Three-dimensional Stagnation Point 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”

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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.

Quadratic Convective Nanofluid Flow at a Three-Dimensional Stagnation Point with the g-Jitter Effect

The nonlinear density variation with temperature happens in many thermal applications like solar collectors, energy production, heat exchangers, and combustions, and it gives a significant impact on heat transfer and fluid flows. Thus, a nonlinear convective of an unsteady stagnation point flow under the influence of gravity modulation in the presence of water-based nanoparticles alumina (Al2O3) is studied here. Suitable variables are utilized to reduce the highly coupled nonlinear governing equations into a system of dimensionless simple partial differential equations. The Keller-box method is then applied to solve the consequent governing equations. Velocity and temperature profiles for various values of pertinent parameters are displayed graphically and discussed. The results indicate that the quadratic convection has enhanced the fluid flow and heat transport. Furthermore, the nonlinear convection parameter and the nanoparticles volume fractions have delivered a positive effect on the skin friction and the rate of heat transfer.

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.

Shape effect of Cu, Al2O3 and TiO2 nanoparticles on stagnation point nanofluid flow in a microgravity environment

The unsteady viscous nanofluid flow near a three-dimensional stagnation point was studied numerically under microgravity environment. g-Jitter is one of the effects occurs under microgravity environment that producing a fluctuating gravitational field. Three different types of nanoparticles were induced in the study that is copper (Cu), alumina (Al2O3), and titania (TiO2) which then produce a water-based typed of nanofluid. In addition, different shape of nanoparticle was applied on the study in analyzing the performance of each types of nanoparticle. The fluid system was then mathematically formulated into a system of partial differential equation based on physical law and principle such as conservation of mass, Newton’s second law and conservation of energy. The system of equation then undergoes semi-similar transformation technique in reducing the complexity of the problem into non dimensionless form. Keller box method was applied into the dimensionless system of equations in solving the problem numerically. The problem was analyzed in term of velocity and temperature profiles together with skin friction coefficient and Nusselt number. The results shown that temperature profile, skin friction coefficient and Nusselt number were increase while velocity profile decreased as nanoparticle volume fraction decreased. The results indicated that, the needle-shaped nanoparticles give the highest enhancement on the heat transfer of the nanofluid compared to sphere and disk-shaped nanoparticles with more than 14% significant different. In addition, alumina hold the highest velocity profile while copper hold the lowest velocity profile.

WITHDRAWN: Three-dimensional stagnation point Casson nanofluid flow along with thermal radiation, heat source/sink and gyrotactic microorganisms

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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.

Stability analysis and modeling for the three-dimensional Darcy-Forchheimer stagnation point nanofluid flow towards a moving surface

In this research, the three-dimensional (3D) steady and incompressible laminar Homann stagnation point nanofluid flow over a porous moving surface is addressed. The disturbance in the porous medium has been characterized by the Darcy-Forchheimer relation. The slip for viscous fluid is considered. The energy equation is organized in view of radiative heat flux which plays an important role in the heat transfer rate. The governing flow expressions are first altered into first-order ordinary ones and then solved numerically by the shooting method. Dual solutions are obtained for the velocity, skin friction coefficient, temperature, and Nusselt number subject to sundry flow parameters, magnetic parameter, Darcy-Forchheimer number, thermal radiation parameter, suction parameter, and dimensionless slip parameter. In this research, the main consideration is given to the engineering interest like skin friction coefficient (velocity gradient or surface drag force) and Nusselt number (temperature gradient or heat transfer rate) and discussed numerically through tables. In conclusion, it is noticed from the stability results that the upper branch solution (UBS) is more reliable and physically stable than the lower branch solution (LBS).

Effects of g-jitter and radiation on three-dimensional double diffusion stagnation point nanofluid flow

The unsteady double diffusion of the boundary layer with the nanofluid flow near a three-dimensional (3D) stagnation point body is studied under a microgravity environment. The effects of g-jitter and thermal radiation exist under the microgravity environment, where there is a gravitational field with fluctuations. The flow problem is mathematically formulated into a system of equations derived from the physical laws and principles under the no-slip boundary condition. With the semi-similar transformation technique, the dimensional system of equations is reduced into a dimensionless system of equations, where the dependent variables of the problem are lessened. A numerical solution for the flow problem derived from the system of dimensionless partial differential equations is obtained with the Keller box method, which is an implicit finite difference approach. The effects studied are analyzed in terms of the physical quantities of principle interest with the fluid behavior characteristics, the heat transfer properties, and the concentration distributions. The results show that the value of the curvature ratio parameter represents the geometrical shape of the boundary body, where the stagnation point is located. The increased modulation amplitude parameter produces a fluctuating behavior on all physical quantities studied, where the fluctuating range becomes smaller when the oscillation frequency increases. Moreover, the addition of Cu nanoparticles enhances the thermal conductivity of the heat flux, and the thermal radiation could increase the heat transfer properties.

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.

Unsteady mixed convection flow at a three-dimensional stagnation point

PurposeThis paper aims to probe the problem of an unsteady mixed convection stagnation point flow and heat transfer past a stationary surface in an incompressible viscous fluid numerically.Design/methodology/approachThe governing nonlinear partial differential equations are transformed into a system of ordinary differential equations by a similarity transformation, which is then solved numerically by a Runge – Kutta – Fehlberg method with shooting technique and a collocation method, namely, the bvp4c function.FindingsThe effects of the governing parameters on the fluid flow and heat transfer characteristics are illustrated in tables and figures. It is found that dual (upper and lower branch) solutions exist for both the cases of assisting and opposing flow situations. A stability analysis has also been conducted to determine the physical meaning and stability of the dual solutions.Practical implicationsThis theoretical study is significantly relevant to the applications of the heat exchangers placed in a low-velocity environment and electronic devices cooled by fans.Originality/valueThe case of suction on unsteady mixed convection flow at a three-dimensional stagnation point has not been studied before; hence, all generated numerical results are claimed to be novel.

Transportation of heat generation/absorption and radiative heat flux in homogeneous–heterogeneous catalytic reactions of non-Newtonian fluid (Oldroyd-B model)

BackgroundThis study addresses the three-dimensional (3D) stagnation point flow of non-Newtonian material (Oldroyd-B) with magnetohydrodynamics. Furthermore, Ohmic heating and radiative flux are used in the modeling of energy expression. The surface is convectively heated. Equal strengths of diffusions for homogeneous and heterogeneous reactions are counted. Results are computed and presented graphically. Heat transfer rate is numerically discussed through table. MethodHere the nonlinear differential system first converted into ordinary differential equation through implementation of appropriate similarity variables. The obtained ordinary system is tackled through homotopy technique for convergent solutions. The outcomes are presented through different graphs and discussed in section six. OutcomesThe remarkable results of the present communication which is obtained from the semi analytical method i.e., “homotopy method” is summarized as(i) Opposite impact is noticed for velocity components i.e., (f′(ξ), g(ξ)) for rising fluid parameter and rotation parameter.(ii) The temperature is direct relation with Biot number and radiative variable.(iii) Heat transfer rate is more versus Biot number and radiation variable.(iv) The concentration field shows opposite impact versus homogeneous and heterogeneous parameters.

Effect of Thermal Radiation on a Three-dimensional Stagnation Point Region in Nanofluid under Microgravity Environment

The unsteady three dimensional boundary layer flow near a stagnation point region is studied numerically under the influence of microgravity environment. The boundary layer plate was embedded by the nanofluid with nanosized copper particles and water as a based fluid together with thermal radiation effect. The problem was mathematically formulated in term of coupled governing equations consisting of continuity, momentum and energy equations derived from the fundamental physical principles with Tiwari and Das nanofluid model. Boundary layer and Boussinesq approximation were then applied to the coupled equations and then reduced into non-dimensional equations to lessen the complexity of the problem using semi-similar transformation technique. Implicit finite different method known as Keller box method was used in this problem. The problem was then analyzed in terms of physical quantities of principal interest known as skin frictions and Nusselt number which explained the flow behavior and heat transfer analysis. From the outcome of the analysis, it was found that the parameter values for curvature ratio lead to the different cases of the stagnation point flow which is either plane stagnation flow or asymmetry stagnation flow. On the other hand, by increasing the nanoparticles volume fraction which is one of the nanofluid parameter may increase the skin frictions on both x- and y- directions. The presence of thermal radiation parameter was found to have increased the rate of change of heat transfer at the boundary layer flow.

G-Jitter Free Convection Flow of Nanofluid in The Three-Dimensional Stagnation Point Region

The three dimensional free convection boundary layer flow near a stagnation point region is embedded in viscous nanofluid with the effect of g-jitter is studied in this paper. Copper (Cu) and aluminium oxide (Al2O3) types of water base nanofluid are cho- sen with the constant Prandtl number, Pr=6.2. Based on Tiwari-Das nanofluid model, the boundary layer equation used is converted into a non-dimensional form by adopting non- dimensional variables and is solved numerically by engaging an implicit finite-difference scheme known as Keller-box method. Behaviors of fluid flow such as skin friction and Nusset number are studied by the controlled parameters including oscillation frequency, amplitude of gravity modulation and nanoparticles volume fraction. The reduced skin friction and Nusset number are presented graphically and discussed for different values of principal curvatures ratio at the nodal point. The numerical results shows that, in- crement occurs in the values of Nusset number with the presence of solid nanoparticles together with the values of the skin friction. It is worth mentioning that for the plane stagnation point there is an absence of reduced skin friction along the y-direction where as for axisymmetric stagnation point, the reduced skin friction for both directions are the same. As nanoparticles volume fraction increased, the skin friction increased as well as the Nusset number. The results, indicated that skin frictions of copper are found higher than aluminium oxide.

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