Effect of External Recycle on Mass Transfer in Countercurrent Double-Pass Cross-Flow Rectangular Dialyzers

A study on mass transfer in countercurrent cross-flow rectangular dialyzers with external recycle was investigated. Theoretical analysis of mass transfer in cross-flow dialyzers is analogous to heat transfer in cross-flow heat exchangers. In contrast to a single-pass cross-flow device without recycle, improvement in mass transfer of about 30% is achievable if a double-pass device of the same size with external recycle is employed, which provides the increase of fluid velocity, resulting in increase of mass-transfer coefficient. Higher effectiveness may be expected when dialysis is operated for the system in which the mass-transfer resistances in the liquid films are comparable with that in the membrane.     

Recycle effect on membrane extraction through cross-flow rectangular modules

The effects of recycle on membrane extraction through a cross-flow rectangular module have been studied both theoretically and experimentally. Theoretical analysis of mass transfer in cross-flow device with and without recycle is analogous to heat transfer in cross-flow heat exchangers. Experiments were carried out with the use of a membrane sheet made of microporous polypropylene as a permeable barrier to extract acetic acid from aqueous solution by methyl isobutyl ketone. Theoretical predictions are in agreement with the experimental results. In contrast to a device without recycle, improvement in mass transfer is achievable if cross-flow membrane extraction is operated in a device of same size with recycle which provides the increase of fluid velocity, resulting in reduction of mass-transfer resistance. It is shown that recycle can enhance mass transfer, especially for large feed-concentration solution with high distribution coefficient operated under high reflux ratio.     

Application of internal reflux in the raffinate phase for membrane extraction in cross-flow rectangular modules

The effect of internal reflux in the raffinate phase for membrane extraction through a cross-flow rectangular module was investigated. Theoretical analysis of mass transfer in cross-flow devices with or without recycle was analogous to heat transfer in cross-flow heat exchangers. In contrast to a device without reflux, considerable improvement in mass transfer is achievable if cross-flow membrane extractors are operated with reflux which provides the increase of fluid velocity, resulting in reduction of mass-transfer resistance. It is concluded that reflux can enhance mass transfer, especially for large flow rate and feed-concentration solution operated under high reflux ratio.     

A study of mass transfer efficiency in a parallel-plate channel with external refluxes

The phenomenon of mass transfer through a parallel-plate channel with uniform wall concentration and external refluxes has been investigated by use of an orthogonal calculation technique. Considerable improvement is achieved when the external refluxes and barrier position are suitably adjusted. Analytical results show that recycle can enhance the mass transfer efficiency for high inlet flow rate compared with that in a single-pass device (without a permeable barrier inserted).     

Analysis of mass transfer in parallel-flow dialyzer with internal recycle for improved performance

The internal reflux effect on dialysis through the retentate phase of a parallel-flow rectangular module is investigated. Theoretical analysis of mass transfer in the membrane devices with or without recycling is analogous to heat transfer in heat exchangers. In contrast to a device without reflux, considerable mass transfer is achievable if parallel-flow dialyzers are operated with reflux, which provides an increase in fluid velocity, resulting in a reduction in mass-transfer resistance. It is concluded that reflux can enhance mass transfer, especially for large flow rate and feed-concentration operated under high reflux ratio.     

On the examination of recycle on heat (and mass) transfer in concentric tubes

The effect of recycle on heat (and mass) transfer in concentric circular tubes has been investigated by finite difference methods. Theoretical results show that recycle can enhance the heat transfer rate for large Graetz numbers compared with that in an open tube (without an inner tube inserted and without recycle). Competition between a preheating effect and a residence-time effect can be used to explain the heat transfer behavior. The heat transfer rate can be further augmented, with nearly no increase in total pressure drop, by employing flow pattern B instead of flow pattern A.     

Recycle Effect on Double‐Pass Concentric Circular Mass Exchangers under Uniform Wall Fluxes

A study on improvement in device performance of a double‐pass concentric circular mass exchanger with uniform wall fluxes and external refluxes was conducted under counterflow operations. The linear superposition of an asymptotic solution and a homogeneous solution with the use of an orthogonal expansion technique for solving such a conjugated Graetz problem is formulated theoretically and the analytical predictions are applied to investigate a substantial masstransfer improvement. A mathematical expression for the average Sherwood numbers and the outlet dimensionless concentration is given. Comparisons of analytical results are made with the single‐pass operations of the same working dimensions (without permeable barriers inserted and without recycle). Considerable device improvement in mass transfer rate is obtained by introducing the recycle‐effect concept in designing such double‐pass devices. The effect of permeable barriers on the mass‐transfer efficiency improvement as well as on the power consumption increment has also been delineated.     

SCALE ANALYSIS AND PARAMETRIC STUDY OF TRANSIENT HEAT/MASS TRANSFER IN THE PRESENCE OF NONPOROUS SOLID ADSORPTION

A transient, two-dimensional theoretical analysis of combined heat and mass transfer in the presence of adsorption/desorption is developed to study the fundamentals of heat and mass transfer dynamics. A parallel-plate rectangular channel is used as a model system. Appropriate surface boundary conditions for heat and mass transfer and adsorption/desorption interactions are formulated. A scale analysis of the governing equations is performed in order to identify the dimensionless physical parameters governing the process and to obtain the order-of-magnitude estimates for characteristic time constants of the system dynamics. Predictions of the scale analysis are validated against the results of the parametric study obtained through the numerical solutions of the governing equations. The findings demonstrate that the scale analysis is a very powerful analytical tool which allows one to evaluate the effects of different process parameters on heat and mass transfer dynamics in the presence of adsorption without performing the exhaustive numerical calculations.     

循环流化床锅炉一体化外置式换热器

大型循环流化床锅炉广泛采用各种形式的外置式换热器。传统的换热器只能实现换热器（EHE）和返料机构（loop seal）之间的物料流量的调节,此时进入EHE的物料将会全部顺次流过各个换热仓室,很难对外置床中的各种受热面的传热量进行单独调节。本文首次提出了一种全新的非机械阀式外置式换热器布置方式,通过控制流入各个换热仓室的固体物料流量,从而达到对各换热仓室中布置的受热面的换热情况进行单独调节。同时把EHE和loop seal结合在一起,保证向炉膛的返料。文中对这种一体化外置式换热器及其返料机构中的物料流动特性进行了冷态试验研究。试验结果表明,这种外置式换热器有很好的物料分流和流量控制特性。可以通过调节运行参数和结构参数来控制两个换热室、EHE和loop seal以及两个返料口之间的物料流量和比例。同时还得到了物料在换热室的流动特性。通过对可见输送分离高度的测量,提出了分配室和换热室相对隔板高度的设计方法。     

A Theoretical Study of the Recycle Effect on Multi‐Pass Mass Exchangers with Three Idealized Membranes Inserted

A new device of multi‐pass mass exchanger was developed by inserting three idealized membranes to divide an open conduit into four subchannels. The mathematical formulations of the device with external recycle, as referred to a well‐known conjugated Graetz problem, were conducted to improve the mass transfer efficiency. The eigenfunction expansion technique with the eigenfunction expanding in terms of an extended power series was used to solve such a conjugated Graetz problem analytically. The theoretical predictions were presented graphically and compared with those in the single‐pass operations (without any idealized membrane inserted and external recycle) of the same working dimensions.     

溶液再生器传热传质过程的数值模拟

根据湿空气和溶液热质交换的基本理论,建立了叉流溶液再生器的传热传质数学模型,并将该模型简化,得出空气和溶液的质量、能量控制方程。根据数值求解的方法,对方程进行离散简化,利用Matlab语言编程模拟计算。将模拟结果和实验结果进行了比较,结果表明本模型可靠。     

Determination of heat transfer formulas for gas flow in fin-and-tube heat exchanger with oval tubes using CFD simulations

Plate fin-and-tube heat exchangers operate in a cross-flow arrangement with the complex path of gas flow, hence in order to determine the velocity field and heat transfer characteristics, the numerical methods must be used. The CFD codes allow obtaining local values of the heat transfer coefficient, however it is impossible to incorporate these values into the analytical formulas for the overall heat transfer coefficient, that is fundamental for the designing procedure of the cross-flow heat exchangers. Therefore this paper presents a method for determination of the average heat transfer coefficient for gas flow in a plate fin-and-tube heat exchanger using the CFD simulations. The values of the heat transfer coefficient obtained using the heat transfer formulas for the Nusselt number, determined with the CFD simulations, can be directly implemented in the thermal designing procedure of the cross-flow heat exchangers. The results of the numerical computations are validated experimentally.     

EXTERNAL RECYCLE ON UPWARD-TYPE DOUBLE-PASS SOLAR AIR HEATERS

The external recycle effect on collector efficiency in an upward-type double-pass flat-plate solar air heater is investigated theoretically. Application of recycle to a solar air heater has two conflicting effects: the desirable effect of increasing the heat transfer coefficient and the undesirable effect of decreasing the heat transfer driving force (temperature difference). The theoretical predictions show that more than 150% improvement in collector efficiency is obtainable if external recycling is carried out in a way that the advantage effect compensates for the disadvantage effect. The collector performance improvement increases with increasing recycling ratio, especially when operating at a lower airflow rate with higher inlet air temperature. The collector efficiency obtained with a double-pass device with recycling improves the efficiency obtained with a single-pass device of the same size with recycling.     

Asymmetric,coupled transport of heat and mass in a duct

Mutually dependent heat and mass transfer for laminar gas flow in a parallel-plate channel is investigated analytically. Sublimation occurs at one of the channel walls, while the other wall is nonsubliming. Both walls are thermally insulated from the external environment. The analysis of the problem requires simultaneous treatment of the energy and mass diffusion equations, with coupling provided by the boundary conditions. Mathematical expressions are derived and numerical results are presented for various quantities that characterize the heat and mass transfer processes. Comparisons are made with the case of symmetric transfer (i.e., both walls actively participating). In general, unsymmetric transfer is found to slow down the axial development of the temperature and mass fraction fields.     

MASS TRANSFER ENHANCEMENT OF CONJUGATED GRAETZ PROBLEMS IN MULTI-PASS PARALLEL-PLATE MASS EXCHANGERS WITH EXTERNAL RECYCLE

A new external recycle design at the ends of multi-pass parallel plate mass exchangers with uniform wall concentration is theoretically investigated in this study. The analytical solutions were obtained using the orthogonal expansion technique and the eigenfunction expanding in power series. The results are graphically represented. The influences of the recycle ratio, mass-transfer Graetz number, channel thickness ratio, and characteristic parameter of the permeable barrier on the mass transfer rate are presented in this study. Compared to the single-pass device, considerable mass transfer improvement is obtainable by employing the new external recycle design at both ends.     

Numerical Study on the Effect of Cross-Flow on Turbulent Flow and Heat Transfer Characteristics Under Normal and Oblique Semi-confined Impinging Slot Jets

Abstract

Impinging jets are commonly used in industrial dryers and electronics chip cooling. Since in industrial practice it is necessary to use multiple jets, the interaction between jets can have important effect on their heat transfer performance. Hence, the study of cross-flow caused by the spent flow of upstream jets is obviously significant. In this study, a computational fluid dynamics simulation was carried out of the flow and heat transfer characteristics for a single semi-confined turbulent slot jet of air impinging normally or obliquely into an imposed air cross-flow of the same or different temperature. The standard k?ε and the Reynolds stress models were used. Effects of the various flow parameter (e.g., jet-to-cross-flow mass ratio) and geometric parameters (e.g., nozzle-to-target spacing and jet angle) were evaluated at a fixed Reynolds number (11,000 and 12,000) for equal and unequal temperatures of the jet and cross-flow. Results indicate the significant degradation of the impingement heat transfer rates due to cross-flow and a relatively minor influence of the temperature difference between the jet and cross-flow over the ranges of parameters studied. Both the turbulence models produced comparable Nusselt number distributions along the impingement surface.     

Numerical Study on the Effect of Cross-Flow on Turbulent Flow and Heat Transfer Characteristics Under Normal and Oblique Semi-confined Impinging Slot Jets

Impinging jets are commonly used in industrial dryers and electronics chip cooling. Since in industrial practice it is necessary to use multiple jets, the interaction between jets can have important effect on their heat transfer performance. Hence, the study of cross-flow caused by the spent flow of upstream jets is obviously significant. In this study, a computational fluid dynamics simulation was carried out of the flow and heat transfer characteristics for a single semi-confined turbulent slot jet of air impinging normally or obliquely into an imposed air cross-flow of the same or different temperature. The standard k-ε and the Reynolds stress models were used. Effects of the various flow parameter (e.g., jet-to-cross-flow mass ratio) and geometric parameters (e.g., nozzle-to-target spacing and jet angle) were evaluated at a fixed Reynolds number (11,000 and 12,000) for equal and unequal temperatures of the jet and cross-flow. Results indicate the significant degradation of the impingement heat transfer rates due to cross-flow and a relatively minor influence of the temperature difference between the jet and cross-flow over the ranges of parameters studied. Both the turbulence models produced comparable Nusselt number distributions along the impingement surface.     

Effect of External Recycle and Double-Pass Barrier Location on Membrane Extraction in Cross-Flow Modules

Abstract

The dispersion free membrane extraction through a cross-flow rectangular membrane module with arbitrary location of an impermeable plate placed for double-pass and external-recycle operations in raffinate phase, has been investigated. Theoretical treatment was analogous to the heat transfer in heat exchangers for the mass transfer in mass exchangers. An experiment was carried out in a cross-flow conduit of stainless steel inserted with a membrane sheet made of microporous polypropylene to extract acetic acid from aqueous solution by methyl iso-butyl ketone. Theoretical predictions are in agreement with the experimental results. Considerable improvement in mass-transfer performance is obtainable if the width of the first-pass subchannel, ΔB decreases, as well as the width of the second-pass subchannel, (1?Δ)B increases. The mass-transfer rate increases also when the reflux ratio increases. Based on the economic point of view, the suitable value of Δ (B is the width of a membrane sheet) may be 0.2.     

Nonlinear coupled heat and mass exchange in a cross-flow regenerator

Simultaneous heat and mass exchange in a cross-flow regenerator has been formulated using Schumann's model. A generalized equilibrium relationship at the gas—solid interface led to a non-linear coupling between the heat and mass transfer processes. The Green's matrix, obtained for the problem of heat transfer alone, has been used to set up integral equations to represent this problem of nonlinear coupled heat and mass exchange. A numerical scheme has been developed for solving the resulting system of multidimensional, nonlinear, Volterra-type integral equations using a modified block-by-block method.It is shown that cross-cooled dehumidifiers can be both smaller and require less power than corresponding adiabatic exchangers.     

错流旋转填料床的质、热同传性能及传热机理研究

为了研究错流旋转填料床的质、热同传性能,采用热空气-氨水体系,考察了进气温度T、超重力因子β、液体喷淋密度q和气速u对错流旋转填料床传热性能的影响,在相同实验条件下对比了丝网填料和乱堆填料的传热性能。研究结果表明：气相体积传质系数k_ya_e、体积传热系数(Ua)_s随进气温度、超重力因子、气速、液体喷淋密度的增大而增大;传热效率ε、传热面积A随超重力因子、气速、液体喷淋密度的增大而增大;传热系数K随超重力因子、气速、液体喷淋密度的增大几乎不变,从而揭示了错流旋转填料床强化气液直接传热的机理是通过提高传热面积进而提高体积传热系数,而不是显著提高传热系数。在相同条件下,以丝网为填料时k_ya_e和(Ua)_s分别是乱堆填料的1.09~1.63倍和1.24~3.53倍。