Two-dimensional Stagnation-point Flow Research Articles

Mixed Convection in a Casson Fluid Flow towards a Heated Shrinking Surface

In this paper, an extensive analysis of mixed convection effects on steady two-dimensional stagnation point flow of a Casson fluid over a heated horizontal sheet has been numerically investigated. The governing Navier-Stokes equations of the present problem are transformed into nonlinear ordinary differential equations by applying a similarity transformation. A numerical solution of the problem has been obtained by employing the linearization technique along with the finite difference discretization. The impact of the Casson fluid parameter, the thermo-radiative parameter, the mixed convection parameter, the slip parameter, and the Prandtl number on the fluid motion and temperature is studied through graphical data. The convection parameter, the slip parameter and the Casson fluid parameter tends to accelerate the flow. The temperature distribution is however reduced by the convection parameter, slip parameter, thermal radiation and the Prandtl number. This work is based on [25] in which micropolar fluid flow over a heated surface was investigated by using the homotopy analysis method. We have extended the problem by considering the combined impact of mixed convection and thermal radiation on the Casson fluid flow towards a heated shrinking sheet, by using a numerical method.

Towards a novel EMHD dissipative stagnation point flow model for radiating copper-based ethylene glycol nanofluids: An unsteady two-dimensional homogeneous second-grade flow case study

A novel EMHD dissipative second-grade nanofluid flow model is proposed exclusively in this numerical inspection for radiating copper-based ethylene glycol nanofluids to reveal the dynamical and thermal aspects of the studied homogeneous mixture during its unsteady two-dimensional stagnation point flow towards a horizontal electromagnetic actuator. Based on admissible physical assumptions and authenticated experimental correlations, the governing PDEs and BCs are derived appropriately for the nanofluid flow problem under consideration. After numerous rearrangements and non-dimensionalization treatments, the resulting ODEs and BCs are handled computationally with the help of a robust GDQ algorithm under the parametric control of several influencing factors, whose strengthening magnitudes affect probably the flow control process and heat transport mechanism. In this context, it proved graphically that the nanoparticles’ loading process exhibits dissimilar dynamical and thermal impacts as compared with the influences of the nanoparticles’ diameter size. Besides, the resistive dynamical effect of the utilized electromagnetic actuator reinforces thermally the enhancing role of the thermal radiative heat flux and Joule’s heating process within the nanofluidic medium.

The significance of Magnetohydrodynamics sutterby nanofluid flow with concentration depending properties across stretching/ shrinking sheet and porosity

In this study, the impact of activation energy and transiting parameters on the two-dimensional stagnation point flow of magnetized Sutterby nanofluid of nano-biofilm incorporating with microorganisms over the porous surface has been examined. Prior research suggests that both the fluid viscosity and thermal conductance are temperature-dependent. Also, the effects of solutal concentration on fluid viscosity, heat capacity and nanofluid properties have been elaborated. In recent years, numerous technical strategies comprising hydromagnetic fluxes and thermal intensification in porosity media, like molding, condenser heat exchanger, liquefied metal filtration, fusion control and nuclear reactor coolant, have been addressed. According to numerous empirical studies, the viscosity and thermal conductivity of the nanoparticles are largely dependent on the intensity of nanoparticles rather than the temperature. The classical RK-4 method with shooting technique has been used. The significance of involving parameters in the domains of heat, velocity, density and concentration has been illustrated. The effect of nondimensional parameters on the skin friction factor, Nusselt number and Sherwood number has been discussed. The nanoparticle density increases with the activating energy effects and thermophoresis factor and rapidly decreases for Lewis number and Brownian factor. The velocity, temperature and concentration profiles increase as the concentration-dependent properties do, but all physical quantities deteriorate for all concentration-varying factors.

MHD convective non-Darcy flow of a nanofluid through a porous stretching sheet with thermal buoyancy and chemical reaction

In this article, magnetohydrodynamic (MHD) the two-dimensional stagnation-point convection flow over a nanofluid through a porous medium due to a solar energy stretching sheet is investigated theoretically. Heat transfer subject to thermal radiation, viscous dissipation, an applied magnetic field, thermal buoyancy, and convective boundary conditions is considered. The governing boundary layer equations are reduced into ordinary differential equations by a similarity transformation. The transformed equations are solved numerically by using an efficient numerical shooting technique with a fourth-fifth order Runge–Kutta method scheme. The effects of the external parameters as jets flow, thermal convective, and mass convective on the flow field and heat transfer characteristics were obtained and discussed. Finally, the results obtained agree with the practical results and applicable in the related fields, especially, medicine, biochemistry, pharmacology, … , etc.

Spline collocation for magnetohydrodynamic stagnation-point flow towards a stretching sheet

Steady two-dimensional stagnation-point flow of an incompressible viscous electrically con– ducting fluid over a flat deformable sheet is investigated when the sheet is stretched in its own plane with a velocity proportional to the distance from the stagnation-point. Using similarity variables, the governing partial differential equations are transformed into a set of non-dimensional ordinary differential equations. These equations are then solved numerically using Spline collocation method. It is shown that the velocity at a point decreases/increases with increase in the magnetic field when the free stream velocity is less/greater than the stretching velocity. Temperature distribution in the flow is obtained when the surface is held at a constant temperature. In the present reported work the effect of magnetic field parameter and Prandtl number on flow have been discussed.

MHD stagnation point flow of nanofluid over a curved stretching/shrinking surface subject to the influence of Joule heating and convective condition

The existing article explores the attributes of convection and Joule heating across a magnetohydrodynamics two-dimensional stagnation point flow of a nano liquid depending on the permeable curved stretching/shrinking surface and mass suction. Applying the non-dimensional variables, the basic model of partial differential equations (PDEs) is converted to the dimensionless ordinary differential equations (ODEs), which are solved through the bvp4c method (bult-in function in MATLAB). Multiple graphical results have been examined to observe the effect of diverse flow parameters against temperature, friction drag, velocity and heat transfer. From these results, it has been determined that the temperature profile escalates with the escalation of Hartmann, Eckert and Biot number, nanoparticles concentration and curvature parameter, although the velocity of fluid reduces with escalating values of nanoparticle concentration parameter, curvature parameter, and Hartmann number. It is equally important to indicate that the friction drag reduces with large curvature and rises with greater suction however the rate of heat transfer declines with least value of Eckert number and improves with strong suction, Hartmann, and Biot number.

RHEOLOGY OF POWER LAW FLUID FLOW AROUND A STAGNATION POINT IN POROUS MEDIUM WITH ENERGY DISSIPATION

An investigation on two-dimensional stagnation point flow past a stretching or shrinking surface in a porous medium with energy dissipation using power law model is carried out in this paper. By applying some similarity transformations, the governing partial differential equations are converted to non-linear ordinary differential equations. Consequently, numerical calculations of these equations are done by using MATLAB built- in bvp4c method. Impact of various parameters such as Prandtl number, permeability parameter and magnetic parameter are depicted graphically on velocity and temperature distributions. Also, the numerical values for velocity gradient and shear stress are shown in tabular form. From the analysis, it is noted that Prandtl number helps in reducing the shear stress, Also, as the power law parameter increases, a decrease in velocity is observed.

Solar radiation effects on MHD stagnation point flow and heat transfer of a nanofluid over a stretching sheet

The aim of this study is investigation of solar radiation influences on two-dimensional stagnation-point flow of nanofluid over a stretching sheet. The magnetic field is considered and the nonlinear Rosseland approximation is applied for thermal radiation in current work. The governing equations are transformed into a system of coupled nonlinear ordinary differential equations using similarity transformations which are solved numerically by means of the efficient differential quadrature method (DQM). The numerical results show the superb accuracy, good convergence with little computational efforts and the great potential of this method. Also, it is found that the temperature and thermal boundary layer thickness are increasing functions of Biot number. The findings narrate that increasing values of Brownian motion parameter make greater temperature values on the profile and thicker thermal boundary layer.

Dual solutions of a magnetohydrodynamic stagnation point flow of a non-Newtonian fluid over a shrinking sheet and a linear temporal stability analysis

The present study accentuates the magnetohydrodynamic and suction/injection effects on the two-dimensional stagnation point flow and heat transfer of a non-Newtonian fluid over a shrinking sheet. The set of Navier-Stokes equations are converted into a system of highly non-linear ordinary differential equations by employing suitable similarity variables. The obtained self-similar equations are then solved numerically with the aid of shooting technique. The similarity equations exhibit dual solutions over a certain range of the shrinking strength. It is observed that the solution domain increases as the suction/injection parameter, the non-Newtonian parameter and the magnetic parameter increase. Moreover, it is further noticed that these two solution branches show opposite behavior on the velocity and temperature profiles for the combined effects of the several flow parameters. Emphasis has been given to determine the most feasible and physically stable solution branch. Thus a linear temporal stability analysis has been carried out and the stability of the these two branches are tested by the sign of the smallest eigenvalue. The smallest eigenvalues are found numerically which suggest that the upper solution branch is stable and the flow dynamics can be describe by the behavior of the upper solution branch.

Dual solutions of magnetohydrodynamic boundary layer flow and a linear temporal stability analysis

In this paper, we have considered the two-dimensional stagnation point flow and heat transfer of an electrically conducting viscous fluid over an exponentially stretching sheet. The Navier-Stokes equations are reduced into a system of highly non-linear ordinary differential equations by similarity transformations. The resulting systems are then solved numerically by shooting method. The effects of suction/injection parameters on the boundary layer are discussed in detail. Our numerical results reveal that for a particular range of the velocity ratio parameter, dual solutions exist. Interestingly these two solution branches show opposite characters in the velocity and temperature profiles. Thus, it is worthwhile to carry a stability analysis of these two solutions to determine the feasible solution. A linear temporal stability analysis has been carried out, and the stability is tested by the sign of the smallest eigenvalue. The smallest eigenvalues are found by two different numerical schemes, which agree well up to the desired accuracy. The effects of the pertinent flow parameters in the velocity and temperature profiles are discussed in detail and are shown graphically.

Entropy generation and heat transfer in magnetohydrodynamic two-dimensional stagnation-point flow on a sliding plate

Entropy generation and heat transfer in magnetohydrodynamic two-dimensional stagnation flow of a viscous fluid over a sliding plate have been investigated. An alternative similarity transformation has been proposed for the temperature field for not to neglect the viscous dissipation and Ohmic heating terms in the energy equation. The governing equations are reduced to a set of nonlinear ordinary differential equations and solved numerically by using a new dimensionless group which represents the magnitude of dissipation. It has been observed that when the magnitude of the dissipation is high, then an increase in the external magnetic field causes the increment of the temperature and entropy generation while decrementing the heat transfer rate. In the other case, the effect of the external magnetic field is opposite. Also, it has been shown that to neglect the viscous dissipation and/or Ohmic heating terms in the energy equation may lead to errors.

Entropy generation and heat transfer in magnetohydrodynamic two-dimensional stagnation-point flow on a sliding plate

Entropy generation and heat transfer in magnetohydrodynamic two-dimensional stagnation-point flow on a sliding plate

Non-linear radiation and chemical reaction effects on slip flow of Williamson nanofluid due to a static/moving wedge: a revised model

In the present study, heat and mass transfer characteristics of unsteady, two-dimensional stagnation-point flow of Williamson nanofluid along a static/moving wedge in the presence of velocity slip and chemical reaction effects are investigated. The Rosseland approximation is adopted for thermal radiation effects and Buongiorno model is used for incorporating the effects of Brownian diffusion and thermophoresis. The wall of wedge is heated by the convection current from hotter fluid and revised model is also considered in this study. The governing boundary-layer equations are altered into a coupled non-linear ordinary differential equations using suitable transformations and then tackled numerically employing Runge–Kutta–Fehberg method with shooting technique. The effects of intricate physical parameters on the dimensionless velocity, temperature, nanoparticle concentration profiles as well as skin friction coefficient and local Nusselt number are explored graphically and discussed in detail. Verification of present code is achieved via benchmarking with previously published results, and generally, very excellent agreement is revealed. Our study reveals that the intensifying values of temperature ratio parameter enhances the nanofluid temperature and thermal boundary-layer thickness. The rate of heat transfer is seen to be higher with the growth of Prandtl number and Biot number. Moreover, the nanoparticle concentration is decreased as the Brownian motion and Schmidt number increasing.

Stagnation-point flow and heat transfer of upper-convected Oldroyd-B MHD nanofluid with Cattaneo–Christov double-diffusion model

Purpose The purpose of this paper is to investigate the two-dimensional stagnation-point flow, heat and mass transfer of an incompressible upper-convected Oldroyd-B MHD nanofluid over a stretching surface with convective heat transfer boundary condition in the presence of thermal radiation, Brownian motion, thermophoresis and chemical reaction. The process of heat and mass transfer based on Cattaneo–Christov double-diffusion model is studied, which can characterize the features of thermal and concentration relaxations factors. Design/methodology/approach The governing equations are developed and similarly transformed into a set of ordinary differential equations, which are solved by a newly approximate analytical method combining the double-parameter transformation expansion method with the base function method (DPTEM-BF). Findings An interesting phenomenon can be found that all the velocity profiles first enhance up to a maximal value and then gradually drop to the value of the stagnation parameter, which indicates the viscoelastic memory characteristic of Oldroyd-B fluid. Moreover, it is revealed that the thickness of the thermal and mass boundary layer is increasing with larger values of thermal and concentration relaxation parameters, which indicates that Cattaneo–Christov double-diffusion model restricts the heat and mass transfer comparing with classical Fourier’s law and Fick’s law. Originality/value This paper focuses on stagnation-point flow, heat and mass transfer combining the constitutive relation of upper-convected Oldroyd-B fluid and Cattaneo–Christov double diffusion model.

Physical aspects of CNTs and induced magnetic flux in stagnation point flow with quartic chemical reaction

Two-dimensional stagnation point flow of single and multi walls carbon nanotubes towards a stretching sheet is addressed. Induced magnetic field is considered. Homogeneous-heterogeneous reactions is accounted. Both SWCNTs (single wall) and MWCNTs (multi wall) are considered as nanoparticles whereas water and kerosene oil are considered as base liquid. Xue’s model is used for the physical characteristics of density, specific heat and thermal conductivity. The consequences of present work is to investigate impact of induced magnetic field in quartic chemical reactive stagnation point flow with influence of SWCNTs (single wall) and MWCNTs (multi wall). Dimensionless variables are introduced to model physical problem mathematically. Equations are then solved numerically with the help of Built-in-Shooting technique for non-dimensional induced magnetic field, velocity, concentration and temperature. The impacts of different dimensionless flow variables like stretching rate ratio parameter, magnetic parameter, thermal radiation, reciprocal magnetic Prandtl number, homogeneous reaction and heterogeneous reactions parameters and heat generation parameter are depicted through graphs. Computational analysis for surface drag force and Nusselt number are tabulated to examine the behaviors at stretched sheet. It is noticed that induced magnetic field enhances via higher nanoparticles volumetric fraction. Furthermore, multi (MWCNTs) has more contribution in enhancing induced magnetic field when compared with single (SWCNTs).

Chebyshev collocation computation of magneto-bioconvection nanofluid flow over a wedge with multiple slips and magnetic induction

In this article, the steady two-dimensional stagnation point flow of a viscous incompressible electrically conducting bio-nanofluid over a stretching/shrinking wedge in the presence of passively control boundary condition, Stefan blowing and multiple slips is numerically investigated. Magnetic induction is also taken into account. The governing conservation equations are rendered into a system of ordinary differential equations via appropriate similarity transformations. The reduced system is solved using a fast, convergent Chebyshev collocation method. The influence of selected parameters on the dimensionless velocity, induced magnetic field, temperature, nanoparticle volume fraction and density of motile microorganisms as well as on the local skin friction, local Nusselt number, local Sherwood number and density of motile microorganism numbers is discussed and presented graphically. Validation with previously published results is performed and an excellent agreement is found. The study is relevant to electromagnetic manufacturing processes involving bio-nanofluids.

Stability analysis on the stagnation-point flow and heat transfer over a permeable stretching/shrinking sheet with heat source effect

PurposeThis paper aims to analyze the behavior of the stagnation-point flow and heat transfer over a permeable stretching/shrinking sheet in the presence of the viscous dissipation and heat source effects.Design/methodology/approachThe governing partial differential equations are converted into ordinary differential equations by similarity transformations before being solved numerically using the bvp4c function built in Matlab software. Effects of suction/injection parameter and heat source parameter on the skin friction and heat transfer coefficients as well as the velocity and temperature profiles are presented in the forms of tables and graphs. A temporal stability analysis will be conducted to verify which solution is stable for the dual solutions exist for the shrinking case.FindingsThe analysis indicates that the skin friction coefficient and the local Nusselt number as well as the velocity and temperature were influenced by suction/injection parameter. In contrast, only the local Nusselt number, which represents heat transfer rate at the surface, was affected by heat source effect. Further, numerical results showed that dual solutions were found to exist for the certain range of shrinking case. Then, the stability analysis is performed, and it is confirmed that the first solution is linearly stable and has real physical implication, while the second solution is not.Practical implicationsIn practice, the study of the steady two-dimensional stagnation-point flow and heat transfer past a permeable stretching/shrinking sheet in the presence of heat source effect is very crucial and useful. The problems involving fluid flow over stretching or shrinking surfaces can be found in many industrial manufacturing processes such as hot rolling, paper production and spinning of fibers. Owing to the numerous applications, the study of stretching/shrinking sheet was subsequently extended by many authors to explore various aspects of skin friction coefficient and heat transfer in a fluid. Besides that, the study of suction/injection on the boundary layer flow also has important applications in the field of aerodynamics and space science.Originality/valueAlthough many studies on viscous fluid has been investigated, there is still limited discoveries found on the heat source and suction/injection effects. Indeed, this paper managed to obtain the second (dual) solutions and stability analysis is performed. The authors believe that all the results are original and have not been published elsewhere.

Effect of temperature on the MHD stagnation-point flow past an isothermal plate for a Boussinesquian Newtonian and micropolar fluid

PurposeThis paper aims to analyze the steady two-dimensional stagnation-point flow of an electrically conducting Newtonian or micropolar fluid when the obstacle is uniformly heated.Design/methodology/approachThe governing boundary layer equations are transformed into a system of ordinary differential equations using appropriate similarity transformations. Some analytical considerations about existence and uniqueness of the solution are obtained. The system is then solved numerically using the bvp4c function in MATLAB.FindingsIf the temperature of the obstacle Tw coincides with the environment temperature T0, then the motion reduces to the usual orthogonal stagnation-point flow; if Tw = T0, then it is necessary to include in the similarity function describing the velocity an oblique part due to the temperature. Also, the presence of a uniform external magnetic field orthogonal to the obstacle is examined. In all cases, the motion is reduced to a system of nonlinear ordinary differential equations with boundary conditions, whose solution is discussed numerically when the Prandtl and the Hartmann number varies.Originality/valueThe present results are original and new for the problem of magnetohydrodynamic mixed convection in the plane stagnation-point flow of a Newtonian or a micropolar fluid over a vertical flat plate. At infinity, the motion approaches the orthogonal stagnation-point flow of an inviscid fluid; the effect of an uniform external magnetic field is considered, and the obstacle has a uniform temperature.

Heat transfer analysis of Prandtl liquid nanofluid in the presence of homogeneous-heterogeneous reactions

Abstract The objective of present research work is to analyze the homogeneous-heterogeneous reactions on the MHD two-dimensional stagnation-point flow of non-Newtonian Prandtl fluid flow and heat transfer towards horizontal linear stretching sheet. The governing boundary layer equations using similarity transformation are reduced to ordinary differential equations suitable to be solved using Finite Difference Method. The quantities of interests are thoroughly analyzed under the effects of various emerging parameters. Comparison of the results obtained from limiting case of present model with already existing literature is in good agreement which shows the validity of the present numerical solution. The study concludes that homogeneous and heterogeneous reaction strength decreases the heat transfer rate. On the other hand, Prandtl fluid parameter and elastic parameter increases heat transfer rate.

Nanofluid flow on the stagnation point of a permeable non-linearly stretching/shrinking sheet

This paper studies a steady two-dimensional stagnation-point flow of nanofluids over a nonlinearly stretching/shrinking sheet in the presence of blowing/suction. The effects of different nanoparticle materials, namely copper, alumina and titania on the flow and heat transfer rate are investigated. Employing similarity variables, the governing partial differential equations including continuity, momentum and energy have been reduced to ordinary equations and are solved numerically via Runge-Kutta-Fehlberg scheme. It is shown that two solutions exist for shrinking sheets in both blowing and impermeable cases, while an additional solution appears in the case of suction (there are three solutions). Moreover, the effects of nonlinearly parameter β, blowing/suction S, and solid volume fraction ϕ on the heat and fluid flow characteristics are investigated in details.