Three-dimensional Stagnation Point Research Articles

Unsteady General Three-Dimensional Stagnation Point Flow of a Maxwell/Buongiorno Non-Newtonian Nanofluid

Unsteady General Three-Dimensional Stagnation Point Flow of a Maxwell/Buongiorno Non-Newtonian Nanofluid

Microfluidic analog of an opposed-jets device

A fully three-dimensional (3D) stagnation point microfluidic device is fabricated that, similar to the classical opposed-jet apparatus, can be operated in either a uniaxial or a biaxial extensional flow mode with an easily controllable strain rate. The microchannel is etched inside fused silica and has optical access through all three planes. A detailed characterization of the Newtonian flow field by microparticle image velocimetry confirms the expected nature of the flow and compares well with the prediction of 3D numerical simulations. Flow-induced birefringence of a model polymer solution demonstrates the extension of macromolecules in both modes of operation and the potential use of the device for quantitative rheo-optical studies. This microfluidic opposed jet device could also be used for examining the deformation and dynamics of drops, cells, fibers, and single molecules in well-defined and relevant flow fields.

On both MHD and slip effect in micropolar hybrid nanofluid past a circular cylinder under stagnation point region

The physical model of the micropolar hybrid nanofluid flow with magnetohydrodynamic and thermal slip effects is considered. The flow of three-dimensional stagnation point of micropolar hybrid nanofluid past a circular cylinder is also taken into account. The flow model is controlled through partial differential equations. These equations are highly nonlinear in character and reduce to ordinary differential equations through applying the suitable similarity transformation. The reduced system is solved numerically using the shooting technique. The mutual effects are presented using graphs while comparative numerical results are presented in the tables. The diverse physical parts of the issue have been talked about. This study aims to investigate the solid nano-sized particle on the surface of a circular cylinder having sinusoidal variation. These nanosized particles are used to analyze the heat transfer improvement of micropolar hybrid nanofluid as compared to micropolar nanofluid.

MHD Stagnation Point Flow of Nanofluid on a Plate with Anisotropic Slip

In this article, an axisymmetric three-dimensional stagnation point flow of a nanofluid on a moving plate with different slip constants in two orthogonal directions in the presence of uniform magnetic field has been considered. The magnetic field is considered along the axis of the stagnation point flow. The governing Naiver–Stokes equation, along with the equations of nanofluid for three-dimensional flow, are modified using similarity transform, and reduced nonlinear coupled ordinary differential equations are solved numerically. It is observed that magnetic field M and slip parameter λ 1 increase the velocity and decrease the boundary layer thickness near the stagnation point. Also, a thermal boundary layer is achieved earlier than the momentum boundary layer, with the increase in thermophoresis parameter N t and Brownian motion parameter N b . Important physical quantities, such as skin friction, and Nusselt and Sherwood numbers, are also computed and discussed through graphs and tables.

Unsteady three-dimensional stagnation point magnetohydrodynamic flow of bionanofluid with variable properties

Unsteady three-dimensional laminar stagnation point forced convective boundary layer magnetohydrodynamic flow of a bionanofluid with variable transport properties is studied theoretically and numerically. Thermal convective and zero mass flux boundary conditions are incorporated in this study. The transport properties are assumed to be a function of nanoparticle volume fraction to get physically realistic results. The dimensional boundary layer equations along with the coupled boundary conditions are transformed via similarity transformations into a system of ordinary differential equations. The transformed equations are solved numerically using the Runge–Kutta–Fehlberg fourth-, fifth-order numerical method. The effect of selected governing parameters, namely, viscosity, thermal conductive, mass diffusivity, microorganism diffusivity, magnetic field and bioconvection Schmidt number, on the dimensionless velocity, temperature, nanoparticle volume fraction, microorganism, skin friction coefficient, heat transfer rate, mass transfer rate and microorganism transfer rate, is illustrated graphically and interpreted in detail. Comparisons with previous works are carried out for some limiting cases and found to be in good agreement.

Heat Transfer Analysis for Three-Dimensional Stagnation-Point Flow of Water-Based Nanofluid Over an Exponentially Stretching Surface

The basic theme of this investigation is to analyze heat and mass transport for three-dimensional (3D) stagnation-point flow of nanofluid caused by an exponentially stretched surface when water is treated as base fluid. In this study, we invoked the boundary layer phenomena and suitable similarity transformation of exponential character; as a result, our 3D nonlinear equations of momentum and energy are transmuted into nonlinear and nonhomogeneous differential equations involving ordinary derivatives. Final equations are then puzzled out by applying homotopy analysis technique. Interesting outcomes of aggressing parameters involved in this study, and effecting profiles of temperature field and velocity are explained in detail. Graphical results of involved parameters appearing in considered nanofluid are presented separately. Different aspects of skin friction coefficient as well as Nusselt number are calculated. It is worth mentioning that skin friction (as we go) along x and y-direction is maximal for Cu-water nanofluid and minimal for AL2O3-water nanofluid. Also, the resulting quantity of local Nusselt number came out maximum for Cu-water nanofluid whereas minimum for TiO2-water nanofluid.

Characteristics of three dimensional stagnation point flow of Hybrid nanofluid past a circular cylinder

The characteristics of three-dimensional stagnation point flow of Hybrid nanofluid past a circular cylinder are explored. The fluid flow is entertained in the presence/absence of thermal slip effects. The flow model is controlled through the partial differential equations. Since these equations are highly non-linear in character. So for the order reduction a suitable set of transformation is used. The reduced system is solved by using shooting method. The obtained results are offered through graphs and tables. It is noticed that the heat transfer rate is high in Hybrid nanofluid as compared to nanofluid. The present work is validated by developing comprising with existing literature.

Three dimensional MHD stagnation point flow of Al-Cu alloy suspended water based nanofluid with second order slip and convective heating

Purpose The paper aims to examine the boundary layers of a three-dimensional stagnation point flow of Al-Cu nanoparticle-suspended water-based nanofluid in an electrically conducting medium. The effect of magnetic field on second-order slip effect and convective heating is also taken into account. Design/methodology/approach The thermophysical properties of alloy nanoparticles such as density, specific heat capacity and thermal conductivity are computed using appropriate formula. The non-linear parabolic partial differential equations are transformed to ordinary differential equations and solved by shooting technique. Findings The influence of compositional variation of alloy nanoparticle, nanoparticle concentration, magnetic effect, slip parameters and Biot number are presented for various flow characteristics. Interesting results on skin friction and Nusselt number are obtained for different composition of aluminium and copper. Originality/value A novel result of the analysis reveals that impact of magnetic field near the boundary is suppressed by the slip effect.

Effects of anisotropic slip on three-dimensional stagnation-point flow past a permeable moving surface

In this paper, the problem of a steady laminar three-dimensional stagnation point boundary layer flow (Homann stagnation flow) on a permeable moving surface with anisotropic slip in a viscous fluid is investigated. A similarity transformation reduces the governing system of nonlinear partial differential equations into the ordinary (similarity) differential equations. The resulting equations are then solved numerically by using the bvp4c function in Matlab. The effects of surface mass transfer parameter, slip parameter and moving parameter on the fluid flow characteristics are presented in the forms of tables and figures and are discussed in detail. Finally, it is concluded from the stability analysis that the first (upper branch) solution is stable and physically realizable, while the second (lower branch) solution is not stable.

Three-Dimensional Stagnation-Point Flow and Heat Transfer of a Dusty Fluid Toward a Stretching Sheet

The steady three-dimensional stagnation-point flow and heat transfer of a dusty fluid toward a stretching sheet is investigated by using similarity solution approach. The freestream along z-direction impinges on the stretching sheet to produce a flow with different velocity components. The governing equations are transformed into ordinary differential equations by introducing appropriate similarity variables and an exact solution is obtained. The nonlinear ordinary differential equations are solved numerically using Runge–Kutta fourth-order method. The effects of the physical parameters like velocity ratio, fluid and thermal particle interaction parameter, ratio of freestream velocity parameter to stretching sheet velocity parameter, Prandtl number, and Eckert number on the flow field and heat transfer characteristics are obtained, illustrated graphically, and discussed. Also, a comparison of the obtained numerical results is made with two-dimensional cases existing in the literature and good agreement is approved. Moreover, it is found that the heat transfer coefficient and shear stress on the surface for axisymmetric case are larger than nonaxisymmetric case. Also, for stationary flat plat case, a similarity solution is presented and a comparison of the obtained results is made with previously published results and full agreement is reported.

Computational Study of Three-Dimensional Stagnation Point Nanofluid Bioconvection Flow on a Moving Surface With Anisotropic Slip and Thermal Jump Effect

The effects of anisotropic slip and thermal jump on the three-dimensional stagnation point flow of nanofluid containing microorganisms from a moving surface have been investigated numerically. Anisotropic slip takes place on geometrically striated surfaces and superhydrophobic strips. Zero mass flux of nanoparticles at the surface is applied to achieve practically applicable results. Using appropriate similarity transformations, the transport equations are reduced to a system of nonlinear ordinary differential equations with coupled boundary conditions. Numerical solutions are reported by means of very efficient numerical method provided by the symbolic code Maple. The influences of the emerging parameters on the dimensionless velocity, temperature, nanoparticle volumetric fraction, density of motile microorganism profiles, as well as the local skin friction coefficient, the local Nusselt number, and the local density of the motile microorganisms are displayed graphically and illustrated in detail. The computations demonstrate that the skin friction along the x-axis is enhanced with the velocity slip parameter along the y-axis. The converse response is observed for the dimensionless skin friction along the y-axis. The heat transfer rate is increased with greater velocity slip effects but depressed with the thermal slip parameter. The local Nusselt number is increased with Prandtl number and decreased with the thermophoresis parameter. The local density for motile microorganisms is enhanced with velocity slip parameters and depressed with the bioconvection Lewis number, thermophoresis, and Péclet number. Numerical results are validated where possible with published results and excellent correlation is achieved.

НЕСТАЦИОНАРНОЕ ТРЕХМЕРНОЕ ТЕЧЕНИЕ И ТЕПЛООБМЕН В НАНОЖИДКОСТИ В ТОЧКЕ ОСТАНОВКИ ПОТОКА С УЧЕТОМ ТЕРМОФОРЕЗА И БРОУНОВСКОГО ДВИЖЕНИЯ

НЕСТАЦИОНАРНОЕ ТРЕХМЕРНОЕ ТЕЧЕНИЕ И ТЕПЛООБМЕН В НАНОЖИДКОСТИ В ТОЧКЕ ОСТАНОВКИ ПОТОКА С УЧЕТОМ ТЕРМОФОРЕЗА И БРОУНОВСКОГО ДВИЖЕНИЯ

On a Seemingly New Three-Dimensional Stagnation-Point Flow

In a recent paper by Abbassi and Rahimi (2009, “Nonaxisymmetric Three-Dimensional Stagnation-Point Flow and Heat Transfer on a Flat Plate,’’ ASME J. Fluids Eng, 131(7), p. 074501) the existence of a new nonaxisymmetric 3D stagnation-point flow has been reported. The present paper shows, however, that the model of Abbassis and Rahimi is fully equivalent to the classical 3D stagnation-point flow of Howarth (1951, “The Boundary Layer in Three-Dimensional Flow—Part II: The Flow Near a Stagnation Point,’’ Philos. Mag., 42, pp. 1433–1440) published more than sixty years ago. Thus their “new’’ solution can be recovered from Howarth's known solution by simple transformations, without any additional research effort. Once this flow problem is solved, the solution of the heat transfer problem of Abbassi and Rahimi (2009, “Nonaxisymmetric Three-Dimensional Stagnation-Point Flow and Heat Transfer on a Flat Plate,’’ ASME J. Fluids Eng, 131(7), p. 074501) can be calculated by a semi-analytical or by a usual numerical procedure.

Series solutions for steady three-dimensional stagnation point flow of a nanofluid past a circular cylinder with sinusoidal radius variation

This article deals with the study of the steady three-dimensional stagnation point flow of a nanofluid past a circular cylinder that has a sinusoidal radius variation. By means of similarity transformation, the governing partial differential equations are reduced into highly non-linear ordinary differential equations. The resulting non-linear system has been solved analytically using an efficient technique namely homotopy analysis method (HAM). Expressions for velocity and temperature fields are developed in series form. In this study, three different types of nanoparticles are considered, namely alumina (Al2O3), titania (TiO2), and copper (Cu) with water as the base fluid. For alumina–water nanofluid, graphical results are presented to describe the influence of the nanoparticle volume fraction φ and the ratio of the gradient of velocities c on the velocity and temperature fields. Moreover, the features of the flow and heat transfer characteristics are analyzed and discussed for foregoing nanofluids. It is found that the skin friction coefficient and the heat transfer rate at the surface are highest for copper–water nanofluid compared to the alumina–water and titania–water nanofluids.

Unsteady Free Convection Flow Over a Three-Dimensional Stagnation Point With Internal Heat Generation or Absorption

This paper considers the effect of heat generation proportional to p (T T ) ∞ − , where T is the local temperature and T ∞ is the ambient temperature, in unsteady free convection flow near the stagnation point region of a three-dimensional body. The fluid is considered in an ambient fluid under the assumption of a step change in the surface temperature of the body. The non-linear coupled partial differential equations governing the free convection flow are solved numerically using an implicit finite -difference method for different values of the governing parameters entering these equations. The results for the flow and heat characteristics when 2 ≤ p show that the transition from the initial unsteady-state flow to the final steady- state flow takes place smoothly. The behavior of the flow is seen strongly depend on the exponent p .

Flow and heat transfer at a general three-dimensional stagnation point in a nanofluid

The problem dealing with steady three-dimensional stagnation point flow in a nanofluid is investigated. By using appropriate transformation for velocity and temperature, the basic equations governing the flow and heat transfer are reduced to a set of ordinary differential equations. These equations subjected to the associated boundary conditions are then solved numerically. The effects of the nanoparticle volume fraction φ and the ratio of the gradient of velocities c on the flow and heat transfer characteristics are thoroughly examined.

Nonaxisymmetric Three-Dimensional Stagnation-Point Flow and Heat Transfer on a Flat Plate

The existing solutions of Navier–Stokes and energy equations in the literature regarding the three-dimensional problem of stagnation-point flow either on a flat plate or on a cylinder are only for the case of axisymmetric formulation. The only exception is the study of three-dimensional stagnation-point flow on a flat plate by Howarth (1951, “The Boundary Layer in Three-Dimensional Flow—Part II: The Flow Near Stagnation Point,” Philos. Mag., 42, pp. 1433–1440), which is based on boundary layer theory approximation and zero pressure assumption in direction of normal to the surface. In our study the nonaxisymmetric three-dimensional steady viscous stagnation-point flow and heat transfer in the vicinity of a flat plate are investigated based on potential flow theory, which is the most general solution. An external fluid, along z-direction, with strain rate a impinges on this flat plate and produces a two-dimensional flow with different components of velocity on the plate. This situation may happen if the flow pattern on the plate is bounded from both sides in one of the directions, for example x-axis, because of any physical limitation. A similarity solution of the Navier–Stokes equations and energy equation is presented in this problem. A reduction in these equations is obtained by the use of appropriate similarity transformations. Velocity profiles and surface stress-tensors and temperature profiles along with pressure profile are presented for different values of velocity ratios, and Prandtl number.

Dye visualization near a three-dimensional stagnation point: application to the vortex breakdown bubble

An analytical model, based on the Fokker–Planck equation, is constructed of the dye visualization expected near a three-dimensional stagnation point in a swirling fluid flow. The model is found to predict dye traces that oscillate in density and position in the meridional plane in which swirling flows are typically visualized. Predictions based on the model are made for the steady vortex breakdown bubble in a torsionally driven cylinder and compared with computational fluid dynamics predictions and experimental observations. Previous experimental observations using tracer visualization techniques have suggested that even for low-Reynolds-number flows, the steady vortex breakdown bubble in a torsionally driven cylinder is not axisymmetric and has an inflow/outflow asymmetry at its tail. Recent numerical and theoretical studies show that the asymmetry of the vortex breakdown bubble, and consequently its open nature, can be explained by the very small imperfections that are present in any experimental rig. Distinct from this, here it is shown that even for a perfectly axisymmetric flow and breakdown bubble, the combined effect of dye diffusion and the inevitable small errors in the dye injection position lead to the false perception of an open bubble structure with folds near the lower stagnation point. Furthermore, the asymmetries in the predicted flow structures can be remarkably similar to those observed in flow observations and computational predictions with geometric asymmetries of the rig. Thus, when interpreting dye-visualization patterns in steady flow, even if axisymmetric flow can be achieved, it is important to take into account the relative diffusivity of the dye and the accuracy of its injection.

An Explicit Analytic Solution of Steady Three-Dimensional Stagnation Point Flow of Second Grade Fluid Toward a Heated Plate

We present a purely analytic solution to the steady three-dimensional viscous stagnation point flow of second grade fluid over a heated flat plate moving with some constant speed. The analytic solution is obtained by a newly developed analytic technique, namely, homotopy analysis method. By giving a comparison with the existing results, it is shown that the obtained analytic solutions are highly accurate and are in good agreement with the results already present in literature. Also, the present analytic solution is uniformly valid for all values of the dimensionless second grade parameter α. The effects of α and the Prandtl number Pr on velocity and temperature profiles are discussed through graphs.

MHD Effects on Natural Convection in a Micropolar Fluid at a Three-Dimensional Stagnation Point in a Porous Medium

MHD Effects on Natural Convection in a Micropolar Fluid at a Three-Dimensional Stagnation Point in a Porous Medium