Boundary layer flow and heat transfer of a micropolar fluid near the stagnation point on a stretching vertical surface with prescribed skin friction

The steady laminar mixed convection boundary layer flow and heat transfer of a micropolar fluid near the stagnation point on a stretched vertical surface with prescribed skin friction were considered.The governing partial differential equations were transformed into a system of ordinary differential equations,which were then solved numerically using the shooting method.Results for the stretching velocity,the local Nusselt number,the temperature,and the velocity profiles are presented for various values of the mixed convection parameter λ and material parameter K when the Prandtl number is equal to 1.Both assisting（heated plate） and opposing（cooled plate） flow regions are considered.It is found that dual solutions exist for both assisting and opposing flows.

Dual solutions in boundary layer flow of Maxwell fluid over a porous shrinking sheet

An analysis is carried out for dual solutions of the boundary layer flow of Maxwell fluid over a permeable shrinking sheet. In the investigation, a constant wall mass transfer is considered. With the help of similarity transformations, the governing partial differential equations（PDEs） are converted into a nonlinear self-similar ordinary differential equation（ODE）. For the numerical solution of transformed self-similar ODE, the shooting method is applied. The study reveals that the steady flow of Maxwell fluid is possible with a smaller amount of imposed mass suction compared with the viscous fluid flow. Dual solutions for the velocity distribution are obtained. Also, the increase of Deborah number reduces the boundary layer thickness for both solutions.

Effects of Solid Matrix and Porosity of Porous Medium on Heat Transfer of Marangoni Boundary Layer Flow Saturated with Power-Law Nanofluids

The effect of the solid matrix and porosity of the porous medium are first introduced to the study of power-law nanofluids, and the Marangoni boundary layer flow with heat generation is investigated. Two cases of solid matrix of porous medium including glass balls and aluminum foam are considered. The governing partial differential equations are simplified by dimensionless variables and similarity transformations, and are solved numerically by using a shooting method with the fourth-fifth-order Runge-Kutta integration technique. It is indicated that the increase of the porosity leads to the enhancement of heat transfer in the surface of the Marangoni boundary layer flow.

Soret and Dufour effects on mixed convection unsteady MHD boundary layer flow over stretching sheet in porous medium with chemically reactive species

This paper studies the thermal-diffusion and diffusion thermo-effects in the hydro-magnetic unsteady flow by a mixed convection boundary layer past an imperme- able vertical stretching sheet in a porous medium in the presence of chemical reaction. The velocity of t^he stretching surface, the surface temperature, and the concentration are assumed to vary linearly with the distance along the surface. The governing partial differential equations are transformed into self-similar unsteady equations using similarity transformations .and solved numerically by the Runge-Kutta fourth order scheme in as- sociation with the shooting method for the whole transient domain from the initial state to the final steady state flow. Numerical results for the velocity, the temperature, the concentration, the skin friction, and the Nusselt and Sherwood numbers are shown graph- ically for various flow parameters. The results reveal that there is a smooth transition of flow from unsteady state to the final steady state. A special case of our results is in good agreement with an earlier published work.

Similarity Solutions of Unsteady Mixed Convective Boundary Layer Flow of Viscous Incompressible Fluid along Isothermal Horizontal Plate

Unsteady mixed convective boundary layer flow of viscous incompressible fluid along isothermal horizontal plate is analyzed through Similarity Solutions. The governing partial differential equations are transformed into ordinary differential equations using the similarity transformation and solved numerically along with shooting technique. The flow field for the fluid velocity, temperature and concentration at the plate surface are significantly influenced by the governing parameters such as unsteadiness parameter, permeability parameter, Prandtl number, Schmidt number and the other driving parameters. The results show that both fluid velocity and temperature decrease but no significant effect on concentration for the increasing values of Prandtl number. It is also exposed that velocity and concentration is higher at lower Schmidt number for low Prandtl fluid. Finally, the dependency of the Skin-friction co-efficient, Nusselt number and Sherwood number, which are of physical interest, are also illustrated in tabular form for the governing parameters.

Near continuum boundary layer flows at a flat plate

The problem of boundary layer flows at a flat plate surface with velocity-slip and temperature-jump boundary conditions is analyzed. With the velocity slip conditions, there are multiple physical factors lumped together, and the boundary layer solutions significantly change their behaviors. The self-similarity in the solutions degenerates, however, the problem is still an ordinary differential equation which can be solved. Shooting methods are applied to solve the flowfield. The results include velocity and temperature for both the surface and flowfield. Unlike the traditional Blasius fiat plate boundary layer solutions which are self-similar through all the plate boundary layer, the new solutions indicate that the front tip is actually a singularity point, especially at locations within one mean flee path from the leading edge.

Large-eddy simulation of turbulent boundary layer flow over multiple hills

Atmospheric boundary layer(ABL)flow over multiple-hill terrain is studied numerically.The spectral vanishing viscosity(SVV)method is employed for implicit large eddy simulation(ILES).ABL flow over one hill,double hills,and three hills are presented in detail.The instantaneous three-dimensional vortex structures,mean velocity,and turbulence intensity in mainstream and vertical directions around the hills are investigated to reveal the main properties of this turbulent flow.During the flow evolution downstream,the Kelvin-Helmholtz vortex,braid vortex,and hairpin vortex are observed sequentially.The turbulence intensity is enhanced around crests and reduced in the recirculation zones.The present results are helpful for understanding the impact of topography on the turbulent flow.The findings can be useful in various fields,such as wind energy,air pollution,and weather forecasting.

Effect of a chemical reaction on magnetohydrodynamic boundary layer flow of a Maxwell fluid over a stretching sheet with nanoparticles

The influences of the convective boundary condition and heat generation/absorption on magnetohydro- dynamic boundary layer flow of a Maxwell fluid over a stretching surface in the presence of nanoparticles have been numerically investigated. In the model, the physical mechanisms responsible for Brownian motion and thermophoresis with a chemical reaction are considered. Similarity equations are derived and then solved using the shooting method with the fourth-order Runge-Kutta integration scheme, The rates of heat and mass transfer are enhanced with a destructive chemical reaction and Blot number. The opposite influence is found with a generative chemical reaction in the presence of Brownian motion and the thermophoretic property.

Linear stability analysis of interactions between mixing layer and boundary layer flows

The linear instabilities of incompressible confluent mixing layer and boundary layer were analyzed.The mixing layers include wake,shear layer and their combination.The mean velocity profile of confluent flow is taken as a superposition of a hyperbolic and exponential function to model a mixing layer and the Blasius similarity solution for a flat plate boundary layer.The stability equation of confluent flow was solved by using the global numerical method.The unstable modes associated with both the mixing and boundary layers were identified.They are the boundary layer mode,mixing layer mode 1（nearly symmetrical mode）and mode 2（nearly anti-symmetrical mode）.The interactions between the mixing layer stability and the boundary layer stability were examined.As the mixing layer approaches the boundary layer,the neutral curves of the boundary layer mode move to the upper left,the resulting critical Reynolds number decreases,and the growth rate of the most unstable mode increases.The wall tends to stabilize the mixing layer modes at low frequency.In addition,the mode switching behavior of the relative level of the spatial growth rate between the mixing layer mode 1 and mode 2 with the velocity ratio is found to occur at low frequency.

BOUNDARY LAYER DEVELOPMENT OF PULSATILE BLOOD FLOW IN A TAPERED VESSEL

The problems of developing flow under unsteady oscillatory condition were studied in this paper by assuming that the tapered angle is small. The formula of velocity distribution was obtained. The analyses for the results show that the blood flow in a converging tapered vessel remains a developing flow throughout the length, and the effects of tapered angle on the developing flow increase with the tapered angle.

EFFECT OF THE RIBLETS SURFACE ON THE BOUNDARY LAYER DEVELOPMENT

The effect of riblets surface on flat plate boundary layer development hasbeen measured with laser Doppler velocimeter (LDV). In the present experiment, although the development of boundary layer can be divided into three regions, the laminarboundary layer region is increased, and the transition occurs at a larger Reynolds number.The Reynolds number of transition to turbulence Rextr is 4. 3 tinies as great as that in thesmooth flat plate case. In the turbulent boundary layer region, greater value of integralconstant C is obtained in log-law for velocity distribution. This indicates that the ribletssurface has obviously drag reduction characteristics. The maximum value of turbulence intensity and its position are less than the smooth surface results in the turbulent boundarylayer region.

Recent Advances in Research of the Distributed Parameters Control System with Moving Boundary

This paper presents a brief summary of the three development stages of investigation on the transpiration cooling and its control for aircraft, missiles and electromagnetic gun, then the control problem of the distributed parameters system with a moving boundary is derived. It introduces the mathematical model of the transpiration cooling control, its control characteristics, and the present situation of the experimental and theoretical study on this problem. This paper also describes the main study results and the existing problems. The prospective application is also reported. The major references in every developing stage are listed systematically for further study.

MHD flow of upper-convected Maxwell fluid over porous stretching sheet using successive Taylor series linearization method

This paper investigates the magnetohydrodynamic （MHD） boundary layer flow of an incompressible upper-convected Maxwell （UCM） fluid over a porous stretching surface. Similarity transformations are used to reduce the governing partial differential equations into a kind of nonlinear ordinary differential equations. The nonlinear prob- lem is solved by using the successive Taylor series linearization method （STSLM）. The computations for velocity components are carried out for the emerging parameters. The numerical values of the skin friction coefficient are presented and analyzed for various parameters of interest in the problem.

VISCOUS-INVISCID INTERACTING FLOW THEORY

In this paper a viscous-inviscid interacting flow theory(IFT)is developed for an incompressible, two-dimensional laminar flow.IFT's main points are as follows.(1)By introducing a concept of interaction lay- er where the normal momentum exchange is dominating,a new three layer structure is established.(2)Through the conventional manipulations and by introducing an interaction model,both the streamwise and normal length scales are proved to be functions of a single parameter m,which is related to the streamwise pressure gradient and Reynolds number.(3)The approximate equations governing the flow of each layer as well as the whole interaction flow are derived.The present IFT is applicable to both attached and attached-separation bubble-reattached flows, The classical boundary layer theory and Triple-deck theory are shown to be two special cases of the present theory under m=0 and 1/4,respectively.Furthermore IFT provides new distinctions of both the normal and streamwise length scales for flow-field numerical computation and also gives a new approach to developing the simpli- fied Navier-Stokes(SNS)equations.

Helicity Dynamics of Atmospheric Flow

Helicity is an important physical variable which is similar to the energy and enstrophy in three-dimensional fluid. It can be used to describe the motion in the direction of fluid rotation and also can be regarded as a new physical variable ill turbulence theory. In recent years, it has been used in atmospheric dynamics. In this paper, helicity of atmospheric flow, especially helicity in the boundary layer and in the vicinity of front was discussed. These results show that helicity is usually positive in the boundary layer due to the effect of friction. The helicity of boundary layer flow is larger in anticyclone than that in cyclone, resulting from the different wind structures of boundary layers in anticyclone and cyclone under the geostrophic momentum approximation. It is possible that the helicity is negative at certain height in the baroclinic boundary layer. The influences of nonlinearity and baroclinity on the helicity are important. The so called 'Cloud Street' in the boundary layer is related to the dynamics of helicity. Helicity in the atmosphere can be expressed as the temperature advection under some conditions, so helicity would be allowed to describe the frontogenesis and development of frontal structure. The amplitude of helicity increases with time in the frontogenesis. A large gradient of helicity is generated in the region located to the northeast of the surface low and in which the front is formed. In warm frontal region, as well as behind the trough of temperature, the felicity is positive, while the helicity is negative in cold frontal sector and in the ahead ridge of temperature. The largest helicity occurs in the boundary.

Effect of viscous dissipation and heat source on flow and heat transfer of dusty fluid over unsteady stretching sheet

This paper investigates the problem of hydrodynamic boundary layer flow and heat transfer of a dusty fluid over an unsteady stretching surface. The study considers the effects of frictional heating （viscous dissipation） and internal heat generation or ab- sorption. The basic equations governing the flow and heat transfer are reduced to a set of non-linear ordinary differential equations by applying suitable similarity transformations. The transformed equations are numerically solved by the Runge-Kutta-Fehlberg-45 order method. An analysis is carried out for two different cases of heating processes, namely, variable wall temperature （VWT） and variable heat flux （VHF）. The effects of various physical parameters such as the magnetic parameter, the fluid-particle interaction pa- rameter, the unsteady parameter, the Prandtl number, the Eckert number, the number density of dust particles, and the heat source/sink parameter on velocity and temperature profiles are shown in several plots. The effects of the wall temperature gradient function and the wall temperature function are tabulated and discussed.

Optimization of heat transfer in the thermal Marangoni convective flow of a hybrid nanomaterial with sensitivity analysis

The heat transfer rate of the thermal Marangoni convective flow of a hybrid nanomaterial is optimized by using the response surface methodology(RSM).The thermal phenomenon is modeled in the presence of a variable inclined magnetic field,thermal radiation,and an exponential heat source.Experimentally estimated values of the thermal conductivity and viscosity of the hybrid nanomaterial are utilized in the calculation.The governing intricate nonlinear problem is treated numerically,and a parametric analysis is carried out by using graphical visualizations.A finite difference-based numerical scheme is utilized in conjunction with the 4-stage Lobatto IIIa formula to solve the nonlinear governing problem.The interactive effects of the pertinent parameters on the heat transfer rate are presented by plotting the response surfaces and the contours obtained from the RSM.The mono and hybrid nanomaterial flow fields are compared.The hybrid nanomaterial possesses enhanced thermal fields for nanoparticle volume fractions less than 2%.The irregular heat source and the thermal radiation enhance the temperature profiles.The high level of the thermal radiation and the low levels of the exponential heat source and the angle of inclination(of the magnetic field)lead to the optimized heat transfer rate(Nux=7.46275).

Approximate solutions to MHD Falkner-Skan flow over permeable wall

The magnetohydrodynamic （MHD） Falkner-Skan boundary layer flow over a permeable wall in the presence of a transverse magnetic field is examined. The approximate solutions and skin friction coefficients of the MHD boundary layer flow are obtained by using a method that couples the differential transform method （DTM） with the Pade approximation called DTM-Pade. The approximate solutions are expressed in the form of a power series that can be easily computed with an iterative procedure. The approximate solutions are tabulated, plotted for the values of different parameters and compared with the numerical ones obtained by employing the shooting technique. It is found that the approximate solution agrees very well with the numerical solution, showing the reliability and validity of the present work. Moreover, the effects of various physical parameters on the boundary layer flow are presented graphically and discussed.

Similarity solutions for non-Newtonian power-law fluid flow

The problem of the boundary layer flow of power law non-Newtonian fluids with a novel boundary condition is studied. The existence and uniqueness of the solutions are examined, which are found to depend on the curvature of the solutions for different values of the power law index n. It is established with the aid of the Picard-Lindelof theorem that the nonlinear boundary value problem has a unique solution in the global domain for all values of the power law index n but with certain conditions on the curva- ture of the solutions. This is done after a suitable transformation of the dependent and independent variables. For 0 〈 n ≤ 1, the solution has a positive curvature, while for n 〉 1, the solution has a negative or zero curvature on some part of the global domain. Some solutions are presented graphically to illustrate the results and the behaviors of the solutions.

Flow and heat transfer over hyperbolic stretching sheets

The boundary layer flow and heat transfer analysis of an incompressible viscous fluid for a hyperbolically stretching sheet is presented. The analytical and numer- ical results are obtained by a series expansion method and a local non-similarity （LNS） method, respectively. The analytical and numerical results for the skin friction and the Nusselt number are calculated and compared with each other. The significant observation is that the momentum and the thermal boundary layer thickness decrease as the distance from the leading edge increases. The well-known solution of linear stretching is found as the leading order solution for the hyperbolic stretching.