advancement in nanotechnology and fluids flow phenomena subject to various fluid models. The model adopted over here is Maxwell–nanofluid model subject to magnetohydrodynamics impact confined within the dimensions of a bi-directional stretching surface. The boundary is assumed to be convective in the context of thermal state and zero mass flux in the context of nanoparticles. Furthermore, slip condition on velocity and a source of heat generation/absorption is also considered in the flow model. It is pertinent to mention that base fluid is assumed to be chemically reactive by involving first order chemical reaction term in the governing equation of concentration of nanoparticles. So formulated, highly nonlinear set of governing equations is converted into nonlinear ODEs involving various parameters including Brownian diffusion, Deborah number, magnetic parameter, Prandtl and Schmidt number, heat generation/absorption and the first order chemical reaction. The ODEs are solved by a semi-analytic technique of OHAM (Optimal Homotopy Analysis Method). The results are plotted graphically. The obtained findings are compared without available literature in the same direction by assuming special cases on various parameters.

Melting heat effect in MHD flow of maxwell fluid with zero mass flux

This study delves into the investigation of Maxwell fluid flow across a sheet with a particular effort on the melting heat and zero mass flux at the boundary. A Maxwell fluid, characterized by both viscous and elastic responses, plays a pivotal role in various industrial and biological applications. The mathematical model describing Maxwell fluid flow is represented using non-linear momentum and energy equations, incorporating MHD. Similarity transformation is used to change from partial differential equation to ordinary differential equation. The introduction of a phase change term in the energy equation accounts for the melting heat effect at the boundary. The BVP4C solver using MATLAB is hired to numerically answer the system of equations, enabling the determination of the steady-state solution. The solution of this investigation offers valuable insights into the interplay between viscoelasticity and melting heat effects on various flow characteristics, including velocity and temperature profiles. The practical significance of this research is evident in polymer processing, food processing, and materials engineering, where the understanding of Maxwell fluids and their interaction with melting boundaries is essential for process optimization and product quality. So far in the literature survey no one have considered Melting heat effect along with Maxwell fluid. The conclusion for this study is that Melting heat effect increases velocity profile and decreases the temperature profile. This is the main conclusion of this research.

MAGNETOHYDRODYNAMIC TERNARY HYBRID NANOFLUID FLOW OVER A STRETCHING SURFACE SUBJECT TO THERMAL CONVECTIVE AND ZERO MASS FLUX CONDITIONS

Nanoparticles have the capability to augment the thermal conductivity of nanofluids. For the transmission of heat, the material’s low thermal conductivity is the key problem. Therefore, to increase the thermal conductivity, researchers mixed different nanoparticles in the base fluids. In this field of study, utilizing three different particles is the most recent strategy to form a ternary hybrid nanofluid that gives us better results in terms of heat transfer. The interaction of three different kinds of nanoparticles, i.e. copper, alumina and silver, is considered with water serving as the base fluid to form a ternary hybrid nanofluid. The paper explores the behavior of ternary hybrid nanofluids on heat and mass transportation phenomena of the two-dimensional magnetohydrodynamic (MHD) micropolar flow across a porous extending surface with zero mass flux and convective conditions. The Brownian motion, thermal radiation, heat source and sink, and joule heating are taken into consideration in the temperature equation. The chemical reaction is incorporated into the concentration equation. Appropriate similarity transformations are used to transform the system of partial differential equations (PDEs) to a coupled system of ordinary differential equations (ODEs). The homotopy analysis method (HAM) is used to solve the system of the flow equations. The effects of the nanoparticle’s volume fractions and other different physical parameters on the surface drag force, Nusselt number, velocities, microrotation, temperature and concentration profiles are scrutinized through figures and tables. The outcomes of the present investigation show that the heat transfer rate is augmented with the increasing value of thermophoresis parameter. The magnetic field has augmented temperature while the opposite result is seen in velocity and microrotation profiles. With the escalating values of thermophoresis parameter, the concentration and temperature of ternary hybrid nanofluids are boosted while the increasing Brownian and chemical reaction parameters have decreased the concentration profile. The surface friction coefficient exhibited by the ternary hybrid nanofluid is higher than hybrid and conventional nanofluids.

Optimum thermal design for heat and mass transfer of non-Newtonian liquid within converging conduit with thermal jump and zero-mass flux

The performance of heat transfer materials is strongly dependent on physical characteristics such as viscosity, thermal conductivity, and density. Among these, evolving thermal conductivity is a critical element in fluid heat transmission. In general, the poor thermal conductivity of industrial fluids is a significant barrier for heat transfer properties. The problem, however, has been revealed with the emergence of nanoparticles generated by various materials. This effort aims to demonstrate the mass and heat transfer attributes of the Carreau nanofluid through non-parallel channel with zero mass flux and variable thermal conductivity. The Buongiorno nanofluid model introduces the dual diffusion phenomena of nanomaterial. The analysis are carried out after reduction of governing ODE's into first order. The reduced equations are tickled numerically with Rung-Kutta method. The findings demonstrate that the thermal source, Brownian motion and thermal conductivity parameters exhibits a linear ascent on temperature profile, whereas effect of Prandtl number Pr is conflicting. The mass transfer rate is impacted negatively by the mass diffusivity value. The existence of the variables thermal conductivity factor ∈1 and mass diffusivity ∈2 leads to an elevated rate of heat and mass transmission. In the current investigation, a comparison is made for heat and mass transfer performance.