Zero Mass Flux Research Articles

Analysis of thermally stratified flow of Sutterby nanofluid with zero mass flux condition

In this attempt, we scrutinize the effects of Sutterby nanoliquid flow deformed by a linearly stretchable sheet. Inclined magnetic field is included to explore the features of electrically conducting fluid. Thermal stratification phenomenon is implemented over a horizontal sheet to elaborate the features of heat transfer. Variable fluid feature is also accounted. Zero mass flux condition is incorporated along with Brownian diffusion and thermophoresis phenomenon Using the suitable transformations, the system of partial differential equations are transmuted into coupled system of ordinary differential equations. Approximate analytical solutions are computed via homotopic approach. Graphical behavior of applicable parameters on temperature, velocity, and concentration fields are illustrated and elaborated. Skin friction coefficient and Nusselt number are computed and analyzed. It is found that increase in fluid parameter declines the velocity field whereas temperature field rises for higher thermal conductivity parameter. Heat transfer rate decays for thermal stratification phenomenon. The current attempt is incorporated in diverse processes of industry and engineering including cooling and heating processes in solar water heater, building insulation, electronics, turbines, transportation, power generation, geothermal systems, and engines. Moreover, Sutterby model predicts the characteristics of pseudo-plastic and dilatant fluids. This model is very useful for high polymer solutions and polymer melts which are important industrial materials. Owing by such applications, the present examination has been established.

Hydromagnetic Carreau Nanoliquid in Frames of Dissipation and Activation Energy

The novel characteristics of magnetic field and entropy generation in mixed convective flow of Carreau fluid towards a stretched surface are investigated. Buongiornio nanoliquid model consists of thermophoresis and Brownian movement aspects is opted for analysis. Energy expression is modeled subject to thermal radiation and viscous dissipation phenomenon. Concentration by zero mass flux condition is implemented. Consideration of chemical reaction and activation energy characterizes the mass transfer mechanism. Total entropy generation rate and Bejan number is formulated. The utilization of transformation variables reduces the PDEs into non-linear ODEs. The obtained nonlinear complex problems are computed numerically through Shooting scheme. The impact of involved variables like local Weissenberg number, magnetic parameter, thermal radiation parameter, Brownian motion parameter, thermophoresis parameter, buoyancy ratio parameter, mixed convection parameter, Prandtl parameter, Eckert number, Schmidt number, non-dimensional activation energy parameter, chemical reaction parameter, Brinkman number, dimensionless concentration ratio variable, diffusive variable and dimensionless temperature ratio variable on velocity, temperature, nanoparticles concentration, entropy generation, Bejan number, surface drag force and heat transfer rate are examined through graphs and tables.

Heat transfer and buoyancy‐driven convective MHD flow of nanofluids impinging over a thin needle moving in a parallel stream influenced by Prandtl number

AbstractThe current study focuses on investigating the influence of transverse magnetic field, variable viscosity, buoyancy, variable Prandtl number, viscous dissipation, Joulian dissipation, and heat generation on the flow of nanofluids over thin needle moving in parallel stream. The theory of nanofluids that includes the Buongiorno model featured by slip mechanism, such as Brownian motion and thermophoresis, has been implemented. Further, convective boundary condition and zero mass flux condition are considered. The nondimensionally developed boundary layer equations have been solved by Runge–Kutta–Fehlberg method with shooting technique for different values of parameters. The most relevant outcomes of the present study are that the augmented magnetic field strength, viscosity parameter, buoyancy ratio parameter, and the size of the needle undermine the flow velocity, establishing thicker velocity boundary layer while Richardson number and Brownian motion show opposite trend. Another most important outcome is that increase in the size of the needle, viscous dissipation, convective heating, and heat generation upsurges the fluid temperature, leading to improvement in thermal boundary layer. The effects of different natural parameters on wall shear stress and heat and mass transfer rates have been discussed.

Entropy generation analysis in flow of thixotropic nanofluid

Purpose The purpose of this paper is to address entropy generation in flow of thixotropic nonlinear radiative nanoliquid over a variable stretching surface with impacts of inclined magnetic field, Joule heating, viscous dissipation, heat source/sink and chemical reaction. Characteristics of nanofluid are described by Brownian motion and thermophoresis effect. At surface of the sheet zero mass flux and convective boundary condition are considered. Design/methodology/approach Considered flow problem is mathematically modeled and the governing system of partial differential equations is transformed into ordinary ones by using suitable transformation. The transformed ordinary differential equations system is figure out by homotopy algorithm. Outcomes of pertinent flow variables on entropy generation, skin friction, concentration, temperature, velocity, Bejan, Sherwood and Nusselts numbers are examined in graphs. Major outcomes are concluded in final section. Findings Velocity profile increased versus higher estimation of material and wall thickness parameter while it decays through larger Hartmann number. Furthermore, skin friction coefficient upsurges subject to higher values of Hartmann number and magnitude of skin friction coefficient decays via materials parameters. Thermal field is an increasing function of Hartmann number, radiation parameter, thermophoresis parameter and Eckert number. Originality/value The authors have discussed entropy generation in flow of thixotropic nanofluid over a variable thicked surface. No such consideration is yet published in the literature.

Insight into the dynamics of ferrohydrodynamic (FHD) and magnetohydrodynamic (MHD) nanofluids inside a hexagonal cavity in the presence of a non-uniform magnetic field

The ferrohydrodynamic (FHD) and magnetohydrodynamic (MHD) are two important effects of a magnetic field in a liquid. FHD is the results of Kelvin force while MHD is the effect of a magnetic field due to Lorentz force. The present study aimed to evaluate the heat and mass transfer behavior of nanofluids inside a hexagonal enclosure in the presence of a non-uniform magnetic field considering the effects of Ferro-hydrodynamic (FHD) and Magneto-hydrodynamic (MHD). First, the concentration gradient of nanoparticles was captured due to the nanoscale forces. Then, the governing equations, including the continuity of nanofluid and nanoparticles, and momentum for vertical and horizontal direction were introduced, along with energy equation. Besides, the practical boundary condition of zero mass flux in nanoparticles at the walls was employed. Further, the governing equations were transformed into their non-dimensional form and solved numerically by the Finite Element Method (FEM). Furthermore, a systematic grid check was performed, and the results were compared with those of previous studies. Increasing magnetic number (Mnf) results in an increase in the heat and mass transfer rate. Increasing Lorentz force, in the form of Hartmann number (Ha) leads to a decrease in the rate of heat and mass transfer.

Effects of chemical reaction and activation energy on a Carreau nanoliquid past a permeable surface under zero mass flux conditions

Arrhenius condition has been broadly utilized as a model of the temperature impact on the rate compound responses and organic procedure. Hence, our aim of this article is to examine the effects of chemical reaction and activation energy on a Carreau nanoliquid in a permeable surface. For thermal and mass transport curiosities, the cumulative upgrade of convective type condition and zero mass transition have been considered. The overseeing sets of partial differential equations are rendered into coupled nonlinear ordinary differential equations. The arrangement of the subsequent ordinary differential equations is acquired with the assistance of the Runge-Kutta-Fehlberg-fourth-fifth order (RKF-45) procedure. The influence of relevant parameters and physical quantities is investigated. The results show that the presence of reaction rate and energy activation term decelerates the temperature and concentration gradients.

Numerical modeling and analysis of non-Newtonian nanofluid featuring activation energy

In this article, activation energy impact in magneto-mixed convective flow of Eyring Powell nanofluid towards a stretched surface is addressed. Nanofluid features are discussed through Brownian motion and thermophoresis effect. Heat transport characteristics are scrutinized through non-linear radiative heat flux and heat source/sink. Furthermore, activation energy and Joule heating effect are also implemented. Zero mass flux condition is imposed at the sheet surface. Appropriate transformations are utilized to reduce the non-linear expressions to ordinary one. Shooting technique is implemented to compute the computational results of non-linear ODEs’ system. Salient attributes of mixed convection parameter, buoyancy ratio parameter, Prandtl number, thermal radiation parameter, Brownian motion parameter, Schmidt number, thermophoresis and Eckert number on velocity, temperature, concentration, surface drag force, and heat transfer rate are examined through graphs and tables. It is scrutinized that nanoparticle volume fraction is reduced via larger Schmidt number while increases when activation energy is incremented.

Time-dependent 3D flow of Maxwell nanofluid due to an unsteady stretching surface through porous space

In the present paper, we investigated unsteady three-dimensional flow of an incompressible magneto Maxwell nanomaterial in the porous medium. The cause of flow is unsteady stretching of sheet in transverse lateral directions taking zero mass flux of nanoparticles. The developed system of partial differential equations is transformed into nonlinear ordinary differential equations by similarity variables, and the obtained system is solved for dimensionless temperature and nanoparticles concentration by homotopy analysis method. The behavior of physical parameters on the temperature and nanoparticles concentrations is examined through graphs and tabular data. The temperature distribution at the surface is also computed and analyzed and noticed that both the temperature and nanomaterial are reduced for higher values of unsteadiness parameter.

Analysis of entropy generation for MHD flow of third grade nanofluid over a nonlinear stretching surface embedded in a porous medium

The main focus of present research work is to elaborate magnetohydrodynamic flow of third grade nanofluid with activation energy and binary chemical reaction. Fluid flow is generated by a nonlinearly stretched surface. Temperature and nano-concentration distributions are analyzed in the presence of Brownian motion and thermophoresis effects. The effects of Joule heating, thermal radiation and porous medium are further investigated for current analysis. Thermodynamic second mechanism is utilized to explore entropy generation rate of the system. Newly developed condition having zero mass flux of nanoparticles at the boundary is also incorporated. Partial differential equations governing the flow problem has been converted into ordinary ones using appropriate similarity variables. Builtin Shooting technique via NDsolve has been used to construct the numerical solution of the resulting problem. Impacts of various physical flow parameters are presented graphically for temperature, nano-concentration, surface drag coefficient and rates of heat trasnfer and entropy generation. It is found that impacts of third grade parameters on the thermal and nano-concentration fields are quite similar. Temperature, concentration and associated layer thicknesses are reduced via higher third grade parameters. It is established that the magnetic field restricts the flow strongly and serves as a potent control mechanism. It can be concluded that an applied magnetic field will play a major role in applications like micropumps, actuators and biomedical sensors. The activation energy aspect reduces the concentration boundary layer thickness. Total entropy of the entire system increases against higher values temperature difference variable, Brinkman number, porosity parameter, radiation parameter and magnetic parameter.

A rheological analysis of nanofluid subjected to melting heat transport characteristics

This work focuses on the characteristics of heat sink–source and melting phenomena for time-dependent Falkner–Skan flow of Cross nanofluid. Additionally, stagnation point flow features are accounted. Modeling is based on thermophoresis diffusion and Brownian moment slip mechanisms. Zero mass flux condition is used at stretchable surface. Compact form of cross fluid equations are converted to component form by employing boundary layer concept. Appropriate transformations are engaged to give rise ODEs. Moreover, system of ODEs is tackled numerically. Detailed discussion for velocity, temperature, concentration, local Nusselt and Sherwood numbers is presented through graphs. Obtained statistical data reveals that velocity of cross nanoliquid boosts for larger melting and velocity ratio parameters. Intensification in Schmidt number corresponds to rise in concentration distribution.

Computational analysis of entropy generation for cross-nanofluid flow

This research work is made to demonstrate diverse characteristics of entropy generation minimization for cross nanomaterial towards a stretched surface in the presence of Lorentz’s forces. Transportation of heat is analyzed through Joule heating and radiation. Nanoliquid model consists of activation energy and Brownian movement aspects. Concentration of cross material is scrutinized by implementing zero mass flux condition. Bejan number and entropy generation (EG) rate are formulated. The employment of transformation variables reduces the PDEs into nonlinear ODEs. Bvp4c scheme is implemented to compute the computational results of nonlinear system. Velocity, temperature, and concentration are conducted for cross nanomaterial. Consequences of current physical model are presented through graphical data and in tabular form. The outcomes for Bejan number and EG rates are presented through graphical data. It is noted that EG rates and Bejan number significantly affect rate of heat-mass transport mechanisms. In addition, graphical analysis reveals that E.G. rate has diminishing trend for diffusive variable. Moreover, achieved data reveal that profiles of Bejan number boost for augmented values of radiation parameter.

Zero mass flux characteristics in Jeffery nanoliquid flow by a non-linear stretchable surface with variable thickness

This attempt featuring the Brownian movement and thermophoretic aspects in two-dimension through non-linearly stretchable surface. Disturbance to the flow is produced by transverse applied magnetic field. Flow governing system is transformed into non-linear system of ODE’s via suitable transformation. Due to appearance of highly nonlinear terms, series solution is carried out via well-known method known as Homotopy Analysis Method (HAM) which easily tackles the non-linear system of ODE’s. The finding indicates the sheet (shapes) depend on the value of parameter n and observed that in case of non-linear stretching, velocity decreases while temperature rises for larger values of n. This is because the liquid has stronger thermal conductivity. The effects of various intensity parameters are studied graphically and compared numerically.

Consequences of activation energy and binary chemical reaction for 3D flow of Cross-nanofluid with radiative heat transfer

In view of ecological concern and energy security, execution of refrigeration system should be enriched which can be done by improving the characteristics of working liquids. The nanoliquids have gained interest in industrial and engineering fields due to their outstanding thermophysical features. Researchers used nanoliquids as working liquid and detected substantial variations in thermal performance. In the present research work, our intention is to explore the impact of nonlinear thermal radiation and variable thermal conductivity on 3D flow of cross-nanofluid. Moreover, heat sink–source, chemical processes and activation energy are implemented. Zero mass flux relation with thermophoresis and Brownian motion mechanisms are scrutinized. The required system of ordinary ones is achieved by implementing appropriate transformations. The achieved system of ordinary ones is computed numerically by implementing bvp4c scheme. Graphs are plotted to explore the impact of various physical parameters on concentration, temperature and velocity fields. It is detected from obtained graphical data that thermophoresis and Brownian motion mechanisms significantly affect heat transport mechanism. Furthermore, graphical analysis reveals that concentration of cross-nanofluid enhances for augmented values of activation energy.

EMHD time-dependant tangent hyperbolic nanofluid flow by a convective heated Riga plate with chemical reaction

The present exploration addresses the boundary layer electro-magnetohydrodynamic (EMHD) flow of time-dependant non-Newtonian tangent hyperbolic nanofluid that is electrically conducting past a Riga surface with variable thickness and slip boundary condition. Configuration flow modeling is deduced considering chemical reaction and heat generation/absorption with the impacts of Brownian motion and thermophoresis. Also a newly proposed boundary condition with zero mass flux has been presented in the current contribution. Numerical solution of the governing non-linear differential equations is presented by considering the shooting technique. Graphical illustrations pointing out the aspects of distinct physical parameters on the non-Newtonian nanofluid velocity, temperature and concentration fields are introduced. From the computational results, the concentration distribution gives a decreasing function of the chemical reaction and Brownian motion parameters. Higher values of shape parameter yield a negative influence on the mechanical properties of the surface. The Hartmann number leads to maximize both of velocity field and skin friction coefficient. Additionally, numerical computed values of the skin friction, local Nusselt and Sherwood numbers are depicted with the needful discussion.

Consequences of nanoparticle diameter and solid–liquid interfacial layer on the SWCNT/EO nanofluid flow over various shaped thin slendering needles

In this research article, we have discussed about the boundary layer flow of single walled CNT– engine oil nanofluid over three distinct nonlinearly slendering isothermal thin needles of cone, paraboloid and cylinder shapes with zero mass flux at boundary condition. We have considered the effects of diameter of SWCNT and solid–liquid interfacial layer in the thermal conductivity model of the nanofluid. We also combined single phase and double phase model to construct our model. Then after some transformations the governing equations are solved numerically and staged the effects of diameter of SWCNT and nanolayer on the characteristics of the flow through proper graphs and charts. Here, we observed that the presence of the SWCNT decreases both temperature and heat flow in the system. Also we established that cone shaped needle is the most affected by the material parameters of consideration.

Nonlinear radiation effect on MHD Carreau nanofluid flow over a radially stretching surface with zero mass flux at the surface

A mathematical model is envisaged to study the axisymmetric steady magnetohydrodynamic (MHD) Carreau nanofluid flow under the influence of nonlinear thermal radiation and chemical reaction past a radially stretched surface. Impact of heat generation/absorption with newly introduced zero mass flux condition of nanoparticles at the sheet is an added feature towards novelty of the problem. Further, for nanofluid the most recently organized model namely Buongiorno’s model is assumed that comprises the effects thermophoresis and Brownian motion. Utilizing suitable self-similar transformations, the set of partial differential equations with high nonlinearity are converted into a dimensionless system of ordinary differential equations. Set of these transmuted equations are numerically solved by MATLAB built-in function bvp4c. Impact of germane parameters on all involved profiles are plotted to examine the heat and mass transfer characteristics. This study reveals that the temperature distribution is an escalating function of the heat generation and nonlinear radiation parameters. Also, it is noted that the incrementing values of chemical reaction parameter lowers the nanoparticles concentration profile. A comparison of the present investigation with already published explorations in limiting case is also added to authenticate the presented results; hence reliable results are being presented.

Numerical Simulation for Magneto Nanofluid Flow Through a Porous Space with Melting Heat Transfer

Melting heat transfer and non-Darcy porous medium effects in MHD stagnation point flow toward a stretching surface of variable thickness are addressed. Brownian motion and thermophoresis in nanofluid modeling are retained. Zero mass flux condition for concentration at surface is imposed. The problem of ordinary differential system are analyzed numerically through shooting technique. Graphically results of various physical variables on the velocity, temperature and concentration are studied. Skin friction coefficient local Nusselt number and Sherwood number are also addressed through tabulated values. The results described here illustrate that the velocity field is higher via larger melting parameter. However reverse situation is examined for Hartman number. Moreover the influence of thermophoresis parameter on temperature and concentration is noted similar.

Characteristics of buoyancy force on stagnation point flow with magneto-nanoparticles and zero mass flux condition

Abstract This attempt dedicated to the solution of buoyancy effect over a stretching sheet in existence of MHD stagnation point flow with convective boundary conditions. Thermophoresis and Brownian motion aspects are included. Incompressible fluid is electrically conducted in the presence of varying magnetic field. Boundary layer analysis is used to develop the mathematical formulation. Zero mass flux condition is considered at the boundary. Non-linear ordinary differential system of equations is constructed by means of proper transformations. Interval of convergence via numerical data and plots are developed. Characteristics of involved variables on the velocity, temperature and concentration distributions are sketched and discussed. Features of correlated parameters on C f and Nu are examined by means of tables. It is found that buoyancy ratio and magnetic parameters increase and reduce the velocity field. Further opposite feature is noticed for higher values of thermophoresis and Brownian motion parameters on concentration distribution.

Radiative Williamson nanofluid flow over a convectively heated Riga plate with chemical reaction-A numerical approach

This exploration studies the effects of chemical reaction and thermal radiation on the flow of a Williamson nanofluid over a convectively heated Riga plate with variable thickness. Mathematical modeling is developed considering heat generation/absorption with the effects of Brownian motion, thermophoresis and a slip condition. A newly suggested zero mass flux condition has also been introduced in the present study. Numerical solution of the non-linear differential equations is achieved by employing the shooting method. Graphical illustrations depicting the effects of the sundry parameters on the velocity, temperature and concentration fields are also presented. Numerically calculated values of the skin friction, local Nusselt and Sherwood numbers with the requisite discussion are also presented. It is seen that the concentration profile is a decreasing function of the chemical reaction and Brownian motion parameters.

MHD stagnation point flow of micro nanofluid towards a shrinking sheet with convective and zero mass flux conditions

AbstractIn this article the stagnation point flow of electrically conducting micro nanofluid towards a shrinking sheet, considering a chemical reaction of first order is investigated. Involvement of magnetic field occurs in the momentum equation, whereas the energy and concentrations equations incorporated the influence of thermophoresis and Brownian motion. Convective boundary condition on temperature and zero mass flux condition on concentration are implemented. Partial differential equations are converted into the ordinary ones using suitable variables. The numerical technique is utilized to discuss the results for velocity, microrotation, temperature, and concentration fields.