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.     

Effects of Thermal Radiation and Slip Mechanism on Mixed Convection Flow of Williamson Nanofluid Over an Inclined Stretching Cylinder

The current investigation highlights the mixed convection slip flow and radiative heat transport of uniformly electrically conducting Williamson nanofluid yield by an inclined circular cylinder in the presence of Brownian motion and thermophoresis parameter.A Lorentzian magnetic body force model is employed and magnetic induction effects are neglected.The governing equations are reduced to a system of nonlinear ordinary differential equations with associated boundary conditions by applying scaling group transformations.The reduced nonlinear ordinary differential equations are then solved numerically by Runge-Kutta-Fehlberg fifth-order method with shooting technique.The effects of magnetic field,Prandtl number,mixed convection parameter,buoyancy ratio parameter,Brownian motion parameter,thermophoresis parameter,heat generation/absorption parameter,mass transfer parameter,radiation parameter and Schmidt number on the skin friction coefficient and local Nusselt are analyzed and discussed.It is found that the velocity of the fluid decreases with decrease in curvature parameter,whereas it increases with mixed convection parameter.Further,the local Nusselt number decreases with an increase in the radiation parameter.The numerical comparison is also presented with the existing published results and found that the present results are in excellent agreement which also confirms the validity of the present methodology.     

Thermal radiation effects on Williamson fluid flow due to an expanding/contracting cylinder with nanomaterials: Dual solutions

The phenomena of heat and mass transfer during the flow of non-Newtonian transfer are amongst the core subjects in mechanical sciences. Recently, the nanomaterials are among the eminent tools for improving the low thermal conductivity of working fluids. Therefore, in view of the existing contributions, this article presents a two-dimensional numerical simulation for the transient flow of a non-Newtonian nanofluid generated by an expanding/contracting circular cylinder. This critical review further explores the impacts of variable magnetic field, thermal radiation, velocity slip and convective boundary conditions. The basic governing equations for Williamson fluid flow are formulated with the assistance of boundary layer approximations. The non-dimensional form of partially coupled ordinary differential equations has been tackled numerically by utilizing versatile Runge–Kutta integration scheme. The momentum, thermal and concentration characteristics are investigated with respect to several critical parameters, like, Weissenberg number, unsteadiness parameter, viscosity ratio parameter, slip parameter, suction parameter, magnetic parameter, thermophoresis parameter, Brownian motion parameter, Prandtl number, Lewis number and Biot number. The outcomes of the systematic reviews of these parameters and forest plots are illustrated. The study reveals that multiple solutions for the considered problem occurs for diverse values of involved physical parameters. The computed results indicate that the friction and heat transfer coefficients are significantly raised by the magnetic parameter for upper branch solutions.     

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.     

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.     

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.     

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.     

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.     

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.     

Brownian motion and thermophoresis effects on unsteady stagnation point flow of Eyring-Powell nanofluid: a Galerkin approach

This article concerns the analysis of an unsteady stagnation point flow of Eyring-Powell nanofluid over a stretching sheet. The influence of thermophoresis and Brownian motion is also considered in transport equations. The nonlinear ODE set is obtained from the governing nonlinear equations via suitable transformations. The numerical experiments are performed using the Galerkin scheme. A tabular form comparison analysis of outcomes attained via the Galerkin approach and numerical scheme (RK-4) is available to show the credibility of the Galerkin method. The numerical exploration is carried out for various governing parameters, namely, Brownian motion, steadiness, thermophoresis, stretching ratio, velocity slip, concentration slip, thermal slip, and fluid parameters, and Hartmann, Prandtl and Schmidt numbers. The velocity of fluid enhances with an increase in fluid and magnetic parameters for the case of opposing, but the behavior is reversed for assisting cases. The Brownian motion and thermophoresis parameters cause an increase in temperature for both cases (assisting and opposing). The Brownian motion parameter provides a drop-in concentration while an increase is noticed for the thermophoresis parameter. All the outcomes and the behavior of emerging parameters are illustrated graphically. The comparison analysis and graphical plots endorse the appropriateness of the Galerkin method. It is concluded that said method could be extended to other problems of a complex nature.     

Effects of surface roughness on mixed convective nanofluid flow past an exponentially stretching permeable surface

A numerical study is carried out to display the effects of surface roughness on mixed convective nanofluid flow along an exponentially stretching surface in presence of suction/injection. The dimensional coupled nonlinear partial differential equations are transformed into dimensionless form by using suitable non-similar transformations. The resulting equations are solved by utilizing the Quasilinearization technique as well as the implicit finite difference scheme. The influence of several non-dimensional parameters on various profiles and gradients is examined. The results are presented graphically, which are analyzed to depict the effects of various physical parameters, for example, Brownian diffusion parameter Nb, thermophoresis parameter Nt, suction/blowing parameter A and Lewis number Le. In order to analyse the influence of surface roughness on mixed convective nanofluid flow, the major part of this research paper is devoted to investigate the effects of the small parameter α and frequency parameter n over the gradients defined at the wall. The results reveal that an increase in the values of Nb and Nt, enhances the velocity and temperature of the fluid. The increasing value of suction parameter (A > 0) reduces the velocity of the fluid. Further, the increasing values of Nb and Le decrease the nanoparticle volume fraction profile. The sinusoidal variations are observed in the skin-friction coefficient, Nusselt number as well as the nanoparticle Sherwood number. Moreover, with the addition of nanoparticles, the magnitude of the skin-friction coefficient increases, while the magnitude of heat transfer rate decreases, significantly.     

Significance of Stefan blowing effect on flow and heat transfer of Casson nanofluid over a moving thin needle

The current mathematical model explains the influence of non-linear thermal radiation on the Casson liquid flow over a moving thin needle by considering Buongiorno's nanofluid model.The influences of Stefan blowing, Dufour and Soret effects are also considered in the model. The equations which represent the described flow pattern are reduced to ordinary differential equations(ODEs) by using apt similarity transformations and then they are numerically solved with Runge–Kutta-Fehlberg's fourth fifth-order method(RKF-45) with shooting process. The impacts of pertinent parameters on thermal, mass and velocity curves are deliberated graphically.Skin friction, rate of heat and mass transfer are also discussed graphically. Results reveal that, the increase in values of Brownian motion, thermophoresis, Dufour number, heating and radiative parameters improves the heat transfer. The increasing values of the Schmidt number deteriorates the mass transfer but a converse trend is seen for increasing values of the Soret number. Finally,the escalating values of the radiative parameter decays the rate of heat transfer.     

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.     

Heat and mass transfer analysis of time-dependent tangent hyperbolic nanofluid flow past a wedge

The candid intension of this article is to inspect the heat and mass transfer of a magnetohydrodynamic tangent hyperbolic nanofluid. The nanofluid flow has been assumed to be directed by a wedge on its way. In addition, the collective stimulus of the convective heating mode with thermal radiation is inspected. The governing set of PDEs is rendered into that of the coupled nonlinear ODEs. The resulting ordinary differential equations are then solved by the well known shooting technique for two different cases; the flow over a static wedge and flow over a stretching wedge. The impact of intricate physical parameters on the velocity, temperature and concentration profiles is analyzed graphically. It is noticed that the intensifying values of the generalized Biot number, Brownian motion parameter, thermophoresis parameter and Weissenberg number enhances the dimensionless temperature profile.     

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.     

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.     

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.