Thermal radiation effects on magnetohydrodynamic free convection heat and mass transfer from a sphere in a variable porosity regime

A mathematical model is presented for multiphysical transport of an optically-dense, electrically-conducting fluid along a permeable isothermal sphere embedded in a variable-porosity medium. A constant, static, magnetic field is applied transverse to the cylinder surface. The non-Darcy effects are simulated via second order Forchheimer drag force term in the momentum boundary layer equation. The surface of the sphere is maintained at a constant temperature and concentration and is permeable, i.e. transpiration into and from the boundary layer regime is possible. 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. Increasing porosity (ε) is found to elevate velocities, i.e. accelerate the flow but decrease temperatures, i.e. cool the boundary layer regime. Increasing Forchheimer inertial drag parameter (Λ) retards the flow considerably but enhances temperatures. Increasing Darcy number accelerates the flow due to a corresponding rise in permeability of the regime and concomitant decrease in Darcian impedance. Thermal radiation is seen to reduce both velocity and temperature in the boundary layer. Local Nusselt number is also found to be enhanced with increasing both porosity and radiation parameters.     

On mass transfer in three‐dimensional flow of a viscoelastic fluid

This attempt theoratically examines the mass transfer analysis of the boundary layer flow caused by a stretching surface. Analytic solutions are derived with the Homptopy analysis method (HAM). Numerical values of skin friction coefficients and the surface mass transfer are reported. The effectiveness of this method is explicitly illustrated by discussing the convergence of the obtained series solutions. Velocity and gradient of mass transfer are shown graphically and discussed. © 2010 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 27: 915–936, 2011     

Laminar swirling flow in an annulus with porous walls

Flow of an incompressible viscous fluid under constant pressure gradient in a porous annulus is considered, with surface mass transfer, both in the radial and circumferential directions. Expressions for the fully developed velocities are then obtained. With these fully developed velocities on a section of the annulus, on which the origin of co-ordinates lies, the downstream decay of the swirl velocity is analysed, subject to the condition that the velocities on the boundaries are now purely radial. The perturbations in the axial and radial velocities, caused by the decaying swirl, are also determined. It is observed that the decay of the swirl velocity is faster for suction at the inner boundary and injection at the outer andvice versa.     

Instationäre Grenzschichten an langsam bewegten Körpern in einer rotierenden Flüssigkeit

Summary In this work equations of boundary layers on arbitrary smooth surfaces are derived which are moving relatively slowly through a rotating fluid. For the case of the impulsive start of the motion from rest, the equations are solved exactly for arbitrary velocities at the outer edge of the boundary layer. The results are applied to the case of the motion of a sphere in the direction of the axis of revolution using Stewartson's velocity at the outer edge. The boundary layer calculated in such a way does not separate from the sphere surface; this makes it possible to calculate the total drag. The formula reduces for the case of non-viscous fluid to the known result given by Stewartson.     

Perturbation analysis of the heat transfer in porous media with small thermal conductivity

An approximate analytical solution for the one-dimensional problem of heat transfer between an inert gas and a porous semi-infinite medium is presented. Perturbation methods based on Laplace transforms have been applied using the solid thermal conductivity as small parameter. The leading order approximation is the solution of Nusselt (or Schumann) problem. Such solution is corrected by means of an outer approximation. The boundary condition at the origin has been taking into account using an inner approximation for a boundary layer. The gas temperature presents a discontinuous front (due to the incompatibility between initial and boundary conditions) which propagates at constant velocity. The solid temperature at the front has been smoothed out using an internal layer asymptotic approximation. The good accuracy of the resulting asymptotic expansion shows its usefulness in several engineering problems such as heat transfer in porous media, in exhausted chemical reactions, mass transfer in packed beds, or in the analysis of capillary electrochromatography techniques.     

具有蒸发液滴两相介质近壁流动的数学分析

在双连续介质理论框架下，采用匹配渐进展开方法导出并求解了具有蒸发液滴的汽雾流中层流边界层方程，给出了控制汽雾流的相似判据。对于沿曲面的流动，边界层方程的形式取决于是否存在液滴的惯性沉积。给出了热钝体驻点附近蒸汽－液滴边界层的数值计算结果。它们表明：由于蒸发，在边界层内近壁处形成了一个无液滴区域；在该区上边界处，液滴半径趋于零而液滴数密度急剧增高。液滴蒸发及聚集的联合效应造成了表面热流的显著增加，甚至在自由来流中液滴质量浓度很低时此效应依然存在。     

Similarity solutions for flow and heat transfer over a permeable surface with convective boundary condition

The steady laminar boundary layer flow over a permeable flat plate in a uniform free stream, with the bottom surface of the plate is heated by convection from a hot fluid is considered. Similarity solutions for the flow and thermal fields are possible if the mass transpiration rate at the surface and the convective heat transfer from the hot fluid on the lower surface of the plate vary like x^−1/2, where x is the distance from the leading edge of the solid surface. The governing partial differential equations are first transformed into ordinary differential equations, before being solved numerically. The effects of the governing parameters on the flow and thermal fields are thoroughly examined and discussed.     

An Analytical Study of Boundary Layer Flows on a Continuous Stretching Surface

In this paper the momentum and heat transfer characteristics for a self-similarity boundary layer on exponentially stretching surface modeled by a system of nonlinear differential equations is studied. The system is solved using the Homotopy Analysis Method (HAM), which yields an analytic solution in the form of a rapidly convergent infinite series with easily computable terms. Homotopy analysis method contains the auxiliary parameter ℏ, which provides us with a simple way to adjust and control the convergence region of solution series. By suitable choice of the auxiliary parameter ℏ, reasonable solutions for large modulus can be obtained.     

Numerical Study on Hypersonic Flow and Aerodynamic Heating北大核心CSCD

基于有限差分法开发了高超声速流动与换热问题气热耦合仿真求解器,运用该求解器对三种典型高超声速流动与换热问题开展了仿真研究,得到了相应的气动参数、热流密度分布。高超声速后台阶的存在使表面气动参数、热流分布不再连续;随着缝深的提高,缝隙局部流速迅速降低,对流换热效应减弱;高超声速无限长圆管绕流中,边界层外部区域气动参数随时间变化不大,边界层内存在较大的温度梯度,壁面温度随时间升高。三个算例的仿真结果均与试验测量值进行了对比,验证了所开发的求解器的计算能力。     

MHD three-dimensional flow of viscoelastic fluid over an exponentially stretching surface with variable thermal conductivity

This study models the magnetohydrodynamic (MHD) three-dimensional boundary layer flow of viscoelastic fluid. The flow is due to the exponentially stretching surface. The heat transfer analysis is performed through prescribed surface temperature (PST) and prescribed surface heat flux (PHF). The thermal conductivity is taken temperature dependent. Series solutions of velocities and temperatures are constructed. Graphical results for PST and PHF cases are plotted and analyzed. Numerical values of skin-friction coefficients and Nusselt numbers are presented and discussed.     

复杂边界旋转Navier-Stokes方程的几何方法及二度并行算法

本文提出了一种求解复杂边界旋转Navier-Stokes方程的微分几何方法及其二度并行算法.此方法可用于求解透平机械内部叶片间流动和飞行器外部绕流等复杂流动问题.假设流动区域可以用一系列光滑曲面■_k,k=1,2,…,K分割为一系列子区域(称作流层),通过应用微分几何的方法,三维N-S算子可以分解为两类算子之和:建立在曲面■_k切空间上"膜算子"和曲面■_k法线方向的"挠曲算子",将挠曲算子应用欧拉中心差商来逼近,由此得到建立在■_k上的"2D-3C"N-S方程.求解2D-3C N-S方程并且反复迭代直到收敛.我们得到"二度并行算法",它是2D-3C N-S方程并行算法与k方向的同时并行.这个算法的优点在于,(1)可以改进由于复杂边界造成的不规则三维网格引起的逼近解的精度;(2)为克服边界层的数值效应,在边界层内可以构造很密的流层,形成三维多尺度的网格,是一个很好的边界层算法;(3)这个方法不同于经典的区域分解算法,这里的每个子区域只需要求解一个"2D-3C"N-S方程,而经典区域分解方法要在每个子区域上求解三维问题.     

Lie group analysis of natural convection heat and mass transfer in an inclined surface with chemical reaction

In this paper we examine the convective flow, heat and mass transfer of an incompressible viscous fluid past a semi-infinite inclined surface with first-order homogeneous chemical reaction by Lie group analysis. The governing partial differential equations are reduced to a system of ordinary differential equations using scaling symmetries. Numerical solutions of the resulting ordinary differential equations are obtained using the fourth-order Runge–Kutta method. From the numerical results, it is observed that the thickness of the momentum boundary layer increases with increasing the chemical reaction parameter and the Schmidt number. The thicknesses of the thermal and concentration boundary layers are decreased with increasing the chemical reaction parameter and the Schmidt number.     

Einfluss eines Verbrennungsvorganges auf den Wärme- und Stoffaustausch in einer laminaren Grenzschicht

Summary The influence of combustion on heat and mass transfer is investigated on the following model. A mixture of an inert with a combustible gas (air) flows in steady, laminar flow over a flat plate. A mass flux of gaseous fuel away from the plate surface is produced by some means. Combustion is assumed to occur with very fast reaction rate so that the process is purely controlled by diffusion and the equilibrium is assumed as very close to complete combustion. It is studied under which conditions the combustion occurs at the surface or when the flame is displaced into the boundary layer. The influence of combustion on the heat transfer from a hot gas to the plate surface is calculated, for the condition that combustion occurs at the surface.      

Heat and mass transfer in annular liquid jets: I. Formulation

Heat and mass transfer phenomena in annular liquid jets are analyzed at high Reynolds numbers by means of a model derived from the governing equations that takes into account the effects of surface tension and boundary conditions at the gas–liquid interfaces and the large differences between the thermal and mass diffusivities, densities, dynamic viscosities, and thermal conductivities between gases and liquids. The model clearly illustrates the stiffness in both space and time associated with the concentration, linear momentum and energy boundary layers, and the initial cooling of the gases enclosed by the jet when, starting from a steady state where gases are injected into the volume enclosed by the jet at a rate equal to the heat and mass absorption rates by the liquid, gas injection is stopped. It is shown that, owing to the non-linear integrodifferential coupling between the fluid dynamics and heat and mass transfer processes, the pressure of the gases enclosed by the jet may vary in either a monotonic or an oscillatory manner depending on the large number of non-dimensional parameters that govern the heat and mass transfer phenomena. For the underpressurized jets considered here, it is shown that thermal equilibrium is achieved at a much faster rate than that associated with mass transfer, double diffusive phenomena in the liquid may occur, and the mass and volume of the gases enclosed by the jet may increase or decrease as functions of time until a steady equilibrium condition is reached.     

Optimal Interplanetary Orbital Transfers via Electrical Engines

The Hohmann transfer theory, developed in the 19th century, is the kernel of orbital transfer with minimum propellant mass by means of chemical engines. The success of the Deep Space 1 spacecraft has paved the way toward using advanced electrical engines in space. While chemical engines are characterized by high thrust and low specific impulse, electrical engines are characterized by low thrust and hight specific impulse. In this paper, we focus on four issues of optimal interplanetary transfer for a spacecraft powered by an electrical engine controlled via the thrust direction and thrust setting: (a) trajectories of compromise between transfer time and propellant mass, (b) trajectories of minimum time, (c) trajectories of minimum propellant mass, and (d) relations with the Hohmann transfer trajectory. The resulting fundamental properties are as follows:

Free magnetohydrodynamic flow and convection from a vertical spinning cone with cross-diffusion effects

A study of cross-diffusion effects on convection from a vertically spinning cone under the influence of an external magnetic field is considered. The non-linear two-point boundary value problem governing the flow is solved numerically. Two different types of surface heating, namely linear surface temperature (LST) and linear surface heat flux (LSHF) are considered. A parametric study addressing the effects of various flow parameters on the fluid properties, the skin friction, heat and mass transfer coefficients is given.     

粘弹性流体流经作依赖时间运动伸展面的三维流动及其传质问题

研究粘弹性流体流经伸展面时的三维边界层流动．假定伸展面的运动速度依赖于时间．进一步考虑了更高阶次化学反应对传质的影响．应用同伦分析法(HAM)进行计算．精确地分析了所得级数解的收敛性．用图形讨论了各参数变化对速度和浓度的影响．还给出了面传质数值的计算,将所得结果与前人的数值解进行了比较．     

Flexoelectric and surface effects on the electromechanical behavior of graphene-based nanobeams

In this novel work, the electromechanical behavior of graphene-based nanocomposite (GNC) beams with flexoelectric and surface effects were investigated using size-dependent Euler-Bernoulli theory, linear piezoelectricity and Galerkin's weighted residual method along with modified strength of materials and finite element (FE) approaches. In addition, analytical and FE models were developed to study the static response of flexoelectric GNC nanobeams with various boundary conditions: cantilever, simply-supported and clamped-clamped. The developed models predict that the effective piezoelectric coefficients of GNC are responsible for the actuation capability of a graphene layer in the transverse direction due to the applied field in its axial direction and the predictions by both the models are found to be in good agreement. Results reveal that the flexoelectric and surface effects on the static response of GNC nanobeams are significant and should be taken into account. The electromechanical response of GNC nanobeams can be tailored to achieve the required coupled electromechanical characteristics of a vast range of NEMS using various boundary conditions and thickness of nanobeam as well as volume fraction of graphene. Our fundamental study sheds a light on the possibility of developing high-performance and lightweight graphene-based NEMS such as nanosensors, nanogenerators and nanoresonators using non-piezoelectric graphene.     

Nonsimilar solutions for double-diffusion boundary layers on a sphere in micropolar fluids with constant wall heat and mass fluxes

This work presents nonsimilar boundary layer solutions for double-diffusion natural convection near a sphere with constant wall heat and mass fluxes in a micropolar fluid. A coordinate transformation is employed to transform the governing equations into nondimensional nonsimilar boundary layer equations and the obtained boundary layer equations are then solved by the cubic spline collocation method. Results for the local Nusselt number and the local Sherwood number are presented as functions of the vortex viscosity parameter, Schmidt number, buoyancy ratio, and Prandtl number. Higher vortex viscosity tends to retard the flow, and thus decreases the local convection heat and mass transfer coefficients, raising the wall temperature and concentration. Moreover, the local convection heat and mass transfer coefficients near a sphere in Newtonian fluids are higher than those in micropolar fluids.     

Modeling of Free Convection Boundary Layer Flow on a Solid Sphere with Newtonian Heating

In this paper, the mathematical model of free convection boundary layer flow on a solid sphere with Newtonian heating, in which the heat transfer from the surface is proportional to the local surface temperature, is considered. The transformed boundary layer equations are solved numerically using an efficient numerical scheme known as the Keller-box method. Numerical solutions are obtained for the local wall temperature, the local skin friction coefficient, as well as the velocity and temperature profiles. The features of the flow and heat transfer characteristics for different values of the Prandtl number Pr and conjugate parameter γ are analyzed and discussed.