Flow Peclet Number Research Articles

The extended Graetz problem with piecewise constant wall temperature for laminar and turbulent flows through a concentric annulus

The effect of axial heat conduction on the heat transfer is of importance if the flow Peclet number is small or if the axial extension of the heating zone is small. This paper therefore presents an analytical solution to the extended Graetz problem in a concentric annulus with piecewise constant temperature at the outer wall. The solution is based on a selfadjoint formalism which results from the decomposition of the elliptic energy equation into two first-order partial differential equations. The gained solution is exact and simple.The need of regarding the axial heat conduction is displayed by evaluating the analytical solution.

Effects of syngas composition on combustion induced vortex breakdown (CIVB) flashback in a swirl stabilized combustor

Flame flashback attributed to combustion induced vortex breakdown (CIVB) is a major design challenge for swirl stabilized burner combustors. This paper presents an experimental investigation of combustion induced vortex breakdown (CIVB) flashback propensity for flames yielded from Hydrogen (H2)–Carbon Monoxide (CO) fuel blends and actual synthesized gas (syngas) mixtures. A two-fold experimental approach, consisting of a high definition digital imaging system and a high speed PIV system, was employed. The main emphasis was on the effect of concentration of different constituents in fuel mixtures on flashback limit. In addition, the effect of Swirl Number on flashback propensity was discussed. The percentage of H2 in fuel mixtures played the dominant role when CIVB flashback occurred. For a given air mass flow rate, the mixture containing a higher percentage of H2 underwent flashback at much leaner conditions. Flashback maps for actual syngas fuel compositions showed a distinct behavior when various concentrations of diluents were introduced in the mixture. For the two major diluents tested, carbon dioxide (CO2) and nitrogen dioxide (NO2), CO2 was more dominant. The effect of Swirl Number on the flashback propensity was also tested and showed a decrease with an increase in Swirl Number. The final portion of this paper also provides an analysis of flow field of reacting flames which revealed complex vortex–chemistry interactions leading to vortex breakdown and flashback. Based on the experimental results a parametric model similar to Peclet Number approach was developed employing a flame quenching concept. A value of the quench parameter, Cquench was obtained from the correlation of flow Peclet Number and flame Peclet Number, which was observed to be dominated by the fuel composition rather than Swirl Number.

Filtration of nano-aerosol using nanofiber filter under low Peclet number and transitional flow regime

The objective of this study is to investigate the filtration of nano-aerosols (50–500 nm) using nanofiber filter for strong diffusion capture wherein Peclet number Pe drops to single digit and even below unity. The effect of strong slip flow or transitional flow, with the dimension of the flow domain comparable in order of magnitude to the distance of mean-free-path of air molecules (i.e. Knudsen number Kn f of order one), has also been investigated with nanofiber diameter reducing below 100 nm. Also, we examined implications due to use of very small diameter nanofibers. Nanofiber filters are made by electrospinning Nylon 6 (N6) nanofibers on microfiber substrate. The diameter of nanofibers electrospun from 12, 20, and 24% N6 solution are 94, 185, and 220 nm, respectively (corresponding Kn f of 1.44, 0.71, and 0.62). Previous studies showed that the conventional semi-empirical correlation as developed by Payet et al. [1] on single fiber efficiency due to diffusion mechanism ( η D ) as developed from moderate slip flow assumption offers good agreement with experimental results even when Kn f increases to 0.65 (i.e. transition flow regime) over Pe starting from 40 and dropping to 6. In this study, under large slip flow ( Kn f equals to 1.44), we show that Payet's correlation on η D deviating from measurements when Pe is below 10 and the deviation gets worse when Pe drops below unity. Therefore, Payet's correlation, pertaining only to moderate diffusion capture, underpredicts the single fiber capture efficiency for nano-particle or ultrafine particle (sized below 100 nm according to ISO Standard [2]), which may lead to respiratory [3] and cardiovascular [4] problems or diseases. As such, an improved empirical correlation on η D should be established based on new measurement to accurately assess the filter performance on these important particles for selection and sizing of filters in exercising preventive measures. In the study of effect of fiber diameter on capture efficiency and pressure drop, reducing d f from 185 to 94 nm facilitates the filtration of 50–500 nm nano-aerosol, but unfortunately elevates the pressure drop (Δ P). The benefit-to-cost effect is judged by the quality factor ( QF) which should be higher for filter with better performance. The QF of a filter with 185-nm nanofibers is higher than the one with 94-nm nanofibers when filtering 50–90 nm nano-aerosol, and vice versa when filtering 100–380 nm nano-aerosol. Filtration efficiency increases when nanofiber basis weight ( W) increases from 0.042 to 0.333 g m −2. However, the QF drops rapidly when W increases from 0.042 to 0.085 g m −2, and decreases slowly from W = 0.085 g m −2 onwards to W = 0.333 g m −2. As such, for a high performance filter a multi-layer filter formed from stacking up of a series of low basis weight nanofiber layers, each independently supported, is more favorable over using a single-layer nanofiber filter with the same total basis weight.

Second Law Analysis of Slip Flow Forced Convection Through a Parallel Plate Microchannel

In the present work, the second law of thermodynamics analysis has been carried out for steady-state fully developed laminar gas flow in a parallel plate microchannel with asymmetrically heated walls. The rarefaction effects as well as viscous heating effects are taken into consideration. Closed-form expressions are obtained for velocity and temperature distributions and entropy generation rates. The results demonstrate that increasing values of the wall heat fluxes ratio result in greater entropy generation for positive Brinkman numbers, whereas the opposite is true for negative values of Brinkman. However, the effect of the wall heat fluxes ratio on entropy generation becomes insignificant at high values of the group parameter and Peclet number. The entropy generation decreases as Knudsen and Peclet numbers increase; however, the effect of increasing values of Brinkman number and the group parameter is to increase entropy generation. Also, it is realized that the influences of rarefaction on entropy generation are negligible for low Peclet number flows.

Thermodynamic Analysis of Slip Flow Forced ConvectionThrough a Microannulus

The present investigation is devoted to the second law of thermodynamics analysis of steady-state hydrodynamically and thermally fully developed laminar gas flow in a microannulus with constant but different wall heat fluxes. Slip velocity and temperature jump boundary conditions are used to describe rarefaction effects. Viscous heating is also included for both the wall cooling and heating cases. Using already available velocity profile, closed-form expressions are obtained for the transverse distribution of temperature and entropy generation rates. The results demonstrate that the effect of the wall heat fluxes ratio on entropy generation is negligible at large values of the group parameter and Peclet number, while the effect of increasing values of the annulus geometrical aspect ratio is to severely increase entropy generation. The entropy generation decreases as Knudsen and Peclet numbers increase, however, the effect of increasing Brinkman number and the group parameter is to increase entropy generation. Furthermore, it is realized that the influences of rarefaction on entropy generation are slighter for low Peclet number flows.

Macroscale lattice‐Boltzmann methods for low Peclet number solute and heat transport in heterogeneous porous media

This paper introduces new methods for simulating subsurface solute and heat transport in heterogeneous media using large‐scale lattice‐Boltzmann models capable of representing both macroscopically averaged porous media and open channel flows. Previous examples of macroscopically averaged lattice‐Boltzmann models for solute and heat transport are only applicable to homogeneous media. Here, we extend these models to properly account for heterogeneous pore‐space distributions. For simplicity, in the majority of this paper we assume low Peclet number flows with an isotropic dispersion tensor. Nevertheless, this approach may also be extended to include anisotropic‐dispersion by using multiple relaxation time lattice‐Boltzmann methods. We describe two methods for introducing heterogeneity into macroscopically averaged lattice‐Boltzmann models. The first model delivers the desired behavior by introducing an additional time‐derivative term to the collision rule; the second model by separately weighting symmetric and anti‐symmetric components of the fluid packet densities. Chapman‐Enskog expansions are conducted on the governing equations of the two models, demonstrating that the correct constitutive behavior is obtained in both cases. In addition, methods for improving model stability at low porosities are also discussed: (1) an implicit formulation of the model; and (2) a local transformation that normalizes the lattice‐Boltzmann model by the local porosity. The model performances are evaluated through comparisons of simulated results with analytical solutions for one‐ and two‐dimensional flows, and by comparing model predictions to finite element simulations of advection isotropic‐dispersion in heterogeneous porous media. We conclude by presenting an example application, demonstrating the ability of the new models to couple with simulations of reactive flow and changing flow geometry: a simulation of groundwater flow through a carbonate system.

Two-Dimensional Analytical Model of Heat Transfer for Flames in Channels

A two-dimensional model for heat transfer in reacting channel flow with a constant wall temperature is developed along with an analytical solution that relates the temperature field in the channel to the flow Peclet number. The solution is derived from first principles by modeling the flame as a volumetric heat source and by applying jump conditions across the flame for plug and Hagen-Poiseuille velocity profiles and is validated via comparison with more detailed computational fluid dynamics solutions. The analytical solution provides a computationally efficient tool for exploring the effects of varying channel height and gas velocity on the temperature distribution in a channel in which a flame is stabilized. The results show that the Peclet number is the principal parameter controlling the temperature distribution in the channel. It is also found that although the Nusselt number is independent of the Peclet number (or velocity) in the postflame region, it can change by nearly 3 ord ers o f magnitude in the preflame region over the range of Peclet numbers (or velocities) expected in microcombustors. This has important implications for quasi-onedimensional numerical modeling of micro/mesoscale combustion, in which it is usual to select a single Nusselt value from the heat transfer literature.Acorrelation to facilitate incorporation of the streamwise Nusselt number variation is provided.

Comparison of Geometries for Diffusion-Based Extraction of Dimethyl Sulphoxide From a Cell Suspension

Microfluidics can be used in a variety of medical applications. In this study, a microfluidic device is being developed to remove cryoprotective agents from cells post thaw (1–150ml). Hematopoietic stem cells are typically cryopreserved with Dimethyl sulphoxide (DMSO), which is toxic upon infusion. Conventional methods of removing DMSO results in cells losses of 25–30%. The overall objective of this study is to characterize the influence of flow geometry on extraction of DMSO from a cell stream. For all the flow geometries analyzed, flow rate fraction, Peclet Number, and channel geometry had the greatest influence on extraction of DMSO from the cell stream. The range of flow rate fractions that can achieve the desired removal ranges between 0.10 and 0.30. Similarly, the range of Peclet numbers is 250–2500. Distinct differences in channel length could be observed between the different flow configurations studied. The flow rates and channel geometries studied suggest that clinical volumes of cell suspensions (1–100ml) can be processed using a multi-stage microfluidic device in short periods of time (<1hr).

Flow Pulsation and Modified Duct Surface for Process Heat Transfer Intensification

An experimental investigation of the combined influence of flow pulsation and modified duct surface on cross-flow transport and convective heat transfer intensification in laminar flow was carried out. The experiments were performed with a fluid with a kinematic viscosity of 1.8x10-6 m2/s and Prandtl number of Pr = 15. The active length L of the channel is 900 mm and lateral extension is W = 90 mm. Pulsation amplitude (A range of 0.28 mm – 0.53 mm) was used together with pulsation frequency (range of 16 Hz ? f ? 54 Hz). A steady flow Reynolds number range of 100 < Re < 600 was studied. All the geometric parameters of the device such as the relative fin spacing and relative fin thickness were constant. The results of the flow visualization showed recirculation eddies formation when flow pulsation and fins are combined. This enhances the mixing of the fluid within the channel. The intensification of the heat transfer coefficient due to pulsation and use of fins becomes more significant with increasing pulsation amplitude. The combined influence of flow pulsation and modified surface geometry on the heat transfer coefficient was found to be significant at moderately low but non-zero net flow rates or Peclet number Pe. Maximum heat transfer intensification of 2.4 was obtained. In general, no significant heat transfer was obtained at very low and very high flow rates.

A numerical study of the effects of loading from diffusive deposition on the efficiency of fibrous filters

This work is aimed at developing numerical methods for calculating diffusive and interceptive deposition on fibres in fibrous filters as a deposit builds up. Calculations are performed of the two dimensional flow field past a single fibre for three different cell models using the boundary element model (BEM). Boundary conditions for the cells correspond to the Kuwabara model and two different rectangular cases, one corresponding to a periodic cell array. The concentration field for particles is then calculated using the equation of Stechkina and Fuchs [1966. Studies on fibrous aerosol filters—I. Calculations of diffusional deposition of aerosols in fibrous filters. Annals of Occupational Hygiene, 9, 59–64], but with the numerical flow field. Resulting deposition rates are compared with their results and also with those of Friedlander [1977. Smoke, dust and haze. Fundamentals of aerosol behaviour. New York: Wiley] for point particles. For deposition on the front of the fibre, we extend their results using the analytic flow field to obtain analytic results for parameter regions where different types of deposition occur. The two relevant parameters are the ratio of the particle to fibre radii and the effective thickness of the diffusion layer. Numerical flow fields are used to calculate particle deposition over the whole fibre, assuming the deposit forms as a smooth solid layer. The new surface shape is parameterised, and the whole process of recalculating the flow field and particle deposition is repeated. Results are obtained for deposition on the new surface as functions of flow Peclet number and fibre packing fraction.

Ice formation around a finned-tube heat exchanger for cold thermal energy storage

This paper addresses a numerical and experimental investigation of a cold thermal energy storage system involving phase-change process dominated by heat conduction. The problem involves a fluid flowing inside a horizontal finned tube surrounded by a phase-change material (PCM). The objective of this paper is to predict the temperature distribution, the phase front distribution along the tube and to analyze the effect of fin density and size on the dynamic performance of the system. The problem is modeled as axisymmetric and two-dimensional, and a control volume computer code has been developed for the solution of the corresponding mathematical model. In the experimental arrangement of the tube configuration, two different fin diameters; D fn = 2.7 and 3.2 are considered and the fin density at each fin diameter is varied in the range of N fn = 14 – 31 fins ⋅ m −1 . For a particular geometry then the heat transfer fluid inlet temperature assumes values between −10 °C and −20 °C, and the flow Peclet number is varied in the range from 14 350 to 200 900 accordingly. Comparison between the numerical predictions and the experimental data shows good agreement, even though some effects that are produced by heat transfer to the environment especially at high flow rates neglected in the model but unavoidable in the experiments. Finally, time-wise variation of energy stored by the system is evaluated through instant images of solidification fronts and the combined effect of fin parameters and the flow rate on energy storage is discussed.

Low Peclet number flow of a reacting mixture past an array of catalytic wires

We describe the diffusion controlled combustion of a reacting mixture flowing past a two-dimensional array of catalytic wires, as a simple model for the flow through catalytic wire-meshes, of interest for small scale combustion devices. In order to minimize the reactant leakage when using only a few layers of wires, the Peclet number based on the upstream velocity, U, the spacing between the wires, l, and the thermal diffusivity of the mixture, D T, must be Pe=U l/D T≪1. Then, the flow field presents two distinct regions: a convective–diffusive region upstream of the wires, of scale l/Pe, and a reactive–diffusive region near the wires, of thickness of order l. Assuming first that the gas phase homogeneous reactions are frozen, the analysis provides the dependence of the downstream values of the temperature and the reactant mass fractions on the Peclet number, the Lewis number of the reactants, the temperature of the wires, and the ratio of the wire radius to the wire spacing. The analysis is then generalized to include the effect of the homogeneous reactions, showing that the rate of fuel consumption in the gas phase grows with the ratio of the adiabatic laminar flame velocity to the upstream flow velocity, the product of the Zeldovich number and the Peclet number, and the nondimensional temperature of the wires.

Modeling shear-induced phase transitions of binary polymer mixtures

The shear-induced phase transitions of binary polymer mixtures have been studied. We solved the two-fluid model numerically in a high Weissenberg number and infinite Peclet number flow regime without linearization of the diffusive equation or the adiabatic approximation. Our simulations have captured key features of flow-induced phase transitions, such as the shift in the phase boundary from the equilibrium phase diagram under flow conditions. Both shear-induced mixing and demixing phenomena have been reproduced. The dynamic phase behavior of polymer mixtures is governed by parameters including φA and χ for thermodynamic forces, τ′ and G′ for the degree of dynamical asymmetry in polymer mixtures, and the imposed nominal shear rate. Dynamic phase diagrams are obtained for steady state flow. We have identified correlations between the microstructure evolution and rheology, and a mechanism to reach the steady state. The rheological signature of demixing fluids under shear is that the dependence of the steady state shear stress on shear rate changes from nonlinear to linear within that range of shear rates in which the demixing occurs.

On the Use of Point Source Solutions for Forced Air Cooling of Electronic Components—Part II: Conjugate Forced Convection From a Discrete Rectangular Source on a Thin Conducting Plate

A model for uniform parallel flow over the surface of a rectangular source of heat on a conducting plate is used to demonstrate the use of analytic Green’s functions to formulate the conjugate problem. The Green’s functions are solutions to the temperature field that arises from a point source of heat on the surface. They provide a relationship between the local heat flux and surface temperature on the plate, effectively serving the same role as the heat transfer coefficient. By coupling the pointwise Green’s function to a finite element discretization of the thin plate, the surface temperature and convective heat flux distributions on the heat source and its substrate are found by a non-iterative procedure. A parametric study shows that at high Peclet numbers, the heat transfer from the source approaches the behavior of an infinite two-dimensional source of heat. The average Nusselt numbers for rectangular sources of different aspect ratios are found to be insensitive to source aspect ratio at high Peclet numbers. Board conduction reduces the average Nusselt numbers over the source when it is defined in terms of the freestream temperature. New correlations for the source Nusselt number as a function of flow Peclet number and board conductivity are presented.

The effect of marangoni convection on fibrous monotectic growth

Directional solidification of monotectic alloys can lead, under certain conditions of growth velocity and temperature gradient in the melt, to composite microstructures with a rodlike appearance. For a theoretical description, most often the Jackson and Hunt model of rod eutectic growth is used. A relation between the mean rod distance R and the solidification velocity v, similar to eutectics, is generally observed in experiments. A comparison between theory and experiments always led to discrepancies not yet fully resolved. In the approach presented here, we propose an additional mode of mass transport ahead of the monotectic solidification front, namely, Marangoni convection. The main difference between monotectic and eutectic solidification seems to be the liquid phase state of the (rod) L2 phase growing simultaneously within a nearly perfectly pure solid matrix. We assume that the thermocapillary effect causes convection at the interface of the fibrous liquid phase. This Marangoni convection induces a flow field in the matrix and has an influence on the solute transport if the fluid flow Peclet number is large enough. First, an analytical model is described using a suitably modified convective diffusion equation for the concentration field; and, second, a numerical model is presented. The main result of both models is a new functional relation between fiber spacing and solidification velocity being explicitly dependent on the temperature gradient ahead of the solidification front.

Mathematical analysis of viscometric (polymer) flow fields in capillaries: Taylor dispersion revisited

A general formulation for capillary flow of two miscible fluids – one a dilute plug of polymer fluid inserted into a fully developed Poiseuille flow of the other, a Newtonian stream – is examined for its long time behavior. Phenomenologically, the system evolves from an initial state, that of a plug within the boundaries of sharp, well defined fronts inside a Newtonian stream, to a more homogenized state in the very long time scale. This problem was addressed by G.I. Taylor but with regard to a system of two Newtonian fluids, leading to the well-known results commonly described as `Taylor axial dispersion'. In this paper, a general and systematic perturbation analysis is presented from which Taylor's result is recovered as a special case of a more general solution which applies to fluids incorporating elastic properties. In particular, the influence of viscoelasticity and (polymer) diffusivity on the observed pressure profile in the capillary conduit is examined. This effect is clearly separated out for small Peclet number flows using asymptotic and numerical analysis. The results identify the influence of fluid viscosity, elasticity, and diffusivity on the observed pressure profile and form the basis for the improved characterization of polymeric elasticity using capillaries – a finding that is of significant scientific and commercial interest. These results were obtained by the authors as a class of observations resulting from the perturbation analysis of forced-flow capillary devices in viscoelastic fluid property investigation.

Estimation of residence times in semi-enclosed basins with steady flows

Abstract The dispersion processes in semi-enclosed basins with stationary flows have been studied by means of an Eulerian advection–diffusion model. Special interest has been given to quantities which characterize the macroscopic state of the system: the normalized total quantity C(t) of a tracer inside the basin, and its residence time T. The sensitivity of the results to a number of parameters, including flow structure, Peclet number, initial and boundary conditions, have been studied. In particular, the difference between unidirectional flows and flows with recirculations has been investigated. A priori estimates of the value of T are provided, valid for a wide range of parameters. For unidirectional flows, T≃Tout+τ0, where Tout is the time a substantial amount of tracer takes to reach the outflow and τ0 is the inverse of the principal eigenvalue of the advection–diffusion operator. Both parameters Tout and τ0 can be computed knowing the flow structure and the Peclet number, and they are representative, respectively, of the initial and asymptotic phase of dispersion. For flows with recirculations it is found that T≃τ0 over the whole parameter space considered. Conceptually, the difference is due to the tendency of the recirculation to trap the tracer, which enhances the importance of the asymptotic phase. For these flows, the values of T do not change significantly in the range of realistic Peclet numbers considered, suggesting that the macroscopic dispersion properties depend only weakly on the eddy diffusion coefficient. This can have obvious consequences in terms of the possibility of a priori estimates of the residence time, even without having available accurate measurements of the diffusivity.

Dendritic growth of randomly oriented nuclei in a shear flow

A numerical study of the effect of an external mean flow on dendritic growth has been performed. All simulations are 2D phase-field computations using an adaptive finite element method. The dendritic growth starts from a small nucleus that is attached to a solid insulated wall. A flow of melt past the wall is maintained by prescribing a shear stress far from the wall. The orientation of the preferred growth directions of the nucleus is varied. In the simulations, a non-dimensional undercooling of 0.1 is used. The Prandtl number of the melt is taken to be 23, which corresponds approximately to that of SCN. Different initial orientations of the preferred growth directions of the nucleus gives different vertical growth velocities. The results depend also on the flow strength (the flow Peclet number) and the degree of anisotropy. The maximal vertical growth velocity tends to be achieved for crystals with a preferred growth direction that is moderately inclined in the upstream direction.

DEVELOPMENT OF A MONOTONIC MULTIDIMENSIONAL ADVECTION-DIFFUSION SCHEME

The objective of this study is to present a finite-element advection-diffusion scheme for the steady scalar transport equation. The novelty is the use of two advection-diffusion schemes in combination in a way which ensures the satisfaction of the monotonicity property in their matrix equation. Common to these two fundamental finite-element models is that matrix equations are all classified to be irreducibly diagonal dominant. The resulting M-matrix finite-element method is the method of choice to resolve sharp profiles in the flow. The first finite-element method unconditionally provides monotonic solutions. The gain in the stability is due to the introduction of the upwind information along the local streamline. The second basic scheme is classified as conditionally monotonic and is well suited to predicting lower Peclet number flows. This Petrov-Galerkin finite-element model manifests itself by the use of Legendre polynomials to span finite-element spaces. An inherent feature of this formulation is the orthogonal property, which enables a considerable saving in the numerical evaluation of integral terms. Computational evidence reveals that the Legendre-polynomial finite-element model can provide more accurate solutions in low Peclet number conditions. As the Peclet number is increased to higher values that forbid a monotonic solution, the unconditionally monotonic finite-element model is used to complement the Legendre-polynomial finite-element model. This helps enhance the stability. A combined formulation renders a composite scheme that offers promise to optimize the scheme performance. In order to show that the present composite scheme is computationally efficient, the method needs to be rigorously tested against available analytic results. This composite scheme was found to provide monotonic solutions under high and low Peclet number conditions and provided accurate solutions at less computational cost. Use of this composite scheme promises a wider range of practical problems that can be modeled numerically.

Enhancement in the effective thermal conductivity in rat spinotrapezius due to vasoregulation.

This study was undertaken to gain a better understanding of the countercurrent heat exchange of thermally significant blood vessels in skeletal muscle by measuring the vascular structure and flow in an exteriorized rat spinotrapezius muscle and estimating the enhancement in the effective thermal conductivity of the muscle. Detailed anatomic measurements of the number density and length of countercurrent vessel pairs between 45 and 165 microns diameter were obtained. Moreover, diameter and blood flow in the 1A to 3A vessels were measured for muscles in which pharmacological vasoactive agents were introduced, allowing one to vary the local blood flow Peclet number from 1 to 18 in the major feeding arteries. These combined measurements have been used to estimate the range of possible enhancement in the effective thermal conductivity of the tissue. The newly derived conduction shape factor in Zhu et al. for countercurrent vessels in two-dimensional tissue preparations was used in this analysis. Our experimental data indicated that the value of this conduction shape factor was about one-third to two-thirds the value for two countercurrent vessels of the same size and spacing in an infinite medium. The experiment also revealed that the Weinbaum-Jiji expression for keff was valid for the spinotrapezius muscle when the largest vessels were less than 195 microns diameter. A fivefold increase in keff was predicted for 195 microns diameter vessels. Vasoregulation was also shown to have a dramatic effect on keff. A tissue that exhibits only small increases in keff due to countercurrent convection in its vasoconstricted state can exhibit a more than fivefold increase in keff in its vasodilated state.