Convective--Diffusive Transport with Chemical Reaction in Natural Convection Flows

A study of laminar natural convection flow over a semi-infinite vertical plate at constant species concentration is examined. The plate is maintained at a given concentration of some chemical species while convection is induced by diffusion into and chemical reaction with the ambient fluid. In the absence of chemical reaction, a similarity transform is possible. When chemical reaction occurs, perturbation expansions about an additional similarity variable dependent on reaction rate must be employed. Two fundamental parameters of the problem are the Schmidt number, Sc, and the reaction order, n. Results are presented for the Schmidt number ranging from 0.01 to 10000 and reaction order up to 5. In the presence of a chemical reaction, the diffusion and velocity domains expand out from the plate. This results in a larger, less distinct convection layer. Received 21 July 1998 and accepted 24 June 1999     

Transient mixed convection flow arising due to thermal and mass diffusion over porous sensor surface inside squeezing horizontal channel

The double diffusion effect on the mixed convection flow over a horizontal porous sensor surface placed inside a horizontal channel is analyzed.With the appropriate transformations,the unsteady equations governing the flow are reduced to non-similar boundary layer equations which are solved numerically for the time-dependent mixed convection parameter.The asymptotic solutions are obtained for small and large values of the time-dependent mixed convection parameter.The results are discussed in terms of the skin friction,the heat transfer coefficient,the mass transfer coefficient,and the velocity,temperature,and concentration profiles for different values of the Prandtl number,the Schmidt number,the squeezing index,and the mixed convection parameter.     

Low-pass filtering effects of viscous sublayer on high Schmidt number mass transfer close to a solid wall

Numerical simulation of high Schmidt number turbulent mass transfer at a solid wall is carried out. Particular attention is paid to the response of the concentration field to the wall-normal velocity fluctuation inside the viscous sublayer. Spatio-temporal correlation shows that the high Schmidt number concentration field becomes insensitive to the wall-normal velocity fluctuation. In addition, there exists a significant time lag in the response of the concentration field to the wall-normal velocity fluctuation. As a result, the instantaneous distribution of the local mass transfer rate is drastically changed. These facts explain why the analogy between the momentum and mass transfer does not hold close to the wall. Based on a one-dimensional advection–diffusion equation, we derive a transfer function connecting the wall-normal velocity and the concentration fluctuations. It is shown that the present model can reproduce the fundamental dynamical features of high Schmidt number concentration field.     

Characteristics of turbulent-exchange coefficients in a viscous underlayer

The transient equations for longitudinal (along the flow) velocity pulsations and pulsations of concentration in the region of a viscous underlayer are considered. Estimates based on experimental data enable the contributions arising from certain terms of these equations to be neglected in turbulent transfer. Subject to this approximation, expressions are obtained for the turbulent viscosity and diffusion coefficients. These coefficients behave differently in the case of large Schmidt (Prandtl) numbers. The behavior of the turbulent Schmidt number in the region of the viscous underlayer is analyzed.     

Solution of general dynamic equation for nanoparticles in turbulent flow considering fluctuating coagulation

A new averaged general dynamic equation (GDE) for nanoparticles in the turbulent flow is derived by considering the combined effect of convection, Brownian diffusion, turbulent diffusion, turbulent coagulation, and fluctuating coagulation. The equation is solved with the Taylor-series expansion moment method in a turbulent pipe flow. The experiments are performed. The numerical results of particle size distribution correlate well with the experimental data. The results show that, for a turbulent nanoparticulate flow, a fluctuating coagulation term should be included in the averaged particle GDE. The larger the Schmidt number is and the lower the Reynolds number is, the smaller the value of ratio of particle diameter at the outlet to that at the inlet is. At the outlet, the particle number concentration increases from the near-wall region to the near-center region. The larger the Schmidt number is and the higher the Reynolds number is, the larger the difference in particle number concentration between the near-wall region and near-center region is. Particle polydispersity increases from the near-center region to the near-wall region. The particles with a smaller Schmidt number and the flow with a higher Reynolds number show a higher polydispersity. The degree of particle polydispersity is higher considering fluctuating coagulation than that without considering fluctuating coagulation.     

Microchannel membrane separation applied to confined thin film desorption

The concept of a confined thin film to enhance the desorption process is based on a reduced mass diffusion resistance. A wide thin film is formed into a microchannel by using a porous membrane as one wall of the channel enabling vapor extraction along the flow. Heat added to the channel results in vapor generation and subsequent extraction through the membrane. This experimental study investigates the performance of vapor extraction as a function of confined thin film thickness, pressure difference across the membrane and inlet concentration to the microchannel. In addition, heat added to the system was varied and results are presented in terms of the wall superheat temperature relative to the inlet saturated conditions of the binary fluid. The test section was equipped with a transparent window to observe bubble formation and vapor extraction. Results show that the performance, measured by the vapor release rate, increases for reduced channel thickness, for increased pressure difference across the membrane, and for lower inlet concentration. Results show that lower wall superheat correspond to higher heat transfer coefficients. Trends of Nusselt number and Sherwood number versus both channel Reynolds number and the product of the Reynolds number and Schmidt number are presented. Bubble formation in the channel does not degrade overall performance provided a critical heat flux condition does not occur.     

Unsteady flow past an impulsively started vertical plate with heat and mass transfer

Finite difference solution of the transient free-convection flow of an incompressible viscous fluid past an impulsively started semi-infinite vertical plate with heat and mass transfer is presented here. The steady state velocity, temperature and concentration profiles are shown graphically. Velocity profiles are compared with exact solution. It has been observed that there is a rise in the velocity due to the presence of a mass diffusion. An increase in Schmidt number, leads to a fall in the velocity. Stability and the convergence of the finite difference scheme are established. Received on 7 January 1998     

Near-field development of gas-phase horizontal laminar jets with positive and negative buoyancy measured with filtered Rayleigh scattering

Near-field mixing characteristics of horizontally issuing jets, alternatively positively and negatively buoyant, are explored. The cross-sectional mass fraction of a buoyant horizontal jet consisting of helium flowing into ambient air is measured using a non-intrusive technique, filtered Rayleigh scattering, for Reynolds numbers ranging from 50 to 1,200, Froude numbers ranging as low as 0.71, and Schmidt numbers on the order of unity for all tests. Several corresponding experiments were carried out using carbon dioxide in place of helium in order to determine whether the direction of the buoyancy changes the characteristic shape of the jet cross-section. Consistent with the literature, mixing rates were consistently higher on the side of the jet where instability, due to density stratification, was present. At jet Froude numbers ranging between 1.5 and approximately 3, the jet cross-section takes a shape consistent with a single plume of fluid being ejected from the core in a vertical direction—upward for a jet with positive buoyancy and downward for a jet with negative buoyancy. Remarkably, for Froude numbers less than unity, the distortion of the jet is quite different in that two separate plumes emanate from each side of the jet while ejection from the center is suppressed. Both the positively and negatively buoyant jet cross-sections exhibited this trait, suggesting that the mechanism that determines the cross-sectional shape of the jet core is only mildly influenced by centripetal effects brought about by streamline curvature. The location of the jet centroid at varied streamwise locations was computed from the mass fraction data, yielding jet trajectory.     

Study of mass and momentum transfer in diesel sprays based on X-ray mass distribution measurements and on a theoretical derivation

In this paper, a research aimed at quantifying mass and momentum transfer in the near-nozzle field of diesel sprays injected into stagnant ambient air is reported. The study combines X-ray measurements for two different nozzles and axial positions, which provide mass distributions in the spray, with a theoretical model based on momentum flux conservation, which was previously validated. This investigation has allowed the validation of Gaussian profiles for local fuel concentration and velocity near the nozzle exit, as well as the determination of Schmidt number at realistic diesel spray conditions. This information could be very useful for those who are interested in spray modeling, especially at high-pressure injection conditions.     

Double stratified radiative flow of an Oldroyd-B nanofluid with nonlinear convection

The nonlinear convective flow of an Oldroyd-B fluid due to a nonlinear stretching sheet with varying thickness is examined. The salient features of the random movement and thermophoresis are described. Formulation is made with the nonlinear thermal radiation and heat generation/absorption. Further, the convective conditions and double stratification are taken into account. The resulting flow problems are tackled by the optimal homotopy analysis method(OHAM). The resulting nonlinear problems are solved for the velocity, temperature, and concentration fields. The temperature and concentration gradients are numerically discussed. The total residual error is calculated.The Nusselt number is an increasing function of the radiation parameter. The Sherwood number increases with the increase in the solutal stratification or the Schmidt number.The main outcomes are presented in conclusions. This study has a wide range of applications such as thermal stratification of oceans, reservoirs, and rivers, density stratification of atmosphere, hydraulic lifts, and polymer processing.     

Deep gravity waves in moist-saturated atmospheric air

The equations of motion of a moist-saturated, dissipative, stratified atmosphere are used in the case of small Schmidt number to describe the propagation of linearized gravity waves in deep cloudy atmosphere: as in dry air, the consequence of the dissipation is the diffusion and the damping of waves through the medium. However, there exist particular cases of stratification, for which the moisture gives rise at locally undamped waves. This property justifies the existence of oscillatory unstable régimes when we study shallow convection in the medium.     

Similarity solution of MHD boundary layer flow with diffusion and chemical reaction over a porous flat plate with suction/blowing

Similarity analysis of diffusion of chemically reactive solute distribution in MHD boundary layer flow of an electrically conducting incompressible fluid over a porous flat plate is presented. The reaction rate of the solute is considered inversely proportional along the plate. Adopting the similarity transformation technique the governing equations are converted into the self-similar ordinary differential equations which are solved by shooting procedure using Runge-Kutta method. For increase of the Schmidt number the solute boundary layer thickness is reduced. Most importantly, the effects of reaction rate and order of reaction on concentration field are of conflicting natures, due to increasing reaction rate parameter the concentration decreases, but for the increase in order of reaction it increases. In presence of chemical reaction, the concentration profiles attain negative value when Schmidt number is large.     

Mass transfer to rotating cones

The mass transfer of oxygen to a rotating cone has been measured in a quiescent fluid. Cones with vertex angles of 19.2°, 30°, 60°, 90°, 120° and 180° (disks) were used in both laminar and turbulent flow at a Schmidt number of 400. The laminar flow mass transfer data is in agreement with an equation derived for cones at high Schmidt numbers. The turbulent flow mass transfer data for cones with vertex angles greater than 19.2° is in agreement with the high Schmidt number expression of Deissler. The 19.2° cone angle, however, results in experimental values for the mass transfer which are greater than the predicted values. Lastly, the values of the Reynolds number for transition from laminar to turbulent flow, as determined directly from the mass transfer data, are in agreement with previous results.     

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.     

Analysis and Modeling of the Turbulent Diffusion of Turbulent Kinetic Energy in Natural Convection

Buoyant flows often contain regions with unstable and stable thermal stratification from which counter gradient turbulent fluxes are resulting, e.g. fluxes of heat or of any turbulence quantity. Basing on investigations in meteorology an improvement in the standard gradient-diffusion model for turbulent diffusion of turbulent kinetic energy is discussed. The two closure terms of the turbulent diffusion, the velocity-fluctuation triple correlation and the velocity-pressure fluctuation correlation, are investigated based on Direct Numerical Simulation (DNS) data for an internally heated fluid layer and for Rayleigh–Bénard convection. As a result it is decided to extend the standard gradient-diffusion model for the turbulent energy diffusion by modeling its closure terms separately. Coupling of two models leads to an extended RANS model for the turbulent energy diffusion. The involved closure term, the turbulent diffusion of heat flux, is studied based on its transport equation. This results in a buoyancy-extended version of the Daly and Harlow model. The models for all closure terms and for the turbulent energy diffusion are validated with the help of DNS data for internally heated fluid layers with Prandtl number Pr = 7 and for Rayleigh–Bénard convection with Pr = 0.71. It is found that the buoyancy-extended diffusion model which involves also a transport equation for the variance of the vertical velocity fluctuation gives improved turbulent energy diffusion data for the combined case with local stable and unstable stratification and that it allows for the required counter gradient energy flux.     

Viscous and Ohmic heating effects in doubly stratified free convective flow over vertical plate with radiation and chemical reaction

An analysis is carried out to study the combined effects of viscous and Ohmic heating in the transient, free convective flow of a viscous, incompressible, and doubly stratified fluid past an isothermal vertical plate with radiation and chemical reactions. The governing boundary layer equations are solved numerically by an implicit finite difference scheme of the Crank-Nicolson type. The influence of different parameters on the velocity, the temperature, the concentration, the skin friction, the Nusselt number, and the Sherwood number is discussed with graphical illustrations. It is observed that an increase in either the thermal stratification or the mass stratification parameter decreases the velocity. An increase in the thermal stratification increases the concentration and decreases the temperature while an opposite effect is observed for an increase in the mass stratification. An augmentation in viscous and Ohmic heating increases the velocity and temperature while decreases the concentration. The results are found to be in good agreement with the existing solutions in literature.     

纳米粒子在方管中传输与沉降的研究

采用有限体积法离散并应用Simple方法对方截面弯曲管道内的纳米粒子传输和沉降进行了数值计算,结果表明Reynolds数和Schmidt数是影响纳米粒子传输和沉降的重要参数。粒子较小时,弯管中轴向速度较大的区域就是粒子的高浓度区域,沉降增强因子最大值出现在外弯侧的中心位置;粒子较大时,截面浓度的梯度值降低,沉降增强因子趋于平均,此时整个截面的粒子平均沉降。弯曲作用对于粒子较大且Dean数也较大时的影响更加明显。     

Investigation of generalized Fick’s and Fourier’s laws in the second-grade fluid flow

The second-grade fluid flow due to a rotating porous stretchable disk is modeled and analyzed. A porous medium is characterized by the Darcy relation. The heat and mass transport are characterized through Cattaneo-Christov double diffusions. The thermal and solutal stratifications at the surface are also accounted. The relevant nonlinear ordinary differential systems after using appropriate transformations are solved for the solutions with the homotopy analysis method (HAM). The effects of various involved variables on the temperature, velocity, concentration, skin friction, mass transfer rate, and heat transfer rate are discussed through graphs. From the obtained results, decreasing tendencies for the radial, axial, and tangential velocities are observed. Temperature is a decreasing function of the Reynolds number, thermal relaxation parameter, and Prandtl number. Moreover, the mass diffusivity decreases with the Schmidt number.     

The role of geometry in rough wall turbulent mass transfer

We report on RANS simulations of high Schmidt number turbulent mass transfer due to a first-order reaction on the surface of a d-type rough wall. We find that for low reaction coefficients, the additional surface area of the rough wall causes an increased mass transfer in comparison with a smooth wall. However, when the reaction coefficient is high, the mass transfer becomes lower than for a smooth wall. A detailed analysis shows that the mass transport in the cavity is dominated by diffusion which becomes the limiting factor at high reaction coefficients. A conceptual model, which is in good agreement with the simulations, highlights that the influence of geometry roughness is not confined to the roughness Reynolds number for molecular-diffusion-dominated cavities.     

振荡潜流带沉积层?水界面污染物输运的研究

潜流带中污染物质交换与输运特性是影响水资源环境的重要问题之一. 本文对底部为高渗透沉积层的三维槽道振荡流高Schmidt数传质问题进行了大涡模拟研究. 采用动力学亚格子模型来封闭滤波后的三维不可压缩Navier-Stokes方程以及污染物输运方程, 同时采用修正的Darcy-Brinkman-Forcheimer模型来描述沉淀有锌离子污染溶质的可渗透沉积层. 通过对沉积层内外流场和浓度场的统计特性以及瞬态结构的分析, 探究了上覆水体中振荡流驱动作用对污染物输运的动力学影响以及扩散率随振荡周期和振荡角的变化规律. 研究结果表明, 浓度通量中的湍流浓度分量在垂向物质交换中起主导作用, 流向、展向速度, 湍流强度和污染物浓度的波动跟随振荡驱动力呈现准周期变化, 同时发现沉积层?水交界面处的湍流浓度通量与法向湍流强度两者之间的变化具有明确的相关性. 并且在较大振荡角和低频振荡的情况下, 沉积层?水交界面处的有效扩散率增大, 这主要是来自于沉积层?水交界面处流体的猝发行为有效促进了湍流混合和物质交换, 进而增强了污染物的垂向输运.