基于Keller-Box格式的三维非静压水动力学模型

将欧拉方程中的压强分为静压和动压,对水平动压梯度项以外的其他项进行σ坐标变换.动压变量布置在网格上下表面中心,并采用Keller-box格式离散垂向动量方程.将包含未知动压变量的流速分量代入仅在垂向进行σ坐标变换的连续方程,得到关于动压的泊松方程并采用稳定双共轭梯度法求解,建立了一种非静压三维水动力学模型,并利用正弦波在潜堤上的传播实验进行了验证.结果表明:本模型严格满足自由水面处的零动压边界条件,当波幅与水深之比不超过0.1时,在垂向仅采用两层就精确模拟出水流运动.

Numerical solution of micropolar fluid flow via stretchable surface with chemical reaction and melting heat transfer using Keller-Box method

The main theme of this research is to find the numerical results of stagnation point flow of micropolar fluid over a porous stretchable surface due to the physical effects of internal heat generation/absorption,melting heat transfer and chemical reaction via Keller-Box method(KBM).The graphs and tables are depicted and explained for various embedded parameters.The range of melting heat transfer parameter is 0≤M≤3,the range of chemical reaction parameter is 0≤K_(r)≤1 whereas the values of space-temperature dependent heat source/sink parameters lies in-0:4≤Q≤0:4 and-2≤Q*≤2.The upshots of the current problem illustrate that at fluid-solid interface,rate of HMT(heat and mass transfer)declined on escalating the values of stretching parameter.Moreover,as the values of internal heat source/sink parameter increases,heat transfer rate declines at fluid-solid interface.

A Finite Difference Approximation for Dynamic Calculation of Vertical Free Hanging Slender Risers in Re-Entry Application

The dynamic calculations of slender marine risers, such as Finite Element Method （FEM） or Modal Expansion Solution Method （MESM）, are mainly for the slender structures with their both ends hinged to the surface and bottom. However, for the re-entry operation, risers held by vessels are in vertical free hanging state, so the displacement and velocity of lower joint would not be zero. For the model of free hanging flexible marine risers, the paper proposed a Finite Difference Approximation （FDA） method for its dynamic calculation. The riser is divided into a reasonable number of rigid discrete segments. And the dynamic model is established based on simple Euler-Bemoulli Beam Theory concerning tension, shear forces and bending moments at each node along the cylindrical structures, which is extendible for different boundary conditions. The governing equations with specific boundary conditions for riser＇s free hanging state are simplified by Keller-box method and solved with Newton iteration algorithm for a stable dynamic solution. The calculation starts when the riser is vertical and still in calm water, and its behavior is obtained along time responding to the lateral forward motion at the top. The dynamic behavior in response to the lateral parametric excitation at the top is also proposed and discussed in this paper.

Boundary Layer Flow past a Stretching Cylinder and Heat Transfer with Variable Thermal Conductivity

The boundary layer flow of viscous incompressible fluid over a stretching cylinder has been considered to study flow field and temperature field. Due to non-linearity, a numerical approach called Keller-box technique has been used to compute the values of velocity function f and temperature field at different points of dynamic region. The expressions for skin friction and Nusselt number have also been obtained. The dependence of velocity profile and temperature profile on the dimensionless parameter of practical interest has been analyzed in detail by graphs. The dependence of Skin friction and Nusselt number has been seen through tables.

化学反应对高对流Maxwell流体在多孔面上作MHD流动和传质的影响

研究导电的高对流Maxwell流体在多孔表面上,作计及物质化学反应时的MHD流动及其传质.将非线性的偏微分控制方程及其相应的边界条件,变换为非线性的常微分方程,并利用Kel-ler-Box法进行数值求解.用图形给出了各种物理参数对流动和传质特性的影响,并对结果进行了讨论.可以看到,化学反应阶次提高了扩散边界层的厚度;还可以看到,传质率强烈地依赖于Schmidt数和反应率参数.此外,在特例情况下得到了以往文献中可供利用的结果.

MHD flow and mass transfer of chemically reactive upper convected Maxwell fluid past porous surface

The magnetohydrodynamic （MHD） flow and mass transfer of an electrically conducting upper convected Maxwell （UCM） fluid at a porous surface are studied in the presence of a chemically reactive species. The governing nonlinear partial differential equations along with the appropriate boundary conditions are transformed into nonlinear ordinary differential equations and numerically solved by the Keller-box method. The effects of various physical parameters on the flow and mass transfer characteristics are graphically presented and discussed. It is observed that the order of the chemical reaction is to increase the thickness of the diffusion boundary layer. Also, the mass transfer rate strongly depends on the Schmidt number and the reaction rate parameter. Furthermore, available results in the literature are obtained as a special case.

Effect of Nonlinear Thermal Radiation on Boundary Layer Flow of Viscous Fluid over Nonlinear Stretching Sheet with Injection/Suction

The present study reveals the effect of nonlinear thermal radiation and magnetic field on a boundary layer flow of a viscous fluid over a nonlinear stretching sheet with suction or an injection. Using suitable similarity transformations, governing partial differential equations were reduced to higher order ordinary differential equations and further these are solved numerically using of Keller-Box method. Effect of flow controlling parameter on velocity, temperature and nanoparticle fluid concentration, local skin friction coefficient, local Nusselt number and local Sherwood numbers are discussed. It is found that the dimensionless velocity decreases and temperature, concentration are increased with the increasing of magnetic parameter. The temperature profile is an increasing function of thermal radiation when it is increasing.

Effects of Velocity and Thermal Slip Conditions with Radiation on Heat Transfer Flow of Ferrofluids

To analyze the thermal convection of ferrofluid along a flat plate is the persistence of this study. The two-dimensional laminar, steady, incompressible flow past a flat plate subject to convective surface boundary condition, slip velocity in the presence of radiation has been studied where the magnetic field is applied in the transverse direction to the plate. Two different kinds of magnetic nanoparticles, magnetite Fe3O4 and cobalt ferrite CoFe2O4 are amalgamated within the base fluids water and kerosene. The effects of various physical aspects such as magnetic field, volume fraction, radiation and slip conditions on the flow and heat transfer characteristics are presented graphically and discussed. The effect of various dimensionless parameters on the skin friction coefficient and heat transfer rate are also tabulated. To investigate this particular problem, numerical computations are done using the implicit finite difference method based Keller-Box Method.

Numerical Modeling of Non-Similar Mixed Convection Heat Transfer over a Stretching Surface with Slip Conditions

In this paper, the heat transfer effect on the steady boundary layer flow of a Casson fluid past a stretching surface in the presence of slip conditions was analyzed. The stretching surface is maintained at a constant temperature. The boundary layer conservation equations, which are parabolic in nature, are normalized into non-similar form and then solved numerically with the well-tested, efficient, implicit, stable Keller-box finite difference scheme. The resulting equations are solved numerically by using the Kellerbox finite-difference method, and the expressions for velocity and temperature are obtained. They satisfy all imposed initial and boundary conditions and reduce to some well-known solutions for non-Newtonian fluids. Numerical results for velocity, temperature, skin friction and Nusselt number are shown in various graphs and discussed for embedded flow parameters. It is found that both velocity and temperature decrease with an increase of the Casson fluid parameter.

Characteristics of Nanofluids over a Non-Linearly Stretched Sheet under the Influence of Thermal Radiation and Magnetic Field

Recent studies carried out in terms of viscous flow and heat transfer of nano-fluids on the non-linear sheets. In this paper, detailed studies to understand the characteristics such as viscous flow and heat transfer of nano-fluids under the influence of thermal radiation and magnetic fields are studied using Keller-Box method. Various governing parameters affecting the viscous flow and heat transfers are drawn based on quantitative results. The raise in temperature affected the velocity to a negative value;however, the same observation was made even for the increasing magnetic field. The impact of radiation parameter is proportional seems to be proportional to temperature and it is observed to be inversely proportional with concentration.

熔化凝固问题的Keller盒式格式

建立了热参数依赖于温度的熔化凝固问题的显热容模型的Keller盒式格式,运用冻结系数法证明了该格式的无条件稳定性,并给出了数值算例.

Effects of Radiations and Heat Source/Sink on a Casson Fluid Flow over Nonlinear Stretching Sheet

The present study deals with the flow over a nonlinearly stretching sheet of Casson fluid with the effects of radiation and heat source/sink. The Casson fluid model is used to characterize the non-Newtonian fluid behaviour. With the help of justified similarity transformations the governing equations were reduced to couple nonlinear ordinary differential equations. The effective numerical technique Keller Box method is used to solve these equations. The variations in velocity, temperature profiles were presented with the various values of nonlinear stretching parameter n and Casson parameter β. The nature of Skinfriction and Local nusselt number has presented. Effects of radiation and heat source/sink on temperature profiles have been discussed.

Magneto Hydrodynamics Stagnation Point Flow of a Nano Fluid over an Exponentially Stretching Sheet with an Effect of Chemical Reaction, Heat Source and Suction/Injunction

A numerical investigation is carried out on the effects of heat source suction and viscous dissipation on Magneto hydrodynamics boundary layer flow of a viscous, steady and incompressible fluid. The flow is assumed to be over on exponentially stretching sheet. The governing system of partial differential equations has been transformed into ordinary differential equation using similarity transformation. Keller box method is simulated on the dimensionless system of differential equations. The skin friction coefficient and the heat and mass transfer rates are very significant parameters that are computed, analysed discussed in detail.

Transient Combined Convective Heat Transfer over a Stretching Surface in a Non-Newtonian Nanofluid Using Buongiorno’s Model

The present paper investigates the transient mixed convective boundary layer flow of an incompressible non-Newtonian quiescent nanofluid adjacent to a vertical stretching surface. The effects of the Brownian motion and thermophoresis are included for the nanofluid. Using appropriate non-similarity transformations the non-dimensional, coupled and highly non-linear system of equations is solved numerically using the efficient Keller-box implicit finite difference method for the whole transient from t=0 (initial state) to (final steady-state flow). The box method is unconditionally stable. Numerical results for dimensionless velocity (f’), micro-rotation (g), temperature (θ), nanoparticle volume fraction (Φ) at final steady state flow, skin friction function (), Nusselt number function () and Sherwood number function () have been presented on various parameters inform of tables and graphs. The results indicate that as Nb and Nt increase, the Nusselt number decreases whereas Sherwood number increases at initial and early state time but decreases at the final steady state time. As the K increases, the friction factor decreases whereas surface mass transfer rate and the surface heat transfer rates slightly increase. 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. The study has many practical applications such as extrusion of plastic sheets, paper production, glass blowing, metal spinning and drawing plastic films.

The effect of variable viscosity on the flow and heat transfer of a viscous Agwater and Cu-water nanofluids

A numerical study is carried out to study the effects of the temperature dependent viscosity on the flow and heat transfer of a nanofluid over a flat surface in the presence of viscous dissipation. The governing nonlinear partial differential equations are transformed into nonlinear ordinary differential equations, and are solved numerically by the Keller-box method. The numerical results indicate that the effect of nanoparticle volume fraction is to increase the heat transfer and hence enhance the thermal boundary layer thickness. This is true even in the presence of variable viscosity and the viscous dissipation. Furthermore, the results obtained for heat transfer characteristics with nanoparticles reveal many interesting behaviors that warrant further study on the effects of the ＂nano-solid-particles＂.

MHD BOUNDARY-LAYER FLOW AND HEAT TRANSFER OVER PERMEABLE PLATE WITH CONVECTIVE SURFACE BOUNDARY CONDITION

A numerical analysis has been carried out to investigate the problem of magnetohydrodynamic(MHD)boundary-layer flow and heat transfer of a viscous incompressible fluid over a fixed plate.Convective surface boundary condition is taken into account for thermal boundary condition.A problem formulation is developed in the presence of thermal radiation,magnetic field and heat source/sink parameters.A similarity transformation is used to reduce the governing boundary-layer equations to couple higher-order nonlinear ordinary differential equations.These equations are numerically solved using Keller–Box method.The effect of the governing parameters such as radiation,Prandtl number,Hartman number,heat source/sink parameter on velocity and temperature profile is discussed and shown by plotting graphs.It is found that the temperature is an increasing function of convective parameter A,radiation and heat source parameters.Besides,the numerical results for the local skin friction coefficient and local Nusselt number are computed and presented in tabular form.Finally a comparison with a previously published results on a special case of the problem has done and shows excellent agreement.

A comprehensive physical insight about thermo physical aspects of Carreau fluid flow over a rotated disk of variable thickness by implementing finite difference approach

Present communication is devoted to analyze thermal characteristics of Carreau liquid flowing on variably thickened non-uniformly rotating disk.Mathematical formulation is constructed in view of complex coupled partial differential system.Afterwards,boundary layer approach is executed for comprehensive examination of under consideration phenomenon with in boundary layer region.Karman’s transformation is capitalized to convert the attained PDE’s into ordinary differential equations system.Solution of attained ODE’s system is solved numerically by implementing Keller-Box scheme.Influence of protuberant involved parameters on momentum and thermal distributions is illustrated through sketches.In addition,impact of flow concerning parameters on wall shear stress and thermal flux is also evaluated.The assurance of present finding is done by making agreement with published results and by restricting considered problem to Newtonian case.Here,we observed that radially and tangentially directed wall drag lessen with growing magnitude of power law exponent index.Moreover,the consequence of disk thickness parameter grows stresses along radial direction whereas opposite behavior is depicted in case of tangentially directed friction and heat flux factors.

Hydromagnetic unsteady slip stagnation flow of nanofluid with suspension of mixed bio-convection

In this paper,stagnation point region(suspended with nanofluid and microorganisms)is examined subjected to velocity and thermal slips.The flow is assumed to be flowing across an exponentially stretching flat surface under magnetic field environment.Governing transport equations(framed under Buongiorno’s model)are converted into self-similar form through suitable unsteady exponential similarity transformations which are then solved by employing implicit finite difference scheme(IFDS)known as Keller-box method(KBM).A parametric analysis is performed along with limited details of KBM.Influence of pertinent constraints on local skin friction,local Nusselt number,local Sherwood number and local density number of micro-organisms are also uncovered through graphs.A significant decrease in skin-friction coefficients has been detected with respect to thermal slip in comparison to velocity slip.