Thermal radiation and slip effects on MHD stagnation point flow of nanofluid over a stretching sheet

Present model is devoted for the stagnation point flow of nanofluid with magneto-hydrodynamics (MHD) and thermal radiation effects passed over a stretching sheet. Moreover, we have considered the combined effects of velocity and thermal slip. Condition of zero normal flux of nanoparticles at the wall for the stretched flow phenomena is yet to be explored in the literature. Convinced partial differential equations of the model are transformed into the system of coupled nonlinear differential equations and then solved numerically. Graphical results are plotted for velocity, temperature and nanoparticle concentration for various values of emerging parameters. Variation of stream lines, skin friction coefficient, local Nusselt and Sherwood number are displayed along with the effective parameters. Final conclusion has been drawn on the basis of both numerical and graphs results.     

Induced magnetic field stagnation point flow of nanofluid past convectively heated stretching sheet with Buoyancy effects

This paper presents the buoyancy effects on the magneto-hydrodynamics stagnation point flow of an incompressible,viscous,and electrically conducting nanofluid over a vertically stretching sheet.The impacts of an induced magnetic field and viscous dissipation are taken into account.Both assisting and opposing flows are considered.The overseeing nonlinear partial differential equations with the associated boundary conditions are reduced to an arrangement of coupled nonlinear ordinary differential equations utilizing similarity transformations and are then illuminated analytically by using the optimal homotopy investigation strategy(OHAM).Graphs are introduced and examined for different parameters of the velocity,temperature,and concentration profile.Additionally,numerical estimations of the skin friction,local Nusselt number,and local Sherwood number are explored using numerical values.     

MHD flow of nanofluids over an exponentially stretching sheet in a porous medium with convective boundary conditions

This article concentrates on the steady magnetohydrodynamic(MHD) flow of viscous nanofluid. The flow is caused by a permeable exponentially stretching surface. An incompressible fluid fills the porous space. A comparative study is made for the nanoparticles namely Copper(Cu), Silver(Ag), Alumina(Al2O3) and Titanium Oxide(TiO2). Water is treated as a base fluid. Convective type boundary conditions are employed in modeling the heat transfer process. The non-linear partial differential equations governing the flow are reduced to an ordinary differential equation by similarity transformations. The obtained equations are then solved for the development of series solutions. Convergence of the obtained series solutions is explicitly discussed. The effects of different parameters on the velocity and temperature profiles are shown and analyzed through graphs.     

Flow and heat transfer of a nanofluid over a hyperbolically stretching sheet

This article explores the boundary layer flow and heat transfer of a viscous nanofluid bounded by a hyperbolically stretching sheet. Effects of Brownian and thermophoretic diffusions on heat transfer and concentration of nanoparticles are given due attention. The resulting nonlinear problems are computed for analytic and numerical solutions. The effects of Brownian motion and thermophoretic property are found to increase the temperature of the medium and reduce the heat transfer rate. The thermophoretic property thus enriches the concentration while the Brownian motion reduces the concentration of the nanoparticles in the fluid. Opposite effects of these properties are observed on the Sherwood number.     

Influences of Marangoni convection and variable magnetic field on hybrid nanofluid thin-film flow past a stretching surface

Investigations on thin-film flow play a vital role in the field of optoelectronics and magnetic devices. Thin films are reasonably hard and thermally stable but quite fragile. The thermal stability of a thin film can be further improved by incorporating the effects of nanoparticles. In the current work, a stretchable surface is considered upon which hybrid nanofluid thin-film flow is taken into account. The idea of augmenting heat transmission by making use of a hybrid nanofluid is a focus of the current work. The flow is affected by variations in the viscous forces, along with viscous dissipation effects and Marangoni convection. A time-constrained magnetic field is applied in the normal direction to the flow system. The equations governing the flow system are shifted to a non-dimensional form by applying similarity variables. The homotopy analysis method is employed to find the solution to the resultant equations. It is noticed in this study that the flow characteristics decline with augmentation of magnetic, viscosity and unsteadiness parameters while they increase with enhanced values of thin-film parameters. Thermal characteristics are supported by increasing values of the Eckert number and the unsteadiness parameter and opposed by the viscosity parameter and Prandtl number. The numerical impact of different emerging parameters upon skin friction and the Nusselt number is calculated in tabular form. A comparison of current work with established results is carried out, with good agreement.     

Unsteady MHD flow and heat transfer near stagnation point over a stretching/shrinking sheet in porous medium filled with a nanofluid

In this article, the unsteady magnetohydrodynamic （MHD） stagnation point flow and heat transfer of a nanofluid over a stretching/shrinking sheet is investigated numerically. The similarity solution is used to reduce the governing system of partial differential equations to a set of nonlinear ordinary differential equations which are then solved numerically using the fourth-order Runge-Kutta method with shooting technique. The ambient fluid velocity, stretching/shrinking velocity of sheet, and the wall temperature are assumed to vary linearly with the distance from the stagnation point. To investigate the influence of various pertinent parameters, graphical results for the local Nusselt number, the skin friction coefficient, velocity profile, and temperature profile are presented for different values of the governing parameters for three types of nanoparticles, namely copper, alumina, and titania in the water-based fluid. It is found that the dual solution exists for the decelerating flow. Numerical results show that the extent of the dual solution domain increases with the increases of velocity ratio, magnetic parameter, and permeability parameter whereas it remains constant as the value of solid volume fraction of nanoparticles changes. Also, it is found that permeability parameter has a greater effect on the flow and heat transfer of a nanofluid than the magnetic parameter.     

Brownian motion and thermophoresis effects on unsteady stagnation point flow of Eyring-Powell nanofluid: a Galerkin approach

This article concerns the analysis of an unsteady stagnation point flow of Eyring-Powell nanofluid over a stretching sheet. The influence of thermophoresis and Brownian motion is also considered in transport equations. The nonlinear ODE set is obtained from the governing nonlinear equations via suitable transformations. The numerical experiments are performed using the Galerkin scheme. A tabular form comparison analysis of outcomes attained via the Galerkin approach and numerical scheme (RK-4) is available to show the credibility of the Galerkin method. The numerical exploration is carried out for various governing parameters, namely, Brownian motion, steadiness, thermophoresis, stretching ratio, velocity slip, concentration slip, thermal slip, and fluid parameters, and Hartmann, Prandtl and Schmidt numbers. The velocity of fluid enhances with an increase in fluid and magnetic parameters for the case of opposing, but the behavior is reversed for assisting cases. The Brownian motion and thermophoresis parameters cause an increase in temperature for both cases (assisting and opposing). The Brownian motion parameter provides a drop-in concentration while an increase is noticed for the thermophoresis parameter. All the outcomes and the behavior of emerging parameters are illustrated graphically. The comparison analysis and graphical plots endorse the appropriateness of the Galerkin method. It is concluded that said method could be extended to other problems of a complex nature.     

Effects of variable properties on MHD heat and mass transfer flow near a stagnation point towards a stretching sheet in a porous medium with thermal radiation

The effect of variable viscosity and thermal conductivity on steady magnetohydrodynamic(MHD) heat and mass transfer flow of viscous and incompressible fluid near a stagnation point towards a permeable stretching sheet embedded in a porous medium are presented,taking into account thermal radiation and internal heat genberation/absorbtion.The stretching velocity and the ambient fluid velocity are assumed to vary linearly with the distance from the stagnation point.The Rosseland approximation is used to describe the radiative heat flux in the energy equation.The governing fundamental equations are first transformed into a system of ordinary differential equations using a scaling group of transformations and are solved numerically by using the fourth-order Rung-Kutta method with the shooting technique.A comparison with previously published work has been carried out and the results are found to be in good agreement.The results are analyzed for the effect of different physical parameters,such as the variable viscosity and thermal conductivity,the ratio of free stream velocity to stretching velocity,the magnetic field,the porosity,the radiation and suction/injection on the flow,and the heat and mass transfer characteristics.The results indicate that the inclusion of variable viscosity and thermal conductivity into the fluids of light and medium molecular weight is able to change the boundary-layer behavior for all values of the velocity ratio parameter λ except for λ = 1.In addition,the imposition of fluid suction increases both the rate of heat and mass transfer,whereas fluid injection shows the opposite effect.     

Numerical study of the onset of chemical reaction and heat source on dissipative MHD stagnation point flow of Casson nanofluid over a nonlinear stretching sheet with velocity slip and convective boundary conditions

The magnetohydrodynamic (MHD) stagnation point flow of Casson nanofluid over a nonlinear stretching sheet in the presence of velocity slip and convective boundary condition is examined. In this analysis, various effects such as velocity ratio, viscous dissipation, heat generation/absorption and chemical reaction are accentuated. Possessions of Brownian motion and thermophoresis are also depicted in this study. A uniform magnetic field as well as suction is taken into account. Suitable similarity transformations are availed to convert the governing nonlinear partial differential equations to a system of nonlinear ordinary differential equations and then series solutions are secured using a homotopy analysis method (HAM). Notable accuracy of the present results has been obtained with the earlier results. Impact of distinct parameters on velocity, temperature, concentration, skin friction coefficient,Nusselt number and Sherwood number is canvassed through graphs and tabular forms.     

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.     

Non-similar mixed convection analysis for magnetic flow of second-grade nanofluid over a vertically stretching sheet

The aspiration of this research is to explore the impact of non-similar modeling for mixed convection in magnetized second-grade nanofluid flow. The flow is initiated by the stretching of a sheet at an exponential rate in the upward vertical direction. The buoyancy effects in terms of temperature and concentration differences are inserted in the $x$-momentum equation. The aspects of heat and mass transfer are studied using dimensionless thermophoresis, Schmidt and Brownian motion parameters. The governing coupled partial differential system (PDEs) is remodeled into coupled non-similar nonlinear PDEs by introducing non-similar transformations. The numerical analysis for the dimensionless non-similar partial differential system is performed using a local non-similarity method via bvp4c. Finally, the quantitative effects of emerging dimensionless quantities on the non-dimensional velocity, temperature and mass concentration in the boundary layer are conferred graphically, and inferences are drawn that important quantities of interest are substantially affected by these parameters. It is concluded that non-similar modeling, in contrast to similar models, is more general and more accurate in convection studies in the presence of buoyancy effects for second-grade non-Newtonian fluids.     

Marangoni effects on forced convection of power-law liquids in a thin film over a stretching surface

The effect of Marangoni convection on the flow and heat transfer within a power-law liquid film on an unsteady stretching sheet is examined. The governing equations are non-dimensionalized using suitable transformation variables and the resulting transformed PDEs are then solved numerically by an implicit finite-difference scheme. Results for the velocity and temperature distributions, the free-surface temperature, and the wall temperature gradient are presented for various values of the unsteadiness parameter S, the power-law index n, the thermo-capillarity number M, and the modified Prandtl number Pr. The velocity and temperature distributions in the film are affected significantly by the thermally-induced Marangoni convection adjacent to the free surface. A fluid with a smaller Pr is more sensitive to the Marangoni effect. For Pr less than a moderate value (e.g., at selected values of n and ξ  , Pr?1$\mathit{Pr}?1$ for S=0.8$S=0.8$ and Pr?10$\mathit{Pr}?10$ for S=1.2$S=1.2$), the Marangoni effect tends to increase the heat transfer rate; whereas this impact diminishes in the high Pr regime.     

A uniformly valid series solution to the unsteady stagnation-point flow towards an impulsively stretching surface

The paper studies the problem of the unsteady two-dimensional stagnation-point flow of an incompressible viscous fluid over a flat deformable sheet. The flow is started impulsively from rest and the sheet is suddenly stretched in its own plane with a velocity proportional to the distance from the stagnation point. An analytical series solution is obtained by means of the homotopy analysis method (HAM). Also, the homotopy-Pade′ technique is employed. An explicit formula for the local friction coefficient is provided. The present formula, different from the perturbation solution, is accurate and uniformly valid for all dimensionless time in the whole spatial region and for all possible values of physical parameter λ, defined as the ratio of the potential flow velocity to the sheet sudden stretching velocity. Numerical tests are done to verify the present formula for its validity and accuracy.     

Exact solutions for the flow of Casson fluid over a stretching surface with transpiration and heat transfer effects

The effects of transpiration on forced convection boundary layer non-Newtonian fluid flow and heat transfer toward a linearly stretching surface are reported.The flow is caused solely by the stretching of the sheet in its own plane with a velocity varying linearly with the distance from a fixed point.The constitutive relationship for the Casson fluid is used.The governing partial differential equations corresponding to the momentum and energy equations are converted into non-linear ordinary differential equations by using similarity transformations.Exact solutions of the resulting ordinary differential equations are obtained.The effect of increasing Casson parameter,i.e.,with decreasing yield stress(the fluid behaves as a Newtonian fluid as the Casson parameter becomes large),is to suppress the velocity field.However,the temperature is enhanced as the Casson parameter increases.It is observed that the effect of transpiration is to decrease the fluid velocity as well as the temperature.The skin-friction coefficient is found to increase as the transpiration parameter increases.     

The effect of a non-aligned unit on double-screen frequency-selective surface transmission characteristics

Double-screen frequency-selective surfaces (FSSs) can bring about a better flattened effect and a rapidly declining edge. They are therefore an effective means to achieve outer-zone stealth of the radar cabin to detect radar waves. In this article, a double-screen wide-bandpass FSS structure is designed and the transmission characteristics of the units under alignment and non-alignment are simulated by means of the spectral domain approach. Meanwhile, the experimental parts fabricated by vacuum evaporation and lithography are tested in a microwave chamber. The results show that the aligned unit structure has good incident angle stability and can achieve high transmittance when the bandwidth is 3.3 GHz, and the transmission loss is less than 1 dB. When the units have a non-aligned structure, the bandwidth decreases and transmission loss increases with increasing incident angle.     

Casson fluid flow and heat transfer over a nonlinearly stretching surface

A boundary layer analysis is presented for non-Newtonian fluid flow and heat transfer over a nonlinearly stretching surface. The Casson fluid model is used to characterize the non-Newtonian fluid behavior. By using suitable transformations, the governing partial differential equations corresponding to the momentum and energy equations are converted into non-linear ordinary differential equations. Numerical solutions of these equations are obtained with the shooting method. The effect of increasing Casson parameter is to suppress the velocity field. However the temperature is enhanced with the increasing Casson parameter.     

Investigation of Ti6Al4V and AA7075 alloy embedded nanofluid flow over longitudinal porous fin in the presence of internal heat generation and convective condition

The thermal attributes of porous fin due to radiation and natural convection have been carried out in the presence of nanofluid flow. The geometry of the fin taken for the analysis is rectangular profiled longitudinal fin. The temperature-dependent internal heat generation condition is also considered along with Darcy's model. The two types of nanofluid containing titanium alloy(Ti6Al4V) and aluminium alloy(AA7075) immersed in water is considered for the investigation.The modelled nonlinear ordinary differential equation is numerically solved by the Runge–Kutta–Fehlberg technique. The impact of geometric parameter on the heat transfer analysis of the fin due to the flow of both nanofluids is plotted and consequences are physically interpreted. It is observed that the presence of the water-based titanium alloy better enhances the fin heat transfer rate.     

Effects of thermal radiation on Casson fluid flow and heat transfer over an unsteady stretching surface subjected to suction/blowing

The unsteady flow of a Casson fluid and heat transfer over a stretching surface in presence of suction/blowing are investigated.The transformed equations are solved numerically by using the shooting method.The exact solution corresponding to the momentum equation for the steady case is obtained.Fluid velocity initially decreases with the increase of unsteadiness parameter.Due to an increasing Casson parameter the velocity field is suppressed.Thermal radiation enhances the effective thermal diffusivity and the temperature rises.     

Oblique stagnation slip flow of a micropolar fluid towards a stretching/shrinking surface: A stability analysis

A numerical solution is obtained for the steady oblique stagnation-point flow of a micropolar fluid over a stretching or shrinking surface with velocity slip condition. Results are obtained for representative values of slip parameter, micropolar parameter and stretching/shrinking parameter for strong particle interaction micropolar fluid. Dual solutions are found for the case of shrinking surface. An analysis of stability of these dual solutions shows that the solution branch that proceeds to large stretching case is stable. The streamlines are not symmetric for the oblique stagnation-point flow and reversed flow are observed near to the shrinking surface. The streamlines plots show that increase of slip parameter will reduce/eliminate the existing of rotating flow near the surface that caused by the shrinking effect.