MIXED CONVECTION BOUNDARY LAYER FLOW OF A MICROPOLAR FLUID ON A HORIZONTAL PLATE

An analysis is performed to study the heat transfer characteristics of laminar mixed convection boundary layer flow of a micropolar fluid past a semi-infinite horizontal fiat plate with variable surface heat flux. A nonsimilar mixed convection parameter £ and a pseudosimilarity variable v are introduced to cast the governing boundary layer equations into a system of dimensionless equations, which are solved numerically using the finite difference method. A single mixed convection parameter is used to cover the entire regime of mixed convection from the pure forced convection limit to the pure free convection limit. The effect of material parameters, the power-law variation of surface heat flux, nonsimilar mixed convection parameter and Prandtl number are considered. The micropolar fluids are observed to display drag reduction and reduced surface heat transfer rate when compared to Newtonian fluids. The effect of the buoyancy force results in the enhancements of friction factor, heat transfer rate and wall couple stress.     

TUBESIDE EXIT CONDITION WITH COMPLETE CONDENSATION IN MULTITUBE CROSS-FLOW HEAT EXCHANGERS

A transition condensate Froude number characterizes the tubeside exit condition or whether condensate fills the tube or is in a stratified flow regime with vapor flowing into the tube exit. The transition Froude number, which defines the boundary between high and low condensate loading conditions, was determined with single-phase water tests and was verified with two-phase tests of large multitube cross-flow heat exchangers. For both cases, the water or condensate is discharged from a tube or tubes into a gas or vapor-filled plenum. With complete condensation and high liquid loading, the flow regimes are progressively annular, slug, and plug followed by the tube running full with subcooled condensate. With complete condensation and low liquid loading, the flow regimes are annular, wavy, and stratified followed by stratified flow with vapor flowing back from the tube exit.     

FLOW IN A RESERVOIR FILLED WITH A NON-NEWTONIAN FLUID INDUCED BY A MOVING PLATE

This paper presents a theoretical solution for the flow field in a reservoir filled with a non-Newtonian (power law) fluid, induced by a moving plate. The flow field consists of a boundary layer in the vicinity of the moving plate, a core “invicid” region in which the flow is driven by the suction effect at the edge of the boundary layer and a second boundary layer in the vicinity of the vertical wall of the reservoir. In addition to the velocity field, results for the friction coefficients at the moving plate and at the vertical wall of the reservoir are reported.     

FORCED CONVECTION BOUNDARY LAYER FLOW AT A FORWARD STAGNATION POINT WITH NEWTONIAN HEATING

The steady forced convection boundary layer flow near the forward stagnation point of an infinite plane wall generated by Newtonian heating in which the heat transfer from the surface is proportional to the local surface temperature is investigated in this study. The governing partial differential equations are first transformed into a system of ordinary differential equations before they are solved numerically by a finite-difference scheme, namely the Keller box method. Numerical solutions are obtained for a large range of values of the Prandtl number.     

COMBINED NATURAL AND FORCED CONVECTION IN A HORIZONTAL FLOW CHANNEL

The effect of natural convection on forced convection in a horizontal flow was investigated during zinc electrodeposition on a horizontal electrode facing upward in a channel. The previous findings of Tobias and Hickman [1] are confirmed. A secondary flow in the form of roll cells whose axes are parallel to the flow direction is formed at some distance from the leading edge. This distance depends linearly on the flow velocity through the critical Rayleigh number for the onset of natural convection across the diffusion boundary layer. Striated zinc deposits reveal the imprint of the secondary flow on the planar cathode facing upward.     

COMBINED NATURAL AND FORCED CONVECTION IN A HORIZONTAL FLOW CHANNEL

The effect of natural convection on forced convection in a horizontal flow was investigated during zinc electrodeposition on a horizontal electrode facing upward in a channel. The previous findings of Tobias and Hickman [1] are confirmed. A secondary flow in the form of roll cells whose axes are parallel to the flow direction is formed at some distance from the leading edge. This distance depends linearly on the flow velocity through the critical Rayleigh number for the onset of natural convection across the diffusion boundary layer. Striated zinc deposits reveal the imprint of the secondary flow on the planar cathode facing upward.     

A MATHEMATICAL MODEL FOR LAMINAR DISPLACEMENT OF ONE NON-NEWTONIAN FLUID BY ANOTHER IN HORIZONTAL CONCENTRIC ANNULI

This paper develops a mathematical model and a computational algorithm, which enable the prediction of laminar displacement efficiency in concentric horizontal annuli. Power-law model is used to characterize rheological properties of both displaced and displacing fluids. This model allows a careful investigation of individual effects of various parameters such as fluid rheology, flow geometry and displacement rate on the displacement efficiency. Simulated results demonstrate the dominant influence of rheological properties of displaced and displacing fluids on the laminar displacement efficiency. The model can be used to optimize fluid flow parameters in chemical process designs.     

A MATHEMATICAL MODEL FOR LAMINAR DISPLACEMENT OF ONE NON-NEWTONIAN FLUID BY ANOTHER IN HORIZONTAL CONCENTRIC ANNULI

This paper develops a mathematical model and a computational algorithm, which enable the prediction of laminar displacement efficiency in concentric horizontal annuli. Power-law model is used to characterize rheological properties of both displaced and displacing fluids. This model allows a careful investigation of individual effects of various parameters such as fluid rheology, flow geometry and displacement rate on the displacement efficiency. Simulated results demonstrate the dominant influence of rheological properties of displaced and displacing fluids on the laminar displacement efficiency. The model can be used to optimize fluid flow parameters in chemical process designs.     

倾斜管内热进口段自然强制复合对流传热

用数值分析方法研究了倾斜管内热进口段自然强制同向复合对流传热 ,分析了浮力、倾斜角及轴向导热对流动和传热特性的影响 ,得到了速度、温度、壁面剪切应力、局部及平均Nusselt数的分布和变化 研究结果显示Pe=71时平均Nusselt数的最大值位于 2 5°～ 45°之间 ,Pe=2 5时则在 90°处出现 .     

NON-NEWTONIAN POWER-LAW FLUID FLOW PAST A SHRINKING SHEET WITH SUCTION

The steady boundary-layer flow of a non-Newtonian fluid, represented by a power-law model, over a shrinking sheet is investigated. The transformed boundary-layer equation is solved numerically for some values of the power-law index n and suction parameter s. The effects of these parameters on the skin friction coefficient are analyzed and discussed. Different from those of a stretching sheet, the solutions are not unique and exist only if adequate suction on the boundary is imposed.     

A GENERALIZED DIFFERENTIAL TRANSFORM METHOD FOR COMBINED FREE AND FORCED CONVECTION FLOW ABOUT INCLINED SURFACES IN POROUS MEDIA

In this article, we apply the differential transform method (DTM) to obtain approximate analytical solutions of combined free and forced (mixed) convection about inclined surfaces (or wedges) in a saturated porous medium. Both aiding and opposing flows are considered. It is found that the parameter mixed convection from inclined surfaces in porous media is Gr/Re, where Gr is the local Grashof number and Re is the local Reynolds number. DTM solutions are obtained for mixed convection from an isothermal vertical flat plate as well as an inclined plate with constant heat flux having an inclination of 45°. Temperature and velocity profiles for these two cases at different values of Gr/Re are presented. The similarity transformations are applied to reduce the governing partial differential equations (PDEs) to a set of nonlinear coupled ordinary differential equations (ODEs) in dimensionless form. DTM is used to solve the nonlinear differential equations governing the problem in the form of series with easily computable terms. Thereafter a Padé approximant is applied to the solutions to increase the convergence of the given series. Excellent correlation between DTM-Padé and numerical quadrature (shooting) solutions is achieved. The DTM-Padé simulation is shown to be a robust benchmarking tool providing an excellent means of validation of numerical methods. The study has applications in geothermal energy systems, chemical engineering filtration systems, and packed beds.     

UNSTEADY HYDROMAGNETIC FREE CONVECTION FLOW OF A DISSIPATIVE AND RADIATING FLUID PAST A VERTICAL PLATE WITH CONSTANT HEAT FLUX

The effect of thermal radiation absorption on an unsteady free convective flow past a vertical plate is studied in the presence of a magnetic field and constant wall heat flux. Boundary layer equations are derived, and the resulting approximate nonlinear ordinary differential equations are solved analytically using asymptotic technique. A parametric study of all parameters involved is conducted, and a representative set of numerical results for the velocity and temperature profiles as well as the skin-friction parameter are illustrated graphically to show typical trends of the solutions.     

DIFFUSION OF CHEMICALLY REACTIVE SPECIES IN BOUNDARY LAYER FLOW OVER A POROUS PLATE IN POROUS MEDIUM

Analysis was made to study the effect of diffusion of chemically reactive species in boundary layer flow of an incompressible fluid over a porous flat plate in porous medium. The first-order chemical reaction was considered and the reaction rate of the reactive species was taken in such a manner that it varied inversely along the plate. Self-similar equations were obtained using similarity transformations and were then solved by the shooting technique using the fourth-order Runge-Kutta method. This analysis revealed that at a fixed point, with increase of the permeability of the porous medium the velocity increases, but the concentration decreases. The suction reduces the thicknesses of momentum and concentration boundary layers but due to blowing the thicknesses become larger. With increase of both the Schmidt number and the reaction rate parameter, the reactive concentration profiles decrease. For a destructive chemical reaction, the concentration profiles exhibit negative value when the Schmidt number is large. It is very significant to note that in some constructive chemical reaction cases the mass absorption at the plate occurs for small Schmidt number.     

HOMOTOPY ANALYSIS OF FREE CONVECTION BOUNDARY LAYER FLOW WITH HEAT AND MASS TRANSFER

A steady two-dimensional laminar boundary layer flow of an incompressible viscous fluid over a semi-infinite surface is considered to investigate the accuracy of the homotopy analysis method. The governing coupled nonlinear system of differential equations is solved by means of the HAM approach. Explicit analytical series solutions are obtained and compared with numerical solutions. Good agreement is observed between the numerical results and HAM analytical solutions.     

COMBINED HEAT AND MASS TRANSFER IN FREE CONVECTION ALONG A ROTATING PLATE UNDER UNIFORM HEAT AND UNIFORM MASS FLUXES

The problem of combined heat and mass transfer in laminar free convection along a vertically rotating plate subjected to a uniform heat flux and/or a uniform mass flux is studied analytically. The governing non-dimensional nonlinear coupled partial differential equations are solved by local similarity and local nonsimilarity approach. Numerical results for the local Nusselt number, the local Sherwood number and the local wall shear stress for the convective-diffusion of hydrogen, water vapor and naphthalene into the air are presented in tabular forms. The analysis extends the range both when the concentration buoyancy force assists as well as opposes the thermal buoyancy force.     

COMBINED HEAT AND MASS TRANSFER IN FREE CONVECTION ALONG A ROTATING PLATE UNDER UNIFORM HEAT AND UNIFORM MASS FLUXES

The problem of combined heat and mass transfer in laminar free convection along a vertically rotating plate subjected to a uniform heat flux and/or a uniform mass flux is studied analytically. The governing non-dimensional nonlinear coupled partial differential equations are solved by local similarity and local nonsimilarity approach. Numerical results for the local Nusselt number, the local Sherwood number and the local wall shear stress for the convective-diffusion of hydrogen, water vapor and naphthalene into the air are presented in tabular forms. The analysis extends the range both when the concentration buoyancy force assists as well as opposes the thermal buoyancy force.     

EFFECT OF MAGNETIC FIELD-DEPENDENT VISCOSITY ON THERMAL CONVECTION IN A FERROMAGNETIC FLUID

This article deals with the theoretical investigation of the effect of magnetic field-dependent (MFD) viscosity on a layer of ferromagnetic fluid heated from below subject to a transverse uniform magnetic field. For a flat fluid layer contained between two free boundaries, an exact solution is obtained using a linear stability analysis and normal mode analysis method. For the case of stationary convection, the MFD viscosity has a stabilizing effect, whereas the departure of linearity in the magnetic equation of state has a destabilizing (or stabilizing) effect on the system under certain conditions. The critical wave number and critical magnetic thermal Rayleigh number for the onset of instability are also determined numerically for large values of buoyancy magnetization, and results are depicted graphically. The principle of exchange of stabilities is valid for the ferromagnetic fluid heated from below.     

UNSTEADY MAGNETOHYDRODYNAMIC NON-NEWTONIAN FLOW DUE TO NON-COAXIAL ROTATIONS OF DISK AND A FLUID AT INFINITY

An analysis is carried out to study the flow generated in a semi-infinite expanse of an incompressible second-grade fluid bounded by a porous oscillating disk. The flow is due to non-coaxial rotations of a disk and a fluid at infinity. The fluid is electrically conducting in the presence of a uniform transverse magnetic field. The solutions of the developed flow are obtained for the cases when the angular velocity is greater than, smaller than, or equal to the frequency of oscillation. The velocity field is found analytically by a Laplace transform technique. It is found that for uniform suction and blowing at the disk, shear oscillations are confined to the Ekman-Hartmann layer near the disk for all values of the frequencies.     

边界层方程求解传热传质复合自然对流的偏差分析

引　言动量、能量及质量的边界层方程是Naveir Stokes完整方程的简化形式 ,自上世纪初提出以来 ,应用极广 .传热传质复合自然对流是自然界和工业过程中常见的现象 ,由于存在热与物质扩散两种浮力相对大小及方向的差异以及Prandtl数和Schmit数的影响 ,使该问题颇为复杂 .Bottema     

矩形截面气升式环流反应器中非牛顿流体的气含率与传质系数的研究

研究了一种矩形截面气升式环流反应器,用幂律τ=η_ογ~n(n<1)来表示流体流变学特性的变化.在这类反应器中,假塑性非牛顿流体的气含率ε_g与传质系数K_La的变化规律可用半经验关联式表示ε_g=0.2535(η_ο5000~(n-1))~(-0.161)(1+A_d/A_r)~(-0.434)u_(gr)~(0.856-0.161n)K_La=0.0192(η_ο5000~(n-1))~(-0.902)(1+A_d/A_r)~(-1.228)u_(gr)~(1.955-0.902n)并讨论了该类反应器结构及运行状况,流体性质变化时,反应器传质动力学特性、流动特性和操作弹性变化的规律.