Stagnation Point Flow Of Nanofluid Research Articles

Analysis of Hybrid Nanofluid Stagnation Point Flow over a Stretching Surface with Melting Heat Transfer

The behavior of hybrid nanofluid and stagnation point flow toward a stretched surface along with melting heat transfer, second-order slip, electric field, and magnetic field effect is investigated in this study. Hybrid nanoparticles alumina A l 2 O 3 and copper (Cu) are considered with the base fluids water H 2 O . The PDEs with corresponding boundary constraints are transformed into a set of nonlinear ODEs using similarities transformation. The set of nonlinear ODEs are analyzed analytically using semianalytical method HAM in Mathematica software. Dual solution is determined which relaying on the emerging parameters included magnetic field, volume fractions, electric field, dimensionless surface velocity slip factors, Eckert number, and Prandtl number. The results are shown in the velocity and temperature curves as well as skin friction coefficient and local Nusselt number. The analysis shows that velocity profile is an increasing function of slip parameter, electric field, while reducing function of magnetic field. Temperature profile is an increasing function of magnetic field parameter, electric field parameter, volume fraction parameter, and Eckert number, while reducing function of Prandtl number. The main outcomes are as follows that hybrid nanofluids are higher thermal properties as compared to conventional fluids. As a result, hybrid nanofluid has numerous uses in engineering cosmetics, automotive industry, home industry, for cancer treatment, food packaging, pharmaceuticals, fabrics, paper plastics, paints, ceramics, food colorants, and soaps as well.

Numerical Study for Magnetohydrodynamic (MHD) Unsteady Maxwell Nanofluid Flow Impinging on Heated Stretching Sheet

The numerous applications of Maxwell Nanofluid Stagnation Point Flow, such as those in production industries, the processing of polymers, compression, power generation, lubrication systems, food manufacturing and air conditioning, among other applications, require further research into the effects of various parameters on flow phenomena. In this paper, a study has been carried out for the heat and mass transfer of Maxwell nanofluid flow over the heated stretching sheet. A mathematical model with constitutive expressions is constructed in partial differential equations (PDEs) through obligatory basic conservation laws. A series of transformations are then used to take the system into an ordinary differential equation (ODE). The boundary conditions (BCs) are also treated similarly for transforming into first-order ordinary differential equations (ODEs). Then these ODEs are computed by using the Shooting Method. The effect of factors on the skin friction coefficient, the local Nusselt number, and the local Sherwood number are explored, and the results are displayed graphically. The obtained results demonstrate that by increasing the values of the Maxwell and slip velocity parameters, velocity deescalates. For investigators tasked with addressing unresolved difficulties in the realm of enclosures used in industry and engineering, we thought this work would serve as a guide.

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.

Unsteady Separated Stagnation Point Flow of Nanofluid past a Moving Flat Surface in the Presence of Buongiorno's Model

This paper explores energy and mass transport behavior of unstable separated stagnation point flow of nanofluid over a moving flat surface along with Buongiorno’s model. Characteristic of Brownian diffusion and thermophoresis are considered. Additionally, characteristics of chemical reaction is taken into account. A parametric investigation is performed to investigate the outcome of abundant parameters such as temperature, velocity and concentration. An appropriate equation is converting into a set of ODEs through employing appropriate transformation. The governing equations has been solved numerically by using the classical fourth-order Runge-Kutta integration technique combined with the conventional shooting procedure after adapting it into an initial value problem. Our findings depict that the temperature field θ(ζ) improves for augmenting values of theromophoresis parameter (Nt) with dual solutions of attached flow without inflection and flow with inflection. Also, the difference of Brownian motion parameter (Nb) with two different solutions of attached flow exists with energy profile. It can be found that an energy profile θ(ζ) elevates due to augmenting values of (Nb). It has been perceived that thermal boundary layer thickness elevates due to large amount of Brownian motion parameter (Nb).

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.

Thermal Radiation Effects on Unsteady Stagnation Point Nanofluid Flow in View of Convective Boundary Conditions

The present communication particularizes nonlinear convective non-Newtonian stagnation point flow and heat transference effects in stretchable flow of nanofluid. Magnetohydromagnetic steady viscous flow of nanofluid is examined. Heat transfer attributes of nanofluids are addressed via a numerical algorithm. Conductivity and diffusivity characteristics of fluid are depending on temperature and concentration and furthermore, on mass conservation, momentum, energy, and concentration yield partial differential equations (PDEs). The boundary layer flow concept pioneered by Prandtl has been employed to simplify the nonlinear constitutive flow laws which are then changed to ordinary differential equations. A built-in bvp4c algorithm in Mathematica software yields convergent outcomes of nonlinear (ODEs) systems. A comprehensive analysis has been made elucidating the physical significance of various governing parameters effects presented graphically. Additionally, the flow nature was confirmed versus streamlines.

Mix convection non- boundary layer flow of unsteady MHD oblique stagnation point flow of nanofluid

This article demonstrates the analysis of hydrodynamics in the existence of a magnetic field. Heat transfer is analyzed for the unsteady flow of non-Newtonian fluid. The thermal conductivity is enhanced by introducing nanoparticles in the non-Newtonian fluid. Magnetohydrodynamics is introduced to control the turbulence in the flow. The dimensional equations satisfying the stated assumptions of the fluid flow and the motion of nanoparticles are presented. Fourier law is incorporated in the evaluation of heat flux. The analysis is tested in the fixed frame of reference. The mathematical coupled equations of motion are solved numerically. It is concluded that the Casson parameter leads to enhance velocity profile whereas the temperature profile is declined.

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).

Unsteady EMHD stagnation point flow over a stretching/shrinking sheet in a hybrid Al2O3-Cu/H2O nanofluid

The present study analyses the unsteady electro-magnetohydrodynamic (EMHD) stagnation point flow in a hybrid nanofluid concerning a stretching/shrinking sheet to which boundary-layer theory is applied. By simplifying the governing differential equations, the ordinary differential equations system is accomplished utilising the appropriate similarity conversions. The bvp4c method in the MATLAB systems software is implemented since this approach is competent in initiating non-uniqueness solutions once sufficient initial assumptions are made available. The results reveal that the skin friction coefficient and the local Nusselt number rise by the inclusion of nanoparticles. The electrical and magnetic field coordination result from the Lorentz force emerges to postpone the progression of the fluid. Moreover, the heat transfer characteristic is exaggerated when the electric and magnetic parameters are involved in the hybrid nanofluid stagnation point flow. The unsteadiness parameter, however, has a decreasing impact on the heat transfer performance.

Numerical Study of Nanofluid Transport Subjected to the Collective Approach of Generalized Slip Condition and Radiative Phenomenon

This study investigates theoretically, the effects of axisymmetric magnetohydrodynamic stagnation point flow of nanofluid over a surface lubricated by taking the general slip condition: The application perspective in biological farming and irrigation system. The impacts of radiation, chemical reaction, thermophoresis, and Brownian motions are further taken into account. In this model, PDEs are appropriately transformed into dimensionless ODEs. A numeric techniques BVP4C is implemented for the solutions of all the involved transport variables. Influences by the physical significance parameters on the velocity, temperature, and concentration profiles are studied. Physically, the effects of the skin friction coefficient on the heat transfer and concentration rate at the surface are analyzed. The Lorentz force has visible diversity on the flow properties. A transition of slip to no-slip condition is evident in the present study.

MHD Heat and Mass Transfer Nanofluid Stagnation Point Flow Along a Stretching Sheet Influenced by Thermal Radiation

MHD Heat and Mass Transfer Nanofluid Stagnation Point Flow Along a Stretching Sheet Influenced by Thermal Radiation

MHD Stagnation Point Flow in Nanofluid Over Shrinking Surface Using Buongiorno's Model: A Stability Analysis

An analysis has been performed using the Buongiorno model on the nanofluid steady 2D stagnation point flow magnetohydrodynamic (MHD) over the shrinking surface to test its stability. Transforming the governing partial equations into a set of ordinary differential equation (ODE) and solved the equations numerically. In this paper, the impact of Brownian motion and thermophoresis has been considered and can be seen in ODE. The physical quantities of interest such as skin friction, local Nusselt number, local Sherwood number as well as the velocity and temperature profiles are acquired by numerical findings for some values of governing parameters such as ?, M, Pr, Le, Nb and Nt. Results show that duality of solutions exist for certain values e <-1 while unique solution exist when e >-1. On the other hand, as the parameter of M increased, the gradient of velocity increased, the rate of transmission heat and mass improved. Throughout the analysis, it demonstrates a linearly stable first solution in comparison to linearly unstable second solution.

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.

Spectral quasi-linearization for MHD nanofluid stagnation boundary layer flow due to a stretching/shrinking surface

This article concentrates on the effect of MHD heat mass transfer on the stagnation point nanofluid flow over a stretching or shrinking sheet with homogeneous-heterogeneous reactions. The flow analysis is disclosed in the neighborhood of stagnation point. Features of heat transport are characterized with Newtonian heating. The homogeneous-heterogeneous chemical reaction between the fluid and diffusing species is included in the mass diffusion equation. The MHD stagnation boundary layer flow is explored in the presence of heat generation/absorption. Numerical convergent solutions are computed via the spectral quasi-linearization method (SQLM). The physical aspects of different parameters are discussed through graphs.

Slip Effects on Unsteady Oblique Stagnation Point Flow of Nanofluid in a View of Inclined Magnetic Field

This study may be applicable in heavy power engine and cooling of a nuclear reactor, insulation for buildings, petroleum reservoir operations, and magnetic material processing solar energy collectors. In this manuscript, the slip results are evaluated for the non-Newtonian fluid on the oblique stagnation point flow of induced magnetic field over the oscillating surface. The valuation of heat flux is examined through the Fourier law of heat transfer. The metallic nanoparticle Copper Cu is within the base fluid, and water is utilized in the analysis. Nanofluids have benefits such as steadiness of the working fluid, decreasing blockage, clogs, decreasing prices, decreasing the friction coefficient, and decreasing the size of the heat transfer system. Similarity variables are utilized to convert the developed flow into higher nonlinear coupled ordinary differential equations (ODE) which are tackled numerically using a mathematical technique such as the bvp4c method in Maple and Matlab software. According to the present geometry, the flow behavior of the operating nanofluid has analyzed by stream lines. Disparities in velocity and temperature profile are demonstrated by graphs to describe the effects of controlling parameters. The Casson fluid parameter enhances the velocity of the fluid. The system heats up by the impact of Joule heating and dissipation.

Numerical analysis of oblique stagnation point flow of nanofluid over a curved stretching/shrinking surface

This work analyses the heat transfer characteristics and the flow properties for two-dimensional oblique stagnation point flow of viscous, incompressible nanofluid over a curved stretching/shrinking surface. The nanofluid mixture is prepared by suspending the nanoparticles into the base fluid water. The governing equations are transformed into a non-linear coupled differential equation and are solved through bvp4c function in MATLAB. The assessment of the present result confirms that the addition of nanoparticles in base fluid strengthens the drag force and lowers the heat transfer rate at the surface. For stable solution, the skin friction coefficient is maximum on the flat surface as compared to the curved surface though the rate of heat transfer is same both over a flat surface and curved surface, however, for the unstable solution it is higher over the flat surface compared to the curved surface. Moreover, the increment of shrinking strengthens the drag force and lowers the heat transfer rate at the surface.

Modeling and dual solutions for magnetized mixed convective stagnation point flow of upper convected Maxwell fluid model with second‐order velocity slip

In the present work, we have studied a numerical solutions of MHD stagnation point flow of nanofluid over a stretching/shrinking sheet with mass suction condition. We have used the upper convected Maxwell (UCM) fluid model for the development of momentum equation and utilized it to explore the characteristics of elasticity of this model. We used the Buongiorno nanofluid model to develop the equations for the present problem. The governing flow, energy, and concentration equations are changed into the ordinary differential equations by means of suitable transformation. The subsequent ordinary ones are solved numerically using bvp4c scheme in MATLAB. The combined results of buoyancy forces, double slip (first‐ and second‐order slip), and elasticity have been investigated, and the influence of various flow parameters such as Hartmann number, suction parameter, and stretching/shrinking parameter on the skin friction coefficient, local Nusselt number, Sherwood number, and streamlines is studied and exposed through graphs. It is found that mass suction parameter and elasticity of UCM fluid increase the range of buoyancy forces for the existence of dual solutions. Also, buoyancy force increases the range of stretching/shrinking parameter where solution exists.

Cu-Al2O3/Water Hybrid Nanofluid Stagnation Point Flow Past MHD Stretching/Shrinking Sheet in Presence of Homogeneous-Heterogeneous and Convective Boundary Conditions

The intent of this research was to present numerical solutions to homogeneous–heterogeneous reactions of the magnetohydrodynamic (MHD) stagnation point flow of a Cu-Al2O3/water hybrid nanofluid induced by a stretching or shrinking sheet with a convective boundary condition. A proper similarity variable was applied to the system of partial differential equations (PDEs) and converted into a system of ordinary (similarity) differential equations (ODEs). These equations were solved using Matlab’s in-built function (bvp4c) for various values of the governing parameters numerically. The present investigation considered the effects of homogeneous–heterogeneous reactions and magnetic field in the hybrid nanofluid flow. It was observed that dual solutions were visible for the shrinking sheet, and an analysis of stability was done to determine the physically realizable in the practice of these solutions. It was also concluded that hybrid nanofluid acts as a cooler for some increasing parameters. The magnetohydrodynamic parameter delayed the boundary layer separation; meanwhile, the nanoparticle volume fraction quickened the separation of the boundary layer that occurred. In addition, the first solution of hybrid nanofluid was found to be stable; meanwhile, the second solution was not stable. This study is therefore valuable for engineers and scientists to get acquainted with the properties of hybrid nanofluid flow, its behavior and the way to predict it.

Cattaneo–Christov Heat Flux Model in Flow of Copper Water Nanofluid Through a Stretching/Shrinking Sheet on Stagnation Point in Presence of Heat Generation/Absorption and Activation Energy

The authors have developed a model to mathematically study Cu–water nanofluid stagnation point flow past a stretching/shrinking sheet. Generalized Fourier’s model famously known as Cattaneo–Christov model in presence of heat generation/absorption is utilized to analyze the heat transfer. The effects of thermal radiation, suction, slip and activation energy are also reported. Moreover, the thermal conductivity of nanofluid is considered as a variable. Similarity transformations are utilized to write the equations in non-dimensional forms. The numerical solution of the flow problem is achieved by means of Runge–Kutta–Fehlberg method. Results depicting the behavior of solution profiles are presented via graphs and tables. Influence on skin friction, heat and mass transfer rates for varying strength of key parameters are also reported. Results show that thermal relaxation parameter and thermal radiation help to escalate heat transfer whereas activation energy compels mass transfer rate to decrease. Slip and suction are seen to decrease mass transfer and increase heat transfer, respectively.

Dual solutions in MHD stagnation point flow of nanofluid induced by porous stretching/shrinking sheet with anisotropic slip

In this article, the steady three-dimensional stagnated flow induced by a porous moving system is investigated. The flow field and thermal distribution are subject to anisotropic slip and a magnetic field. The existing nonlinear equations are unraveled numerically using a bvp4c code in Matlab. The impact of various parameters on flow profiles temperature surface friction and surface heat transfer rate is put together in graphs and tables. The accomplished results depict that the velocity fields enhance for both S < 0 (suction) and S > 0 (injection). Similarly, it is noticed that surface shear stress and heat transfer possess stronger behavior for the case of injection. The behavior of temperature fields is opposite for upper and lower solutions when checked for the Prandtl number Pr. Stability analysis shows that the primary solution is stable and substantially feasible, whereas the second solution is not stable. The velocity h(η) decays with the magnetic field for both solutions.