Orthogonal Stagnation-point Flow Research Articles

A thin layer lubricant surface applications due to nonlinear radiated hybrid nanoparticles with orthogonal stagnation point flow

ABSTRACT The improved thermal association of heat transfer is considerably observed due to hybrid nanoparticles. Being to suspension of base fluids with two distinct nanoparticles, the stable properties of hybrid nanofluids are measured. Current contribution reports the enhancement in thermal impact of water (base liquid) uniformly decomposed with hybrid nanoparticles theoretically. The hybrid nanofluid properties are justified with copper and aluminum oxide nanoparticles. With improved heat transfer mechanism, the motivations for observing the aspect of lubrication phenomenon in the vicinity of stagnation points are associated to the manufacturing systems and chemical processes ample applications in fluid bearing, assembling of thin films, coating and printing. Moreover, the treatment of heat transfer is further influenced by nonlinear radiation and mixed convection applications. The dimensionless variables successfully transformed the system into a dimensionless form, which is further solved using the Keller box method. The comparative heating transfer onsets are predicted for the traditional nanofluid with suspension and hybrid nanofluid with decomposition. The results show that the lubrication phenomenon controls the wall shear force while enhancement in Nusselt number is noticed. Increasing observations for skin friction and Nusselt number are resulted for hybrid nanofluid as compared to simple nanofluid.

Non-linear radiation influence on oblique stagnation point flow of Maxwell fluid

Non-linear thermal radiation effects on non-aligned stagnation point flow of Maxwell fluid have been carried out in the present investigation. It is observed that the non-linear radiation augments the temperature and heat transfer rate. This physical phenomenon is translated into a system of partial differential equations (PDEs). After useful transformation, these non-linear constitutive equations are transformed into a system of ordinary differential equations (ODEs) and interpreted numerically by means of parallel shooting technique. Effects of pertinent parameters on flow and heat transfer are elaborated through tables and graphs. It is observed that radiation and surface heating enhance the rate of heat transfer, however Prandtl number has inverse relation with thermal boundary layer thickness. It has been observed that for increasing Prandtl number, heat transfer rate enhances. The detailed discussion of heat transfer rate is also presented in this study. Flow pattern is judged through streamlines graphs. It is also observed that oblique stagnation point flow behaves like orthogonal stagnation point flow, when free stream velocity is very large as compared to stretching velocity.

Effect of temperature on the MHD stagnation-point flow past an isothermal plate for a Boussinesquian Newtonian and micropolar fluid

PurposeThis paper aims to analyze the steady two-dimensional stagnation-point flow of an electrically conducting Newtonian or micropolar fluid when the obstacle is uniformly heated.Design/methodology/approachThe governing boundary layer equations are transformed into a system of ordinary differential equations using appropriate similarity transformations. Some analytical considerations about existence and uniqueness of the solution are obtained. The system is then solved numerically using the bvp4c function in MATLAB.FindingsIf the temperature of the obstacle Tw coincides with the environment temperature T0, then the motion reduces to the usual orthogonal stagnation-point flow; if Tw = T0, then it is necessary to include in the similarity function describing the velocity an oblique part due to the temperature. Also, the presence of a uniform external magnetic field orthogonal to the obstacle is examined. In all cases, the motion is reduced to a system of nonlinear ordinary differential equations with boundary conditions, whose solution is discussed numerically when the Prandtl and the Hartmann number varies.Originality/valueThe present results are original and new for the problem of magnetohydrodynamic mixed convection in the plane stagnation-point flow of a Newtonian or a micropolar fluid over a vertical flat plate. At infinity, the motion approaches the orthogonal stagnation-point flow of an inviscid fluid; the effect of an uniform external magnetic field is considered, and the obstacle has a uniform temperature.

MHD orthogonal stagnation-point flow of a micropolar fluid with the magnetic field parallel to the velocity at infinity

An exact solution is obtained for the steady MHD plane orthogonal stagnation-point flow of a homogeneous, incompressible, electrically conducting micropolar fluid over a rigid uncharged dielectric at rest. The space is permeated by a not uniform external magnetic field He and the total magnetic field H in the fluid is parallel to the velocity at infinity. The results obtained reveal many interesting behaviours of the flow and of the total magnetic field in the fluid and in the dielectric. In particular, the thickness of the layer where the viscosity appears depends on the strength of the magnetic field. The effects of the magnetic field on the velocity and on the microrotation profiles are presented graphically and discussed.

MHD stagnation-point flow of an electrically conducting fluid on the surface of another quiescent fluid

An analysis is made of the orthogonal stagnation-point flow of an incompressible viscous electrically conducting fluid on the surface of another incompressible viscous electrically conducting quiescent fluid in the presence of a uniform magnetic field normal to the interface between the fluids. It is found that for small magnetic Reynolds number, the velocity at a point in the upper fluid increases and that at a point in the lower fluid decreases with increase in the magnetic field. It is also observed from the temperature distributions in the two given fluids that the interface temperature increases with increase in the magnetic field.

Oscillatory oblique stagnation-point flow towards a plane wall

Two-dimensional oscillatory oblique stagnation-point flow towards a plane wall is investigated. The problem is a generalisation of the steady oblique stagnation-point flow examined by previous workers. Far from the wall, the flow is composed of an irrotational orthogonal stagnation-point flow with a time-periodic strength, a simple shear flow of constant vorticity, and a time-periodic uniform stream. An exact solution of the Navier–Stokes equations is sought for which the flow stream function depends linearly on the coordinate parallel to the wall. The problem formulation reduces to a coupled pair of partial differential equations in time and one spatial variable. The first equation describes the oscillatory orthogonal stagnation-point flow discussed by previous workers. The second equation, which couples to the first, describes the oblique component of the flow. A description of the flow velocity field, the instantaneous streamlines, and the particle paths is sought through numerical solutions of the governing equations and via asymptotic analysis.

Oblique stagnation-point flow of a viscoelastic fluid with heat transfer

The two-dimensional forced convection stagnation-point flow and heat transfer of a viscoelastic second grade fluid obliquely impinging on an infinite plane wall is considered as an exact solution of the full partial differential equations. This oblique flow consists of an orthogonal stagnation-point flow to which a shear flow whose vorticity is fixed at infinity is added. The relative importance of these flows is measured by a parameter γ . The viscoelastic problem is reduced to two ordinary differential equations governed by the Weissenberg number W e , two parameters α and β , the later being a free parameter β , introduced by Tooke and Blyth [A note on oblique stagnation-point flow, Physics of Fluids 20 (2008) 033101-1–3], and the Prandtl number Pr . The two cases when α = β and α ≠ β are, respectively, considered. Physically the free parameter may be viewed as altering the structure of the shear flow component by varying the magnitude of the pressure gradient. It is found that the location of the separation point x s of the boundary layer moves continuously from the left to the right of the origin of the axes ( x s < 0 ).

A note on oblique stagnation-point flow

Previous analyses of oblique stagnation-point flow at a plane wall are discussed and unified with reference to a free parameter. The oblique flow consists of orthogonal stagnation-point flow to which is added a shear flow whose vorticity is fixed at infinity. Physically the free parameter may be viewed as altering the structure of the shear flow component by varying the magnitude of the pressure gradient. For large adverse pressure gradients, the shear component has a region of reversed flow near the wall. Remarkably, combining an orthogonal flow with shear flows featuring different levels of reversed flow always produces the same oblique flow but with the stagnation-point of attachment shifted along the wall by a predictable amount.

Effect of stretching on interfacial stability

The effect of stretching on the stability of a horizontal interface between two fluids with different viscosities and densities is discussed. A local elongational flow acts to reduce the amplitude of perturbations and increase the wavelength of periodic waves, and thereby alter the instantaneous growth rate of disturbances. Linear stability analysis for Stokes flow reveals that, in the case of a horizontal interface between two semi-infinite fluids subjected to orthogonal stagnation-point flow, interfacial stretching is not able to suppress the Rayleigh-Taylor instability of unstably stratified fluids. In contrast, stretching is able to suppress the growth of periodic waves on the surface of a flat film resting on a horizontal surface. Numerical simulations based on the boundary-integral method for Stokes flow confirm that localized perturbations on the film surface are suppressed when the elongational flow is sufficiently strong.

Evolution Equations for the Surface Concentration of an Insoluble Surfactant; Applications to the Stability of an Elongating Thread and a Stretched Interface

The general form of the convection–diffusion equation governing the evolution of the surface concentration of an insoluble surfactant over an evolving interface is reviewed and discussed for three-dimensional, axisymmetric, and two-dimensional configurations. The linearized form of the evolution equation is then derived around cylindrical and planar shapes in a framework that is suitable for carrying out a linear stability analysis for axisymmetric or two-dimensional perturbations. Particular attention is paid to the cases of quiescent unperturbed fluids, unidirectional shear flow, and elongational flow. By way of application, the linearized transport equations are combined with Stokes-flow hydrodynamics to investigate the stability of an elongating cylindrical viscous thread suspended in an ambient viscous fluid or in a vacuum, and the stability of a two-dimensional interface separating two semi-infinite fluids and stretched under the action of an orthogonal stagnation-point flow. The results illustrate the possibly important role of the surfactant on the linear growth of periodic waves on the cylindrical interface, and reveal that the surfactant has no effect on the stability of the planar interface.