Three-dimensional Stagnation-point Flow Research Articles

Bi-directional Forced Convective Stagnation Points Flow of Oldroyd-B Liquid with Joule Heating Effects: A Finite Difference Simulations

The impact of Joule heating for the three-dimensional stagnation point flow of non-Newtonian liquid (namely Oldroyd-B) nanomaterial has been inspected. The influence of mixed convection and the magnetic force is also considered. The flow is induced by the bidirectional stretched surface which moves linearly. The partial differential equations for the developed model are altered into dimensionless statements first. The numerical simulations with the implementation of a finite difference scheme are used for the numerical description. The physical description of parameters is presented against the flow parameters. The results reveal that there is a reverse change in velocity observed for both the relaxation time constant and the retardation constant. Furthermore, the heat transfer rate decreases as the ratio parameter increases. The thickness of the boundary layer increases due to the retardation time and can also be regulated by the application of a magnetic field. An increase in the magnetic parameter leads to an enhancement in temperature and an increase in thermal boundary layer thickness.

Modeling the hydromagnetic transient three-dimensional stagnation point flow of a couple stress Casson fluid over a bi-directional stretching sheet

A numerical study is performed to examine the magnetohydrodynamic effects on the transient three-dimensional stagnation point flow of a Casson fluid along a bi-directional stretching sheet. The physical model of the flow includes a sheet which is stretched in both the tangential directions and is thus called “bi-directional stretching”. The heat transfer mechanism includes the influences of space- and time-dependent non-uniform heat generation/absorption, as well as dissipation due to viscosity. The mathematical modeling of the problem involves the constitution of a set of coupled nonlinear boundary layer equations, together with suitable boundary conditions. The mathematical model thus developed is then subjected to suitable similarity transformations to arrive at a set of ordinary differential equations, which were then treated with the successive linearization method (SLM) to obtain approximate solutions for the velocity and temperature fields. A parametric study is carried out, and the results are discussed and presented graphically to analyze the behavior of the primary and secondary velocity distributions, as well as fluid temperature, along with significant physical quantities such as skin friction and Nusselt number for various values of the nondimensional parameters. Multiple quadratic regression analysis is also carried out to investigate the significance of parameters and to estimate the skin-friction and heat transfer coefficients.

Discussion on “Three-Dimensional Stagnation Point Flow and Heat Transfer of a Dusty Fluid Toward a Stretching Sheet, M. R. Mohaghegh, and A. B. Rahimi, 2016, ASME J. Heat Mass Transfer-Trans. ASME, 138(11), p. 112001”

Abstract Some errors exist in the above paper.

Entropy Generation and Regression Analysis of Magnetohydrodynamic Stagnation Point Flow of a Casson Fluid with Radiative and Dissipative Heat Transfer and Hall Effects

The phenomenon of heat transfer is prevalent in industries and has an extensive range of applications. However, mostly the discussion of heat transfer problems is limited to the study of the first law of thermodynamics, which deals with energy conservation. It is just restricted to the quantity of energy, not to its quality; i.e., there is no difference between the work (high-grade energy) and the heat (low-grade energy). A measurement of the degree of randomness of energy in a system is known as entropy. It is unavailable for doing useful work because work takes place only from ordered molecular motion. Even though many boundary layer models exist in the literature to investigate the flow and heat transfer of various fluids along a stretching surface, they have not yet been used at their maximum ability. The main motive of the current research is to discuss entropy generation or its minimization during heat transfer. This work presents an entropy generation analysis for the transient three-dimensional stagnation point flow of a hydromagnetic Casson fluid flowing over a stretching surface in the existence of Hall current, viscous dissipation, and nonlinear radiation. The physical configuration of the present work is described in terms of partial differential equations (PDEs) of nonlinear nature. Furthermore, these PDEs are converted into ordinary differential equations by using some relevant similarity transformations. An efficient numerical method named as the spectral quasilinearization method (SQLM) is used to solve this model. The expression of the Bejan number and volumetric entropy generation rate is also computed. A parametric analysis, including the essential physical parameters, is performed to examine the influences of distinct flow parameters on the velocity profile, temperature profile, Bejan number, entropy generation number, and the coefficients of skin friction and the Nusselt number. In order to further insight into the emerging physical quantities of engineering interest, multiple quadratic regression models are used to estimate the coefficients of skin friction and heat transfer.

Radiation effect on MHD three-dimensional stagnation-point flow comprising water-based graphene oxide nanofluid induced by a nonuniform heat source/sink over a horizontal plane surface

This research aims to study the 3D magnetohydrodynamics stagnation-point flow (SPF) over a horizontal plane surface (HPS) carrying water-based graphene oxide (GO) nanoparticles caused by an irregular heat source/sink used in heat transfer procedures. In addition, a Tiwari–Das model is used to inspect the dynamics of fluid flow behavior and heat transmission features of the nanoparticles with experiencing the impacts of thermal radiation. The acquired nonlinear set of partial differential equations (PDEs) is transfigured to a system of ordinary differential equations (ODEs) using similarity transformations. The accumulative dimensionless ODEs are then further tackled in MATLAB using the bvp4c solver. Tables and figures are prepared for the execution of several relevant constraints along with nodal/saddle indicative parameter, internal heat source/sink parameter, radiation parameter and nanoparticles volume fraction which divulges and clarify more accurately the posited quantitative data and graphical findings. Also, the velocity profile decelerated in the axial and transverse coordinate axes for a higher value of the nanoparticle volume fraction but the dimensionless temperature distribution is augmented. Additionally, thermal boundary layer thickness and profile of temperature enriches with higher impressions of radiation constraint. However, the internal heat sink factor declines the profiles of temperature while escalating with the superior value of the internal heat source parameter.

Radiation effect on three-dimensional stagnation point flow involving copper-aqueous titania hybrid nanofluid induced by a non-Fourier heat flux over a horizontal plane surface

This research numerically investigates 3D stagnation-point flow (SPF) past a horizontal plane surface conveying copper-aqueous titania hybrid nanofluid induced by non-Fourier heat flux (NFHF) that utilized in heat transfer processes. A Tiwari-Das model is engaged to examine the fluid flow dynamics and the heat transfer features of the hybrid nanofluid with thermal radiation effect. With aid of similarity variables, the leading nonlinear system involving partial differential equations (PDEs) is reduced to a system of ordinary differential equations (ODEs). This set of dimensionless coupled ODEs is then tackled through the bvp4c solver in MATLAB. For hybrid nanofluid, the graphical findings of the pertaining parameters as well as the saddle/nodal indicative parameter are disclosed and explained with the assist of figures and tables. The results illustrate that the rise of hybrid nanoparticles declines the motion of the fluids in both axes of coordinates ( and directions), while the temperature enhances. In addition, the temperature distribution declines due to relaxation parameter but uplifts due to radiation. Also, the thermal relaxation parameter reduces the temperature. Moreover, the present solution displays an excellent agreement with earlier published works in the limited cases of normal fluid and nanofluid.

THREE-DIMENSIONAL STAGNATION-POINT FLOW OVER A PERMEABLE STRETCHING/SHRINKING SHEET WITH A SECOND ORDER SLIP FLOW

The problem of steady laminar three-dimensional stagnation-point flow on a permeable stretching/shrinking sheet with second order slip flow model is studied numerically. Similarity transformation has been used to reduce the governing system of nonlinear partial differential equations into the system of ordinary (similarity) differential equations. The transformed equations are then solved numerically using the \texttt{bvp4c} function in MATLAB. Multiple solutions are found for a certain range of the governing parameters. The effects of the governing parameters on the skin friction coefficients and the velocity profiles are presented and discussed. It is found that the second order slip flow model is necessary to predict the flow characteristics accurately.

Mixed convection of a three-dimensional stagnation point flow on a vertical plate with surface slip in a hybrid nanofluid

Hybrid nanofluid has become one of the major interest topics among researchers nowadays due to its significant impact in myriad applications. This paper modeled and explored the properties of flow and heat transfer of mixed convection stagnation point flow for hybrid nanofluid (alumina-copper/water) on a vertical plate with slips and suction. By using the method of similarity transformation, the governing set of partial differential equations (PDEs) are transformed into ordinary differential equations (ODEs). These derived equations are then evaluated numerically by adopting the bvp4c function that is available in Matlab software. In the presence of slips together with the opposing flow of mixed convection, the local Nusselt number (heat transfer rate) can be augmented by increasing the solid volume fraction of copper. The surge of 0.5% of copper volume fraction can accelerate the heat transfer rate by approximately 1.3% in this present analysis within the specified value of slips, mixed convection, and suction. The stability analysis is conducted due to the existence of dual solutions and only the first solution is stable for practical application.

Analysis of three-dimensional stagnation point flow over a radiative surface

This article aims to explore the three-dimensional stagnation point flow over a radiative wavy cylindrical shaped body. Two cases, namely, nodal and saddle stagnation point flow are examined. Nonlinear Rosseland approximation is employed to model the radiative heat transfer phenomena. Modelled equations are firstly converted in dimensionless forms after defining dimensionless quantities and then transformed into self-similar equations using appropriate similarity variables. Numerical solution of the nonlinear system is computed using shooting method with Runge–Kutta–Fehlberg algorithm and to verify the authenticity, obtained results are also compared with finite-difference based built-in routine bvp5c in MATLAB software. Heat transfer rate in the absence of thermal radiation is juxtaposed with the cases of linear and nonlinear radiation cases.

Unsteady MHD Mixed Convection Flow in Hybrid Nanofluid at Three-Dimensional Stagnation Point

There has been significant interest in exploring a stagnation point flow due to its numerous potential uses in engineering applications such as cooling of nuclear reactors. Hence, this study proposed a numerical analysis on the unsteady magnetohydrodynamic (MHD) mixed convection at three-dimensional stagnation point flow in Al2O3–Cu/H2O hybrid nanofluid over a permeable sheet. The ordinary differential equations are accomplished by simplifying the governing partial differential equations through suitable similarity transformation. The numerical computation is established by the MATLAB system software using the bvp4c technique. The bvp4c procedure is excellent in providing more than one solution once sufficient predictions are visible. The influence of certain functioning parameters is inspected, and notable results exposed that the rate of heat transfer is exaggerated along with the skin friction coefficient while the suction/injection and magnetic parameters are intensified. The results also signified that the rise in the volume fraction of the nanoparticle and the decline of the unsteadiness parameter demonstrates a downward attribution towards the heat transfer performance and skin friction coefficient. Conclusively, the observations are confirmed to have multiple solutions, which eventually contribute to an investigation of the analysis of the solution stability, thereby justifying the viability of the first solution.

Impact of anisotropic slip on the stagnation-point flow past a stretching/shrinking surface of the Al2O3-Cu/H2O hybrid nanofluid

The characteristics of heat transfer in the three-dimensional stagnation-point flow past a stretching/shrinking surface of the Al2O3-Cu/H2O hybrid nanofluid with anisotropic slip are investigated. The partial differential equations are converted into a system of ordinary differential equations by valid similarity transformations. The simplified mathematical model is solved computationally by the bvp4c approach in the MATLAB operating system. This solving method is capable of generating more than one solutions when suitable initial guesses are proposed. The results are proven to have dual solutions, which consequently lead to the application of a stability analysis that verifies the achievability of the first solution. The findings reveal infinite values of the dual solutions at several measured parameters causing the non-appearance of the turning points and the critical values. The skin friction increases with the addition of nanoparticles, while the escalation of the anisotropic slip effect causes a reduction in the heat transfer rate.

Numerical simulation for MHD Darcy–Forchheimer three-dimensional stagnation point flow by a rotating disk with activation energy and partial slip

The Buongiorno nanofluid model is utilized to scrutinize the impacts of important slip mechanisms, i.e., thermophoresis diffusion and Brownian momentum on the Darcy–Forchheimer three-dimensional stagnation point flow of viscous fluid towards a flat surface with multi slips (velocity, temperature, concentration). The thermo-physical and experimental correlations for the thermal conductivity, density and dynamic viscosity of nanoliquid are implemented in the governing expressions. Nanoliquids are mostly utilized in the continuous phase liquid to enhance their thermal characteristics as coolants in transport equipment, i.e., electronic cooling system, heat exchangers and radiators. Heat transport subject to flat plate has been examined by numerous analyst. Appropriate similarity transformations which is derived from Lie point symmetry is incorporated to alter the system of governing equation into ordinary one. The transformed system is solved numerically through bvp4v (built-in-shooting) technique. The influences of important flow parameters on the dimensionless temperature, velocity, Nusselt number, concentration, wall shear stress and Sherwood number are plotted graphically and tabular form.

G-Jitter effect on heat and mass transfer of 3D stagnation point nanofluid flow with heat generation

Abstract The dynamics of viscous copper nanofluid double diffusion problem driven at three-dimensional stagnation point flow induced by heat generation under microgravity environment was analyzed numerically. The nature of the flow was interpreted into a system of differential equation. By imposing Keller box approach, profiles and physical quantities of principle interest result were analyzed. Profiles results showed a natural convection pattern and satisfied the boundary condition. Besides that, curvature ratio gives a significant effect on skin friction. Larger size of frequency of oscillation reduce the peak values of all physical quantities. The analysis on Nusselt shows an enhancement with the additional of nanoparticles into the conventional fluid. Meanwhile, additional resistance at the boundaries was produced due to the presence of copper nanoparticles. A heat source was produced from the heat generation effect inside the fluid reduced the rate of heat transfer at the body due to the additional temperature at the fluid.

Non-axisymmetric three-dimensional stagnation-point flow and heat transfer under a jet impingement boiling

The non-axisymmetric three-dimensional flow and heat transfer in the stagnation-point region of a planar jet impingement boiling on a flat surface has been investigated by using similarity solution approach, considering additional diffusivity terms in momentum and energy equations as a result of bubble-induced mixing in flow. The free jet stream along z direction impinges on the surface and produces a flow with different velocity components. This situation may happen if the flow pattern on the plate is bounded from both sides in one of the directions, because of any physical limitation or due to conditions of the surface such as moving plates or stretching sheets with different values of stretching velocities in the x and y directions. The governing equations have been transformed into ordinary differential equations by introducing appropriate similarity variables, and an exact solution has been obtained for three-dimensional boiling problem for the first time. The similarity variables have been presented based on non-axisymmetric three-dimensional and additional diffusivity effects. The bubble-induced diffusion due to bubble formation, growth, departure and collapse causes an enhancement in heat transfer rate from the surface to the bulk flow. The total heat flux transferred from the surface to the flow has been estimated as summation of the single-phase heat transfer due to forced convection and the nucleate boiling heat flux due to bubble-induced diffusion. The effects of the velocity components ratio and the ratio between the maximum total diffusivity to the molecular diffusivity on the flow field and heat transfer characteristics have been obtained and discussed and illustrated graphically. A comparison of the predicted heat flux has been made with previously published experimental data. As expected, the average deviation values show relatively more accurate results for the three-dimensional simulation than the two-dimensional one because of being closer to the experimental conditions.

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

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.

Stagnation-point flow of an aqueous titania-copper hybrid nanofluid toward a wavy cylinder

PurposeThe purpose of this paper is to investigate analytically the steady general three-dimensional stagnation-point flow of an aqueous titania-copper hybrid nanofluid past a circular cylinder that has a sinusoidal radius variation.Design/methodology/approachFirst, the analytic modeling of hybrid nanofluid is presented, and using appropriate similarity variables, the governing equations are transformed into nonlinear ordinary differential equations in the dimensionless stream function, which is solved by the well-known function bvp4c from MATLAB.FindingsThe current solution demonstrates good agreement with those of the previously published studies in the special cases of regular fluid and nanofluids. Graphical results are presented to investigate the influences of the titania and copper nanoparticle volume fractions and also the nodal/saddle indicative parameter on flow and heat transfer characteristics. Here, the thermal characteristics of hybrid nanofluid are found to be higher in comparison to the base fluid and fluid containing single nanoparticles. An important point to note is that the developed model can be used with great confidence to study the flow and heat transfer of hybrid nanofluids.Originality/valueAnalytic modeling of hybrid nanofluid is the important originality of present study. Hybrid nanofluids are potential fluids that offer better heat transfer performance and thermophysical properties than convectional heat transfer fluids (oil, water and ethylene glycol) and nanofluids with single nanoparticles. In this investigation, titania (TiO2, 50 nm), copper (Cu, 20 nm) and the hybrid of these two are separately dispersed into the water as the base fluid and analyzed.

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.