Three-dimensional flow of Powell–Eyring nanofluid with heat and mass flux boundary conditions

This article investigates the three-dimensional flow of Powell–Eyring nanofluid with thermophoresis and Brownian motion effects. The energy equation is considered in the presence of thermal radiation. The heat and mass flux conditions are taken into account. Mathematical formulation is carried out through the boundary layer approach. The governing partial differential equations are transformed into the nonlinear ordinary differential equations through suitable variables. The resulting nonlinear ordinary differential equations have been solved for the series solutions. Effects of emerging physical parameters on the temperature and nanoparticles concentration are plotted and discussed. Numerical values of local Nusselt and Sherwood numbers are computed and examined.     

Thermo-bioconvection transport of nanofluid over an inclined stretching cylinder with Cattaneo–Christov double-diffusion

In this paper, Newtonian nanofluid flow is observed under the effects of the magnetic field, activation energy and motile microorganisms over an inclined stretchable cylinder. The magnificent aspects of nanoliquid are demonstrated by enduring the Brownian motion and thermophoresis diffusion features.Nonlinear higher order partial differential equations are transformed into first-order ordinary differential equations with suitable similarity variables. The attained sets of governing equations are then cracked by bvp4 c procedure in MATLAB mathematical software. The numerical and graphical outcomes of controlling parameters such as Prandtl number, mixed convection, activation energy, thermophoresis,Brownian parameter, Biot number, Lewis number, Peclet number and motile concentration parameter against the velocity, temperature, volumetric concentration and motile concentration of nanoparticles of the fluid are discussed. The velocity is enhanced with the growth valuation in mixed convection and decay by rising variation of buoyancy ratio parameter, magnetic parameter and bio-convective Rayleigh parameter. The evolution in motile microorganisms is due to the increasing values of microorganisms Biot number. The presented data can be helpful in enhancement of manufacturing processes, biomolecules, extrusion systems applications and energy production improvement.     

Entropy generation applications in flow of viscoelastic nanofluid past a lubricated disk in presence of nonlinear thermal radiation and Joule heating

Entropy generation is the loss of energy in thermodynamical systems due to resistive forces,diffusion processes, radiation effects and chemical reactions. The main aim of this research is to address entropy generation due to magnetic field, nonlinear thermal radiation, viscous dissipation, thermal diffusion and nonlinear chemical reaction in the transport of viscoelastic fluid in the vicinity of a stagnation point over a lubricated disk. The conservation laws of mass and momentum along with the first law of thermodynamics and Fick's law are used to discuss the flow, heat and mass transfer, while the second law of thermodynamics is used to analyze the entropy and irreversibility. The numbers of independent variables in the modeled set of nonlinear partial differential equations are reduced using similarity variables and the resulting system is numerically approximated using the Keller box method. The effects of thermophoresis,Brownian motion and the magnetic parameter on temperature are presented for lubricated and rough disks. The local Nusselt and Sherwood numbers are documented for both linear and nonlinear thermal radiation and lubricated and rough disks. Graphical representations of the entropy generation number and Bejan number for various parameters are also shown for lubricated and rough disks. The concentration of nanoparticles at the lubricated surface reduces with the magnetic parameter and Brownian motion. The entropy generation declines for thermophoresis diffusion and Brownian motion when lubrication effects are dominant. It is concluded that both entropy generation and the magnitude of the Bejan number increase in the presence of slip. The current results present many applications in the lubrication phenomenon,heating processes, cooling of devices, thermal engineering, energy production, extrusion processes etc.     

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.     

Axisymmetric Stagnation-Point Flow of Nanofluid over a Stretching Surface

This paper investigates the laminar boundary layer flow of nanofluid induced by a radially stretching sheet. Nanofluid model exhibiting Brownian motion and thermophoresis is used. Series solutions for a reduced system of nonlinear ordinary differential equations are obtained by homotopy analysis method (HAM). Comparative study between the HAM solutions and previously published numerical results shows an excellent agreement. Velocity, temperature and mass fraction are displayed for various values of parameters. The local skin friction coefficient, the local Nusselt number and the local Sherwood number are computed. It is observed that the presence of nanoparticles enhances the thermal conductivity of base fluid. It is found that the convective heat transfer coefficient (Nusselt number) is decreased with an increase in concentration of nanoparticles whereas Sherwood number increases when concentration of nanoparticles in the base fluid is increased.     

Numerical study of the onset of chemical reaction and heat source on dissipative MHD stagnation point flow of Casson nanofluid over a nonlinear stretching sheet with velocity slip and convective boundary conditions

The magnetohydrodynamic (MHD) stagnation point flow of Casson nanofluid over a nonlinear stretching sheet in the presence of velocity slip and convective boundary condition is examined. In this analysis, various effects such as velocity ratio, viscous dissipation, heat generation/absorption and chemical reaction are accentuated. Possessions of Brownian motion and thermophoresis are also depicted in this study. A uniform magnetic field as well as suction is taken into account. Suitable similarity transformations are availed to convert the governing nonlinear partial differential equations to a system of nonlinear ordinary differential equations and then series solutions are secured using a homotopy analysis method (HAM). Notable accuracy of the present results has been obtained with the earlier results. Impact of distinct parameters on velocity, temperature, concentration, skin friction coefficient,Nusselt number and Sherwood number is canvassed through graphs and tabular forms.     

Influence of thermophoresis on heat and mass transfer under non-Darcy MHD mixed convection along a vertical flat plate embedded in a porous medium in the presence of radiation

The paper presents an investigation of the influence of thermophoresis on MHD mixed convective heat and mass transfer of a viscous, incompressible and electrically conducting fluid along a vertical flat plate with radiation effects. The plate is permeable and embedded in a porous medium. To describe the deviation from the Darcy model the Forchheimer flow model is used. The Rosseland approximation is used to describe the radiative heat flux in the energy equation. The governing partial differential equations are transformed into a system of ordinary differential equations using similarity transformation. The nonlinear ordinary differential equations are linearized by using quasilinearization technique and then solved numerically by using implicit finite difference scheme. The numerical results are analyzed for the effects of various physical parameters such as magnetic parameter Ha, mixed convection parameter Ra _d /Pe _d , Reynolds number Red, radiation parameter R, thermophoretic parameter τ, Prandtl number Pr, and Schmidt number Sc. The heat transfer coefficient is also tabulated for different values of physical parameters.     

Impact of nanoparticles and radiative heat flux in von Kármán swirling flow of Maxwell fluid

In this paper, the classical von Kármán swirling flow problem due to a rotating disk is modeled and studied for the rate type Maxwell nanofluid together with heat and mass transfer mechanisms. The model under consideration predicts the relaxation time characteristics. The novel aspects of thermophoresis and Brownian motion features due to nanoparticles are investigated by employing an innovative Buongiorno’s model. The analysis further explores the impact of linear Rosseland radiation on heat transfer characteristics. The concept of boundary layer approximations is utilized to formulate the basic governing equations of Maxwell fluid. The dimensionless form of a system of ordinary differential equations is obtained through similarity approach adopted by von Kármán. The system of equations is integrated numerically in domain [0,∞) by using bvp midrich scheme in Maple software. The obtained results intimate that higher rotation raises the radial and angular velocity components. The nano-particles concentration enhances with Brownian motion parameter. Further, the heat transfer rate at the disk surface diminishes with thermophoresis parameter. The achieved numerical computations of velocity profiles, friction coefficient and Nusselt number are matched in limiting cases with previously published literature and an outstanding agreement is observed.     

Transient thin film flow of nonlinear radiative Maxwell nanofluid over a rotating disk

In this letter, a mathematical model for transient nature thin film flow of Maxwell nanofluid over a rotating disk is studied in the presence of a uniform magnetic field and non-linear thermal radiation. The Brownian motion and thermophoresis features due to nanofluid are captured by adopting the Buongiorno model. The prime emphasize is to explore the temperature field and nanoparticles volume fraction in nanofluid thin film flow. The reduced system of differential equations is solved numerically by finite difference based method namely bvp4c. The numerical outcomes regarding film thickness, Nusselt number, Sherwood number, velocity, temperature, and concentration are revealed for varying estimation of involved physical parameters. It is shown that the film thickness decreases with increasing values of the magnetic number. Further, the impact of thermophoresis and thermal radiation parameters is worthwhile in enhancing the fluid temperature. The Solute concentration is found to decrease with Brownian motion and Schmidt number.     

Upshot of Chemical Species and Nonlinear Thermal Radiation on Oldroyd-B Nanofluid Flow Past a Bi-directional Stretched Surface with Heat Generation/Absorption in a Porous Media

A three-dimensional mathematical model is developed to examine the flow of nonlinear thermal radiation Oldroyd-B nanofluid past a bidirectional linearly stretched surface in a porous medium. The flow is induced by temperature dependent thermal conductivity, chemical reaction and convective heat and mass conditions. Novel characteristics of Brownian motion and thermophoresis are accompanied by magnetohydrodynamic and heat generation/absorption.Self-similar transformations are employed to convert the system of nonlinear partial differential equations to a system of ordinary differential equations with high nonlinearity and are solved by strong analytic technique named as Homotopy Analysis method(HAM). Effects of varied arising parameters on involved distributions are reflected through graphical illustrations. From this study, it is perceived that strong magnetic field hinders the fluid's motion and leads to rise in temperature that eventually lowers heat transfer rate from the surface. Further, decrease in heat transfer rate is also observed for enhanced values of thermal radiation parameter. To validate our results, a comparison with already published paper in limiting case is also given and results are found in excellent oncurrence; hence reliable results are being presented.     

Upshot of Chemical Species and Nonlinear Thermal Radiation on Oldroyd-B Nanofluid Flow Past a Bi-directional Stretched Surface with Heat Generation/Absorption ina Porous Media

A three-dimensional mathematical model is developed to examine the flow of nonlinear thermal radiation Oldroyd-B nanofluid past a bidirectional linearly stretched surface in a porous medium. The flow is induced by temperature dependent thermal conductivity, chemical reaction and convective heat and mass conditions. Novel characteristics of Brownian motion and thermophoresis are accompanied by magnetohydrodynamic and heat generation/absorption. Self-similar transformations are employed to convert the system of nonlinear partial differential equations to a system of ordinary differential equations with high nonlinearity and are solved by strong analytic technique named as Homotopy Analysis method (HAM). Effects of varied arising parameters on involved distributions are reflected through graphical illustrations. From this study, it is perceived that strong magnetic field hinders the fluid's motion and leads to rise in temperature that eventually lowers heat transfer rate from the surface. Further, decrease in heat transfer rate is also observed for enhanced values of thermal radiation parameter. To validate our results, a comparison with already published paper in limiting case is also given and results are found in excellent oncurrence; hence reliable results are being presented.     

Effects of Thermal Radiation on a 3D Sisko Fluid over a Porous Medium Using Cattaneo-Christov Heat Flux Model

This paper investigates the three-dimensional flow of a Sisko fluid over a bidirectional stretching sheet, in a porous medium. By using the effect of Cattaneo-Christov heat flux model, heat transfer analysis is illustrated. Using similarity transformation the governing partial differential equations are transferred into a system of ordinary differential equations that are solved numerically by applying Nachtsheim-Swigert shooting iteration technique along with the 6-th order Runge-Kutta integration scheme. The effect of various physical parameters such as Sisko fluid, ratio parameter, thermal conductivity, porous medium, radiation parameter, Brownian motion, thermophoresis, Prandtl number, and Lewis number are graphically represented.     

Effects of Thermal Radiation on a 3D Sisko Fluid over a Porous Medium Using Cattaneo-Christov Heat Flux Model

This paper investigates the three-dimensional flow of a Sisko fluid over a bidirectional stretching sheet, in a porous medium. By using the effect of Cattaneo-Christov heat flux model, heat transfer analysis is illustrated. Using similarity transformation the governing partial differential equations are transferred into a system of ordinary differential equations that are solved numerically by applying Nachtsheim-Swigert shooting iteration technique along with the 6-th order Runge-Kutta integration scheme. The effect of various physical parameters such as Sisko fluid, ratio parameter,thermal conductivity, porous medium, radiation parameter, Brownian motion, thermophoresis, Prandtl number, and Lewis number are graphically represented.     

Significance of power average of sinusoidal and non-sinusoidal periodic excitations in nonlinear non-autonomous system

The steady laminar boundary layer flow of Carreau nanofluid over a stretching sheet is investigated. Effects of Brownian motion and thermophoresis are present. Heat transfer is characterized using convective boundary condition at the sheet. The governing partial differential equations are reduced into a set of nonlinear ordinary differential equations through suitable transformations. Results of velocity, temperature and concentration fields are computed via homotopic procedure. Numerical values of skin-friction coefficient, local Nusselt and Sherwood numbers are computed and discussed. A comparative study with existing solutions in a limiting sense is made.     

Unsteady boundary layer flow of a nanofluid over a stretching sheet with variable fluid properties in the presence of thermal radiation

In this paper, we investigated numerically an unsteady boundary layer flow of a nanofluid over a stretching sheet in the presence of thermal radiation with variable fluid properties. Using a set of suitable similarity transformations, the governing partial differential equations are reduced into a set of nonlinear ordinary differential equations. System of the nonlinear ordinary differential equations are then solved by the Keller-box method. The physical parameters taken into consideration for the present study are: Prandtl number Pr, Lewis number Le, Brownian motion parameter N _b, thermophoresis parameter N _t, radiation parameter N _r, unsteady parameter M. In addition to these parameters, two more new parameters namely variable thermophoretic diffusion coefficient parameter e and variable Brownian motion diffusion coefficient parameter β have been introduced in the present study. Effects of these parameters on temperature, volume fraction of the nanoparticles, surface heat and mass transfer rates are presented graphically and discussed briefly. To validate our method, we have compared the present results with some previously reported results in the literature. The results are found to be in a very good agreement.     

Boundary layer flow and heat transfer of a nanofluid over a permeable unsteady stretching sheet with viscous dissipation

A numerical study of the boundary layer flow past unsteady stretching surface in nanofluid under the effects of suction and viscous dissipation is investigated. The model used for the nanofluid incorporates the effects of Brownian motion and thermophoresis. A similarity solution is presented, which depends on the unsteadiness parameter A, Eckert number Ec, ζ suction or injection parameter, Prandtl number Pr, Lewis number Le, Brownian motion number Nb, and thermophoresis number Nt. The governing partial differential equations were converted to nonlinear ordinary differential equations by using a suitable similarity transformation, which are solved numerically using the Nactsheim-Swigert shooting technique together with Runge-Kutta six-order iteration scheme. The accuracy of the numerical method is tested by performing various comparisons with the previously published work, and the results are found to be in excellent agreement. Numerical results are presented both in tabular and graphical forms illustrating the effects of these parameters on thermal and nanoparticle volume fraction boundary layers. The thermal boundary layer thickens with a rise in the local temperature as the Brownianmotion, thermophoresis, and convective heating each intensify.     

Double-diffusive radiative magnetic mixed convective slip flow with Biot and Richardson number effects

This paper investigates combined heat and mass transfer by mixed magneto-convective flow of an electrically conducting flow along a moving radiating vertical flat plate with hydrodynamic slip and thermal convective boundary conditions. The governing transport equations are converted into a system of coupled nonlinear ordinary differential equations with prescribed boundary conditions using similarity variables developed by Lie group theory. The transformed nondimensional boundary value problem is then solved numerically with MAPLE13 quadrature. Excellent correlation with previous nonmagnetic, no-slip studies is achieved. Surface shear stress function and local Nusselt number (heat transfer gradient at the wall) are increased with Richardson number, whereas local Sherwood number is found to initially decrease then subsequently increase. The “thermally thick” scenario (Biot number > 0.1) is investigated and increasing Biot number is observed to enhance shear stress function (skin friction), local Nusselt number, and local Sherwood number. Increasing thermal radiation flux increases thermal boundary layer thickness as does increasing the magnetic field effect. Increasing hydrodynamic slip parameter reduces skin friction but enhances local Nusselt and Sherwood numbers. The study has applications in high-temperature polymeric synthesis and magnetic field flow control.     

Modern development on the features of magnetic field and heat sink/source in Maxwell nanofluid subject to convective heat transport

Nanofluids are forthcoming new generation heat transfer fluids, which have been scrutinized precisely, in current years. Thermophysical assets of these fluids have noteworthy impact on their heat transfer features. In this current investigation a mathematical relation for two dimensional (2D) flow of magnetite Maxwell nanofluid influenced by a stretched cylinder is established. To visualize the stimulus of Brownian moment and thermophoresis phenomena on Maxwell fluid Buongiorno's relation has been considered. Moreover, heat sink/source and convective condition are also presented for heat transport mechanism. The homotopic scheme has been developed for the solutions of nonlinear ordinary differential equations (ODEs). The achieved outcomes are planned and consulted in aspects for somatic parameters. It is noteworthy that the velocity of Maxwell fluid display conflicting performance for curvature parameter and Deborah number. It is also reported that the liquid velocity decays for magnetic parameter, whereas the nanoliquid temperature and concentration field enhance for magnetic parameter. Furthermore, the liquid temperature intensifies for the progressive values of thermophoresis parameter and Brownian motion. Additionally, endorsement of current significances is organized via benchmarking with earlier famous limiting situations and we pledge a marvelous communication with these outcomes.