Counterflow Systems Research Articles

Modelling and Theoretical Analysis of Laminar Flow and Heat Transfer in Various Protruding-Edged Plate Systems

Laminar flow and heat transfer in different protruding-edged plate systems are modelled and analyzed in the present work. These include the Parallel Flow (PF) and the Counter Flow (CF) protruding-edgedplate exchangers as well as those systems being subjected to Constant Wall Temperature (CWT) and Uniform Heat Flux (UHF) conditions. These systems are subjected to normal free stream having both power-law velocity profile and same average velocity. The continuity, momentum and energy equations are transformed to either similarity or nonsimilar equations and then solved by using well validated finite difference methods. Accurate correlations for various flow and heat transfer parameters are obtained. It is found that there are specific power-law indices that maximize the heat transfer in both PF and CF systems. The maximum reported enhancement ratios are 1.075 and 1.109 for the PF and CF systems, respectively, at Pr = 100. These ratios are 1.076 and 1.023 for CWT and UHF conditions, respectively, at Pr = 128. Per same friction force, the CF system is preferable over the PF system only when the power-law indices are smaller than zero. Finally, this work demonstrates that by appropriately distributing the free stream velocity, the heat transfer from a plate can be increased up to 10% fold.

Pressure losses during steam flow and condensation in tubes and channels

Theoretical and experimental investigations have revealed the dependence of parameters of the process of steam condensation in tubes and channels on the scheme of heat-exchange fluid flow, including counter, forward, and cross flow systems. The total pressure losses in the case of counter flow are greater than those in the case of forward and cross flow. This dependence is valid for the flow of gases and plasma in channels with significant density variation (e.g., due to heating and cooling). Pressure losses have been evaluated using various computational models, and the results are compared to experimental data.

Erratum: “Duality of Heat Exchanger Performance in Balanced Counter-Flow Systems” (ASME J. Heat Transfer, 2003, 125, pp. 530–532)

Erratum: “Duality of Heat Exchanger Performance in Balanced Counter-Flow Systems” (ASME J. Heat Transfer, 2003, 125, pp. 530–532)

Duality of Heat Exchanger Performance in Balanced Counter-Flow Systems

The duality of heat exchangers to act as both heat conductors and insulators when considering heat exchanger performance is studied from the viewpoint of entropy generation. By defining an appropriate index of the entropy generation rate, it is clarified that the performance paradox pointed out by Bejan can be resolved. The case of a balanced counter-flow system was examined and it has been shown that a heat exchanger can be regarded as both a heat conductor and a heat insulator in terms of entropy generation.

On Soot Inception in Nonpremixed Flames and the Effects of Flame Structure

A simplified three-step model of soot inception has been employed with high activation energy asymptotics to study soot inception in nonpremixed counterflow systems with emphasis on understanding the effects of hydrodynamics and transport. The resulting scheme yields three zones: (1) a fuel oxidation zone wherein the fuel and oxidizer react to form product as well as a radical R, (e.g., H), (2) a soot/precursor formation zone where the radical R reacts with fuel to form “soot/precursor” S, and (3) a soot/precursor consumption zone where S reacts with the oxidizer to form product. The kinetic scheme, although greatly simplified, allows the coupling between soot inception and flame structure to be assessed. The results yield flame temperature, flame location, and a soot/precursor index S1 as functions of Damkohler number for S formation. The soot/precursor index indicates the amount of S at the boundary of the formation region. The flame temperature indirectly indicates the total amount of S integrated over the formation region because as S is formed less heat release is available. The results show that unlike oxidation reactions, an extinction turning-point behavior does not exist for soot. Instead, the total amount of S slowly decreases with decreasing Damkohler number (increasing strain rate), which is consistent with counterflow flame experiments. When the Lewis number of the radical is decreased from unity, the total S reduces due to reduced residence time for the radical in the soot formation region. Similarly, when the Lewis number of the soot/precursor is increased from unity the amount of S increases for all Damkohler numbers. In addition to studying fuel-air (low stoichiometric mixture fraction) flames, the air-side nitrogen was substituted into the fuel, yielding diluted fuel-oxygen (high stoichiometric mixture fraction) flames with the same flame temperature as the fuel-air flames. The relative flame locations were different however, and, consistent with counterflow flame experiments, this difference was found to dramatically reduce the total amount of S generated because the change in stoichiometric mixture fraction affects residence times, temperatures and concentrations in the soot/precursor formation and consumption zones. Furthermore, while the soot/precursor consumption reaction had a negligible effect on the soot process for fuel-air flames it was very important to diluted fuel-oxygen flames.

Mean residence time and variance in steady counterflow separations

Analytical expressions for the mean residence time and variance of species separated in steady couterflow have been derived. The counterflow column was modelled as a multiport sytem composed of discrete equilibrium stages with inlets and outlets closed to diffusion. Limiting cases of the relations for residence time and variance reduce to well-known expressions for fixed-bed separations. Mean residence times of species separated in fixed-bed and counterflow systems are compared.

A mathematical modeling technique for renal counterflow systems

Realistic and comprehensive mathematical models of the renal concentrating mechanism lead to large systems of nonlinear differential equations. Their complexity can be considerably reduced by combining like tubules into common structures. Then the different lengths of the combined tubules have to be modeled by the shunt flow technique. The present paper investigates the validity of this methodology.

Function of thin loops of Henle

The existence of a steep osmotic gradient in the renal medullary interstitium is the most critical in the formation of concentrated urine [1]. The architectural organization of the renal tubules and blood vessels in the medulla constitutes counterflow systems which are essential for both generating and maintaining high osmotic pressure of the renal medulla [2–4]. While it has been generally accepted that active NaCl transport in the thick ascending limb of Henle's loop plays the most fundamental role in the operation of the countercurrent multiplication system in the renal medulla, it is still a matter of considerable dispute whether the thin ascending limb (tAL) also has an active salt transport system to provide a single effect necessary for the operation of the countercurrent multiplication system.

Continuous separation using an annular chromatograph with rotating inlet and outlet.

A continuous rotating annular chromatograph is developed for preparative separation. An annular bed is fixed while a feed nozzle and product coDectqrs are rotated at the same speed. To evaluate the performance of this device, sodium chloride and methanol were separated by the action of ion exclusion. The rotation speed and feed rate were varied. The theoretical model predicted well the experimental concentration profile. Dispersion in the angular direction was negligible. The separation was efficiently achieved and the concentration of products was almost as high as that in the feed. The HETP was determined from the concentration profile and the contribution of respective mass transfer resistance was evaluated. The system was found to be a promising process for preparative chromatographic separation.Several techniques have been proposed for continuous chromatographic systems in preparative separations. Use of moving chromatographic beds permits continuous introduction of feed and continuous withdrawal of products. The systems may operate in counterflow or crossflow fashion. Counterflow systems were used industrially almost 40 years ago.2) Simulated counter-current systems were also established.5) However, most counterflow systems are restricted to two-component separation.

On the numerical solution of differential equations for renal counterflow systems

The mathematical models of the renal concentrating mechanism contribute toward an increased understanding of renal function. These models involve the solution of a system of differential equations for the renal counterflow systems. Analytic solutions of these differential equations, except for very simple models, cannot be obtained. Therefore numerical methods have to be used. One of the principal considerations, in the selection of a numerical method, is to strike a proper balance between the total computational effort and the minimization of discretization (truncation) errors, so that the resulting numerical solution is a reasonably close approximation to the correct solution of the differential equations. There are two ways in which the discretization error can be decreased. The first is to decrease the size of the discretization step-usually called the space chop or step size. Naturally, this leads to an increase in the total amount of storage and computation and often also an increase in the computer round-off errors. The second alternative is to select a numerical method which, for a given space chop, has a small discretization error. This also leads to an increase in the computational effort, particularly in the number of function evaluations. In a recent paper in this Journal (I) we described how the physiological connectivity and flow directions in the various tubules constituting a nephron can be exploited to develop sparse matrix methods which lead to a decrease in the

An efficient numerical method for solving the differential equation of renal counterflow systems

It is well known that the crucial step in the mathematical modeling of the kidney involves the determination of the roots of large systems of sparse non-linear algebraic equations. We utilize the information about the flow directions and the physiological connectivity of the various tubes in the kidney to develop a sparse matrix version of Newton's method for the solution of these equations. The storage requirement for our method is independent of the number of tubes in the model, and its rate of convergence is that of Newton's method.

Use of sparse matrix techniques in numerical solution of differential equations for renal counterflow systems

Mammals concentrate urine by intricate counterflow systems in their kidneys. The mathematical models of such systems involve the numerical solution of a system of differential equations. (A preliminary report of this work was given in Notices of the American Mathematical Society 21, A498 (1974).) This leads to a system of nonlinear algebraic equations, that are solved by the Newton-Raphson method. The basic step in the Newton-Raphson method is the repeated solution of a system of linear equations with the Jacobian of the nonlinear equations as the coefficient matrix. It is shown that the zero-nonzero structure of the Jacobian can be predicted from the physical connectivity of the model. We exploit this zero-nonzero structure to permute the Jacobian to a bordered block triangular form, which is then used to compute the correction to the solution vector of the nonlinear equations. For this computation a modified form of partial pivoting is used. Results are given that show the high accuracy of the computed solutions, the optimum use of the internal computer storage, and the fast rate of computation.

Assessment of fluidised bed ion exchange equipment

AbstractContinuous countercurrent fluidised bed ion exchange equipment has certain advantages over moving packed bed or fixed bed equipment. The treatment of high flow rate dilute waste streams containing particulate matter and the processing of uranium ore unfiltered pulps are considered in the application of fluidised bed systems. Methods of obtaining design data are outlined and techniques for calculating the performance of continuous counterflow systems are proposed for various situations.

Free-energy balance in renal counterflow systems

In the steady state at constant temperature and pressure it is shown that for an arbitrary open system with no sources ∑ k ∫ V J k·grad μ kdV− ∫ S μ kJ k·dσ = 0 where V is the volume, S is the bounding surface, μ k the chemical potential of the kth component, J k its vector flux, and dσ an outwardly directed volume element. By application of this relation to a system of mutually exchanging parallel flow tubes, and summation over tubes and species it is shown that the net rate of free-energy change from membrane transport exactly equals the volume integral of free-energy dissipation by diffusion plus the difference between the rate of free-energy outflow and inflow. By introducing phenomenological laws for membrane transport, expressions are derived for the surface integrals of membrane transport. On the basis of this thermodynamic analysis the power requirements of urinary concentration are discussed qualitatively.

Measures taken against water pollution in the food processing industry.

The food processing industry is involved with the total environment from the farm to the consumer. Particular emphasis is placed upon the need for precise sanitary control in order to assure that water reuse and reclamation programmes provide maximum protection for the safety and quality of the product. Various means to minimise water use such as counter-flow systems, temperature control. pH control, turbidity control and chlorination control are reviewed. Design of equipment is a factor in effective sanitary conditions and proper water utilisation. Abatement of waste water pollution load must start in the plant and be integrated with proper water utilization technique to reduce waste. Wherever possible, waste solids should be handled dry and not flumed. Consideration should be given to segregation of particularly concentrated waste streams within a plant for separate treatment in order to reduce overall treatment costs or surcharges from the municipalities. Interesting concepts for utilizing the land as a sink for treatment processes and solid waste disposal are discussed. A new concept of spray irrigation by overland flow wherein the waste water is spread in a thin sheet to have a good interaction zone with soil humus and the microbiological activity of the soil organisms purify to achieve 99 per cent BODreduction, in a travel of approximately 225 feet. This is accomplished on relatively impervious soils with slopes of approximately two to six per cent. Solid waste disposal is a source of much concern now and especially for the future. There is an interdependence with this problem between the grower, the processor and the consumer. More research work has to be conducted to reclaim the nutritional value in food wastes and to avoid unsanitary conditions both on the farm, at processing plants, and in municipalities. There is a need for attacking these problems on a regional basis and the possibility of centralising recovery areas of wastes for by-product reclamation purposes in order to achieve a more economical, feasible programme may be necessary, especially for smaller processors. Our goal should be the elimination of transporting any waste solids in any form in the various steps from the farm to the processor to the consumer. Ideally, only perfect crops without culls, trims or rejects should reach the food processor. In turn, the food processor should develop convenience foods in edible packages, thus eliminating solids disposal at the home. INTRODUCTION A food processing industry is involved with the total environment from the farm to the customer. It is dependent upon good quality water and therefore

Concentration in Renal Counterflow Systems

In this paper earlier work on two-loop counterflow systems is extended to n-loop systems. It is shown that a large class of such systems in which exchange between the flow tubes is passive is unable to concentrate or dilute.

Analysis of heat or mass transfer in some countercurrent flows

An orthogonal expansion technique for solving some heat- or mass-transfer problems in counterflow systems is developed and applied to two idealized transport problems. The method of solution is based on Sturmian theory and requires both positive and negative eigenvalues for completeness. Local and mean Nusselt numbers are reported as functions of the parameters of the two systems. An iterative finite difference method for solving the same problems is described and the results of the two methods compared.

Ability of Counterflow Systems to Concentrate

Ability of Counterflow Systems to Concentrate

Ability of Counterflow Systems to Concentrate

Ability of Counterflow Systems to Concentrate