Mixed convection adjacent to inclined flat surfaces embedded in a porous medium

An analysis is performed to study the flow and heat transfer characteristics of laminar mixed convection boundary layer flows from inclined (including horizontal and vertical) surfaces embedded in a saturated porous medium with constant aiding external flows and uniform surface temperature. Both the streamwise and normal components of the buoyancy forces are retained in the momentum equations. Nondimensionalization of the boundary layer equations results in the following three governing parameter: (1)Gr/Re, the ratio of the Grashof number to the Reynolds number; (2)Pe _x =Re _x Pr, the Peclet number; (3) φ, the angle of inclination from the horizontal. The resulting nonsimilar equations are solved by an efficient implicit finite-difference scheme. Numerical results are presented for flows with different values ofGr/Re in the range of 0 to 50, over a wide range of the Peclet numbersPe _x, and various values of φ ranging from 0 to 90 degrees. It is found that the local surface heat transfer rate increases with increasing the local Peclet number. In addition, as the plate is tilted from the horizontal to the vertical orientation, the local Nusselt number increases for a given Peclet number and the effect of the buoyancy force on the surface heat transfer rate increases.     

Onset of Double-Diffusive Reaction–Convection in an Anisotropic Rotating Porous Layer

The linear and non-linear stability of a rotating double-diffusive reaction–convection in a horizontal anisotropic porous layer subjected to chemical equilibrium on the boundaries is investigated considering a Darcy model that includes the Coriolis term. The effect of Taylor number, mechanical, and thermal anisotropy parameters, reaction rate, solute Rayleigh number, Lewis number, and normalized porosity on the stability of the system is investigated. We find that the Taylor number has a stabilizing effect, chemical reaction may be stabilizing or destabilizing and that the anisotropic parameters have significant influence on the stability criterion. The effect of various parameters on the stationary, oscillatory, and finite-amplitude convection is shown graphically. A weak nonlinear theory based on the truncated representation of Fourier series method is used to find the finite amplitude Rayleigh number and heat and mass transfer.     

Numerical investigation of particle lateral migration in straight channel flows using a direct-forcing immersed boundary method

Inertia-induced cross-stream migration has been recently exploited for precise position of particles in confined channel flows. In this work, a three-dimensional finite volume based immersed boundary method has been developed to study the lateral migration and hydrodynamic self-assembly of neutrally-buoyant particles in pressure-driven flows. Simulation results show that, in 2D channel flows, the equilibrium position for a circular particle is closer to the centreline for larger particle Reynolds number due to the increasing flow rate, while in 3D square duct flow, the equilibrium position for a spherical particle is near a face centre and is closer to the wall for larger particle Reynolds number. Self-assembly of a pair of particles is observed in 3D square duct flows but not in 2D channel flows. Mechanisms for the self-assembly are discussed.     

颗粒在黏弹性流体扩张和收缩流中沉降的格子Boltzmann模拟分析

对于Oldroyd-B型黏弹性流体,本文应用格子Boltzmann方法(LBM),实现了流体在二维1:3扩张流道及3:1收缩流道中流动的数值模拟,获得了黏弹性流体在扩张和收缩流道中的流场分布．结合颗粒的受力和运动规则,基于点源颗粒模型,数值分析了颗粒在扩张流和收缩流中的沉降过程和特征,讨论了颗粒相对质量和起始位置以及雷诺数Re和威森伯格数Wi对颗粒沉降特征的影响．结果表明,颗粒相对质量和起始位置以及Re对颗粒沉降轨迹和落点影响较大,而Wi的影响则较小．     

A general heat transfer correlation for non-boiling gas–liquid flow with different flow patterns in horizontal pipes

A general heat transfer correlation for non-boiling gas–liquid flow with different flow patterns in horizontal pipes is proposed. In order to overcome the effect of flow pattern on heat transfer, a flow pattern factor (effective wetted-perimeter) is developed and introduced into our proposed correlation. To verify the correlation, local heat transfer coefficients and flow parameters were measured for air–water flow in a pipe in the horizontal position with different flow patterns. The test section was a 27.9 mm ID stainless steel pipe with a length to diameter ratio of 100. A total of 114 data points were taken by carefully coordinating the liquid and gas superficial Reynolds number combinations. The heat transfer data were measured under a uniform wall heat flux boundary condition ranging from about 3000 W/m² to 10,600 W/m². The superficial Reynolds numbers ranged from about 820 to 26,000 for water and from about 560 to 48,000 for air. These experimental data including different flow patterns were successfully correlated by the proposed general two-phase heat transfer correlation with an overall mean deviation of 5.5%, a standard deviation of 11.7%, and a deviation range of −18.3% to 37.0%. Ninety three percent (93%) of the data were predicted within ±20% deviation.     

多层平行裂隙型多孔介质通道内流体流动传热特性

基于Brinkman-extended Darcy模型和局部热平衡模型,对多层平行裂隙型多孔介质通道内的流动传热特性进行研究.获得了多层平行裂隙型多孔介质通道内各区域的速度场、温度场、摩擦系数及努塞尔数解析解,并分析了裂隙层数、达西数、空心率、有效热导率之比等对通道内流动传热特性的影响.结果表明:达西数较小时,通道多孔介质层内会出现不随高度变化的达西速度,此达西速度会随裂隙层数的增加而增大,但却不受各裂隙层下多孔介质层位置变化的影响.增加裂隙层数会减弱空心率对压降的影响,会使通道内流体压降升高,但升高程度会逐渐降低.增大热导率之比或减小空心率会使多裂隙通道内出现阶梯式温度分布,而在较小热导率之比或较大空心率时多裂隙情况下的温度分布曲线会趋于一致.此外,当热导率之比较小时,多层裂隙通道内的传热效果在任何空心率下都要优于单裂隙情况,当热导率之比较大时,存在临界空心率使各裂隙层数通道内的传热效果相同,且多裂隙通道内继续增加裂隙层数对传热强度影响不大.     

Numerical simulation of particle sedimentation in 3D rectangular channel

The 3D lattice Boltzmann method is used to simulate particle sedimentation in a rectangular channel. The results of single particle sedimentation indicate that the last position of the particle is along the center line of the channel regardless of the initial position, the particle diameter, and the particle Reynolds number. The wall effect on the terminal velocity is in good agreement with experimental results quantitatively. The drafting, kissing, and tumbling (DKT) process is reproduced and analyzed by simulating two-particle cluster sedimentation. The effects of the diameter ratio, initial position, and wall on the DKT process are investigated. When the two particles have equal diameter sediment in the rectangular channel, a periodical DKT process and the spiraling trajectory are found. The last equilibrium configuration is obtained from the simulation results. The interesting regular sedimentation phenomena are found when 49 particles fall down under gravity.     

Heat and mass transfer in a dispersive medium

Macroscopic equations for the conservation of heat (or the mass of a diffusing impurity) in a continuous medium containing distributed particles of a dispersed phase are formulated neglecting the effect of random fluctuations of the medium and particles by the transfer process. The problem of convective heat conduction or diffusion near an isolated particle is also formulated, the solution of which permits calculation of all the parameters entering into the indicated equations. This problem has been solved in the particular case of small Peclet numbers, which characterize heat and mass exchange in the vicinity of a single particle.     

Heat and mass transfer in the initial microchannel section with chemical conversions of methane in water vapor

The Navier-Stokes equations for a laminar flow of a compressible multispecies gas have been used to model numerically the heat and mass transfer processes in high-temperature chemical reactions of methane in water vapor with activation of reactions on the microchannel walls and external heat supply. The temperature and concentration fields are obtained, as well as the distributions of heat fluxes, reacting species, and local coefficients of heat and mass transfer along the channel. It is shown that a high degree of chemical conversion leads to nonmonotonical changes in reaction rates and velocities of transverse heat flows, and species along the microchannel, considerably affecting the local coefficients of heat and mass transfer.     

Mathematical and numerical modeling of melting in metal-ceramic composite beds

Many of the ceramics used in the manufacture of the metal-ceramic composites are available as powders, which has encouraged investigators to develop tool less manufacturing techniques. Innovative processes like combustion synthesis and laser sintering processes offer great potential for specific material combinations. These processes involve heat and mass transfer in porous matrix with melting, solidification and may be chemical reaction. Since the resulting transport is relatively complex, there are few mathematical models available. In the present study, melting and transport of metal is demonstrated for a one-dimensional bed with uniform heat generation and convectively cooled boundaries. The effects of different Bond, Biot and Prandtl numbers are discussed using constant and temperature varying material properties. At low bond number the transport is controlled by capillary forces and temperature and saturation distribution is symmetric about the center of the bed. For Biot number larger than ten the process is internally controlled. Effect of Prandtl number is opposite of that of the Bond number. Use of constant properties overpredicts the process rate by 13%.     

Mixing and segregation assessment of bi-disperse solid particles in a double paddle mixer

A double paddle blender's flow patterns and mixing mechanisms were analyzed using discrete element method (DEM) and experiments. The mixing performance of this type of the blender containing bi-disperse particles has been rarely studied in the literature. Plackett-Burman design of experiments (DoE) methodology was used to calibrate the DEM input parameters. Subsequently, the impact of the particle number ratio, vessel fill level, and paddle rotational speed on mixing performance was investigated using the calibrated DEM model. The mixing performance was assessed using relative standard deviation and segregation intensity. Mixing performance was significantly affected by the paddle rotational speed and particle number ratio. Moreover, the Peclet number and diffusivity coefficient were used to evaluate the mixing mechanism in the blender. Results revealed that the diffusion was the predominant mixing mechanism, and the best mixing performance was observed when the diffusivity coefficients of 3 mm and 5 mm particles were almost equal.     

Stagnation-point viscous flow of an incompressible fluid between porous plates with uniform blowing

The axially-symmetric laminar flow of an incompressible viscous fluid resulting from uniform injection through two parallel porous plates is analyzed. An exact numerical solution as well as asymptotic solutions for high and low Reynolds numbers are obtained. It is found that the velocity component normal to the porous plates is everywhere independent of radial position. This property of uniform accessibility may make this flow geometry a useful experimental tool analogous to the rotating disc. The analysis of high Peclet number mass transfer across the center plane of this geometry is presented as an example.     

Cooling of a viscoelastic film during unsteady extrusion from an annular die

The unsteady extrusion of a viscoelastic film from an annular and axisymmetric die is examined. External, elastic, viscous and inertia forces deform the film, which is simultaneously cooled via forced convection to the ambient air. This moving boundary problem is solved by mapping the liquid/air interfaces onto fixed ones and by employing a regular perturbation expansion for all the dependent variables. The ratio of the film thickness to its inner radius at the exit of the die is used as the small parameter in the perturbation expansion. The fluid mechanical aspects of the process depend on the Stokes, Deborah, Reynolds, and Capillary numbers. The heat transfer in the film and to the environment gives rise to four additional dimensionless groups: the Peclet, Biot and Brinkman numbers and the activation energy, which determines the temperature dependence of fluid viscosity and elasticity. A variable heat transfer coefficient is also considered. For typical fluid properties and process conditions, the Peclet number is very large. In this case it is the ratio of the Biot to the Peclet number, the Stanton number, which arises in the energy conservation equation. It is shown that film cooling becomes important when the Stanton number and/or the activation energy are in the high-end of their typical values. In such cases, the cooling of the parison leads to a more uniform flow and shape for the film. The influence on the process of a variable heat transfer coefficient and the Brinkman number is small. Received: 7 April 1999/Accepted: 10 August 1999     

Drift-flux model for upward two-phase cross-flow in horizontal tube bundles

In relation to void fraction prediction of cross-flow in horizontal tube bundle of shell-tube heat exchangers, a drift-flux correlation has been developed to meet the demand on the study of two-phase flow gas and liquid velocities, two-phase pressure drop, heat transfer, flow patterns and flow induced vibrations in the shell side. Two critical parameters such as distribution parameter and drift velocity have been modeled. The distribution parameter is obtained by constant asymptotic values and taking into account the differences in channel geometry. The drift velocity is modelled depending on the density ratio and the non-dimensional viscosity number. The relationship between the channel averaged and gap mass velocity has been discussed in order to obtain the superficial gas and liquid velocities in the drift-flux correlation. The newly developed drift-flux correlation agrees well with cross-flow experimental databases of air-water, R-11 and R-113 in parallel triangular, normal square and normal triangular arrays with the mean absolute error of 1.06% and the standard deviation of 4.47%. In comparison with other existing correlations, the newly developed drift-flux correlation is superior to other studies due to the improved accuracy. In order to extend the applicability of the newly developed drift-flux correlation to void fraction of unity, an interpolation scheme has been developed. The newly developed drift-flux correlation is able to calculate the void fraction of cross-flow over a full range with different sub-channel configurations in shell-tube type heat exchangers.     

Heat transfer correlation for boiling flows in small rectangular horizontal channels with low aspect ratios

In the present experimental study, a correlation is proposed to represent the heat transfer coefficients of the boiling flows through horizontal rectangular channels with low aspect ratios. The gap between the upper and the lower plates of each channel ranges from 0.4 to 2 mm while the channel width being fixed to 20 mm. Refrigerant 113 was used as the test fluid. The mass flux ranges from 50 to 200 kg/m² s and the channel walls were uniformly heated up to 15 kW/m². The quality range covers from 0.15 to 0.75 and the flow pattern appeared to be annular. The modified Lockhart–Martinelli correlation for the frictional pressure drop was confirmed to be within an accuracy of ±20%. The heat transfer coefficients increase with the mass flux and the local quality; however the effect of the heat flux appears to be minor. At the low mass flux condition, which is more likely to be with the smaller gap size, the heat transfer rate is primarily controlled by the liquid film thickness. A modified form of the enhancement factor F for the heat transfer coefficient in the range of Re_LF200 well correlates the experimental data within the deviation of ±20%. The Kandlikar's flow boiling correlation covers the higher mass flux range (Re_LF>200) with 10.7% mean deviation.     

Migration of settling particles in a horizontal viscous flow through a vertical slot with porous walls

Particle migration in a horizontal flow of dilute suspension through a vertical slot with porous walls is studied using the two-continua approach. The lateral migration is induced by two opposite effects: an inertial lift force due to particle settling and directed toward the slot centre-line, and a drag due to leak-off entraining particles toward the walls. An expression for the inertial lift on a settling particle in a horizontal channel flow found recently is generalized to the case of a low leak-off velocity. The evolution of an initial uniform particle concentration profile is studied within the full Lagrangian approach. Four migration regimes are found differing by the direction of particle migration and numbers of equilibrium positions. Conditions of the regime change and a critical value of dimensionless leak-off velocity for particle deposition on the walls are obtained analytically. Suspension flows with zones where the particle concentration is zero or increases infinitely, are studied numerically.     

Nanoparticle coagulation in a planar jet via moment method

Large eddy simulations of nanoparticle coagulation in an incompressible pla- nar jet were performed.The particle is described using a moment method to approximate the particle general dynamics equations.The time-averaged results based on 3000 time steps for every case were obtained to explore the influence of the Schmidt number and the Damkohler number on the nanoparticle dynamics.The results show that the changes of Schmidt number have the influence on the number concentration of nanoparticles only when the particle diameter is less than 1 nm for the fixed gas parameters.The number concentration of particles for small particles decreases more rapidly along the flow di- rection,and the nanoparticles with larger Schmidt number have a narrower distribution along the transverse direction.The smaller nanoparticles coagulate and disperse easily, grow rapidly hence show a stronger polydispersity.The smaller coagulation time scale can enhance the particle collision and coagulation.Frequented collision and coagulation bring a great increase in particle size.The larger the Damkohler number is,the higher the particle polydispersity is.     

Finite element method solution of simultaneous two-dimensional heat and mass transfer in laminar film flow

A finite element solution is given for the coupled heat and mass transfer taking place when a vapour with considerable heat of absorption is absorbed into a laminar film flow. Convection and diffusion parallel and perpendicular to the direction of flow are taken into account. Temperature and mass fraction profiles across the film are given as well as results in film flow direction for several values of the Peclet number. Comparison with a solution based on one-dimensional flow and diffusion perpendicular to the flow, shows that deviations from this case by our two-dimensional solution increase for decreasing Peclet number.     

Triple-Diffusive Mixed Convection in a Porous Open Cavity

The triple-diffusive mixed convection heat and mass transfer of a mixture is analyzed in an enclosure filled with a Darcy porous medium. The mass transfer buoyancy effects due to concentration gradients of the dispersed components (pollutant components) are taken into account using the Boussinesq approximation model. The governing equations are transformed into a non-dimensional form, and six groups of non-dimensional parameters, including Darcy–Rayleigh number, Peclet number, two Lewis numbers for pollutant components 1 and 2 and two buoyancy ratio parameters for pollutant components 1 and 2, are introduced. The governing equations are numerically solved for various combinations of non-dimensional parameters using the finite element method. The effect of each group of non-dimensional parameters on the pollutant distribution and the heat transfer in the cavity is discussed. The results indicate that the presence of one pollutant component can significantly affect the pollutant distribution of the other component. When the Lewis number of a pollutant component is small, the increase in the bouncy ratio parameter of the proposed component always increases the Nusselt and Sherwood numbers in the cavity.     

Natural convection and conduction heat transfer in open shallow cavities with bounding walls

A numerical study has been carried out on inclined open shallow cavities, which are formed by a wall and horizontal fins. Constant heat flux is applied on the surface of the wall inside the cavity while its other surface was kept isothermal. The wall and the fins are conductive. Conjugate heat transfer by natural convection and conduction is studied by numerically solving equations of mass, momentum and energy. Streamlines and isotherms are produced, heat and mass transfer is calculated. A parametric study is carried out using following parameters: Rayleigh number from 10⁶ to 10¹², conductivity ratio from 1 to 60, open cavity aspect ratio from 1 to 0.125, dimensionless end wall thickness from 0.05 to 0.20, horizontal walls from 0.01 to 0.15 and inclination of the end wall from 90° to 45°. It is found that the volume flow rate and Nusselt number are a decreasing function of the cavity aspect ratio, horizontal fin thickness and conductivity ratio. They are an increasing function of end wall thickness and inclination angle, except in the latter case optima exist at high Rayleigh numbers.