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The influence of wall-corrugation-induced swirl flow on enhanced forced convection in wavy-plate-fin cores has been investigated. Three-dimensional computational simulations were carried out for steady-state periodically developed air flow (Pr ∼ 0.71; 50 ≤ Re ≤ 4000) with channel walls subject to constant-uniform temperature conditions. The recirculation that develops in the wall troughs and grows to have an axially helical character is scaled by the Swirl number Sw. As Sw increases with higher flowrate and/or corrugation severity, tornado-shaped vortices appear in the wave trough region midway of the interfin channel height, then extend longitudinally to encompass majority of the flow channel. The local wall-shear and heat transfer coefficient variations indicate that boundary-layer thinning upstream of the wave peak aids in intensifying momentum and heat transfer. However, the flow recirculation in wall trough impedes heat transfer at low Sw due to flow stagnation but promotes it at high Sw because of the vortices-induced augmented fluid mixing. The effects of this secondary flow are quantified by Φf(or j), which is seen to increase log-linearly as fin corrugation aspect ratio γ and/or fin spacing ratio ζ increases; the influence of cross section aspect ratio α is marginal. Moreover, the pressure drag penalty due to swirl critically affects overall pressure loss, and its proportion remains nearly constant when α varies, but grows as Sw, γ, and/or ζ increases and can be as much as 80% of the total pressure drop.

An experimental study of bubble growth from submerged orifice plates in pools of water is carried out to scale and correlate the effects of surface wettability and orifice diameter D0 on ebullience. Measurements of bubble growth on surfaces with nine different contact angles (38 deg ≤ θ ≤ 128 deg) and varying air flow rates (1–300 ml/min) were made using high speed videography and image processing. In the static or constant-volume regime, below a critical contact angle θc, the bubble base remains attached to the orifice, and the equivalent departure diameter Db is independent of θ. On the other hand, above the critical contact angle, the bubble base spreads on the surface resulting in larger Db. For θ > θc, Db is strongly dependent on θ and increases with it. Using minimum energy method, it is shown that the wettability effects can be scaled and correlated by a modified capillary length, defined as a function of the Laplace length and contact angle. The proposed correlation provides predictions of Db that agree with experimental data of this study as well as those available in the literature to within ±15%. Moreover, for a hydrophobic surface when D0 > twice the modified capillary length, the bubble grows inside the orifice; for a hydrophilic surface, this scales with twice the capillary length, and effect of θ is not seen.

The characterization and scaling of the thermal-hydraulic performance in wavy plate-fin compact heat exchanger cores, based on the understanding of the physical phenomena and heat transfer enhancement mechanism is delineated. Experimental data are presented for forced convection in air (Pr = 0.71) with flow rates in the range 50 ≤ Re ≤ 4000. A variety of wavy-fin cores that span viable applications, with geometrical attributes described by the cross section aspect ratio α (ratio of fin spacing to height), fin corrugation aspect ratio γ (ratio of 2× corrugation amplitude to wave pitch), and fin spacing ratio ζ (ratio of fin spacing to wave pitch), are considered. To characterize and correlate the vortex-flow mixing in interfin spaces, a Swirl number Sw is introduced from the balance of viscous, inertial and centrifugal forces. It is shown that the laminar, transitional and turbulent flow regimes can be explicitly identified by this Swirl number. Based on the experimental results and extended analysis, new correlations for Fanning friction factor f and Colburn factor j are developed with Sw, α, γ, and ζ as scaling parameters. Requisite expressions are devised by a superposition of both enhancement components due to the corrugated surface area enlargement and induced swirl flow field, and they are combined to cover the laminar, transitional and turbulent regimes by the method of asymptotic matching. The resulting generalized correlations are further shown to predict all available experimental data for f and j factors to within ±20% and ±15%, respectively.

Laminar forced convection in viscous, non-Newtonian polymeric liquids that exhibit pseudoplastic or shear-thinning behavior is characterized. The fluid rheology is characterized by a new asymptotic power-law (APL) model, which appropriately represents extensive data for apparent viscosity variation with shear rate—from the low-shear constant-viscosity plateau to shear thinning at high shear rates. This is contrasted with the traditional Ostwald-de-Waele or power-law (PL) model that invariably over-extends the pseudoplasticity in the very low shear-rate region. The latter's limitations are demonstrated by computationally obtaining frictional loss and convective heat transfer results for fully developed laminar flows in a circular pipe maintained at uniform heat flux. The Fanning friction factor and Nusselt number, as would be anticipated from the rheology map of pseudoplastic fluids, are functions of flow rate with the APL model unlike the Newtonian-like constant value obtained with the PL model. Comparisons of the two sets of results highlight the extent of errors inherent in the PL rheology model, which range from 23% to 68% for frictional loss and 3.8% to 13.7% for heat transfer. The new APL rheology model is thus shown to be the more precise characterization of viscous shear-thinning fluids for their thermal processing applications with convective heat transfer.

New generalized correlations for predicting the average fanning friction factor f and average Nusselt number Nu for laminar flow in plain plate-fin compact cores of rectangular cross section are presented. These are based on extended experimental data, as well as three-dimensional computational simulations, obtained for a broad range of fin density and geometrical attributes. The results indicate that while the fully developed forced convection scales only with the interfin channel cross-sectional ratio α (fin spacing by fin height), the entrance region hydrodynamic and thermal performance is additionally a function of the fin-core length L, flow Reynolds number Re, and fluid Prandtl number Pr. The developing flow and convection is further shown to scale as: (fRe)∼(L/dhRe)1/2, and Nu ∼(L/dhRe)1/2Pr1/3ϕ(α), where f, Re, and Nu are all based on the hydraulic diameter dh of the interfin flow channel. Generalized correlations for both (fRe) and Nu are developed by the corresponding scaling of the forced convection behavior and asymptotic matching of the entrance or developing flow (short fin-core flow length) and the fully developed flow (large fin-core flow length) region performance. Finally, the predictions from these correlations are found to be within ±15% of all available experimental data for air, water, and glycol (0.71 ≤ Pr ≤ 10), and fin cores with 0

The growth dynamics of isolated gas bubbles from a submerged capillary-tube orifice in a pool of an aqueous surfactant (sodium dodecyl sulfate or SDS) solution is computationally investigated. The governing equations for surfactant mass transport in the bulk liquid and interfacial adsorption–desorption are solved simultaneously with the Navier–Stokes equations, employing the volume-of-fluid (VOF) technique to track the deforming liquid–air interface. The VOF method tends to spread the liquid–air interface over two to three computational cells, creating an interface region with finite thickness. A new numerical treatment is developed to determine the surfactant transport and adsorption/desorption in the interface region. From the variation of the surfactant interfacial concentration, the spatio-temporal variation in interfacial tension is determined and the shape of the growing bubble is predicted. To validate the numerical model, experimental measurements of bubble shape and size are carried out using high speed videography. Because of the decrease in surface tension with surface age, bubble departure diameters in SDS–water solutions are smaller than those obtained in pure water, and they are a function of bubble frequency. At higher air-flow rates (smaller surface age), the bubble departure diameters tend toward those in pure water, whereas at low flow rates (larger surface age), they are significantly smaller than those in water and are closer in size to those in a pure liquid having surface tension equal to the equilibrium value in SDS solution. Furthermore, the nonuniform surfactant adsorption–desorption at the evolving interface results in variation in interfacial tension around the bubbles, and thus their shapes in surfactant solution are different from those in a pure liquid.

Nucleate pool boiling heat transfer and its ebullient dynamics in polymeric solutions at atmospheric pressure saturated conditions are experimentally investigated. Three grades of hydroxyethyl cellulose (HEC) are used, which have intrinsic viscosity in the range 5.29 ≤ [η] ≤ 10.31 [dl/g]. Their aqueous solutions in different concentrations, with zero-shear viscosity in the range 0.0021 ≤ η0 ≤ 0.0118 [N⋅s/m2], exhibit shear-thinning rheology in varying degrees, as well as gas–liquid interfacial tension relaxation and wetting. Boiling heat transfer in solutions with constant molar concentrations of each additive, which are greater than their respective critical polymer concentration C*, is seen to have anomalous characteristics. There is degradation in the heat transfer at low heat fluxes, relative to that in the solvent, where the postnucleation bubble dynamics in the partial boiling regime is dominated by viscous resistance of the polymeric solutions. At higher heat fluxes, however, there is enhancement of boiling heat transfer due to a complex interplay of pseudoplasticity and dynamic surface tension effects. The higher frequency vapor bubbling train with high interfacial shear rates in this fully developed boiling regime tends to be influenced by increasing shear-thinning and time-dependent differential interfacial tension relaxation at the dynamic gas–liquid interfaces.

The growth dynamics of isolated gas bubbles from a submerged capillary-tube orifice in a pool of aqueous solution of Cetyl Trimethyl Ammonium Bromide (CTAB) was studied by multi-scale modeling. The macro-scale bubble ebullience is controlled by the molecular scale surfactant adsorption/desorption on the liquid-gas interface. Molecular dynamics simulations were carried out to predict the interfacial adsorption/desorption kinetics. The results of the molecular dynamics simulations were input to the volume-of-fluid based macro-scale computations. The size and shape of bubbles from incipience to departure were measured using high speed videography for model validation. Predictions of the multi-scale model agree with the experimental measurements of bubble size evolution and bubble diameter at departure. The surfactant mass transfer and adsorption on the liquid gas interface gives rise to dynamic surface tension. As a result of the surfactant presence, the bubble departure diameters were smaller in CTAB solution compared to pure water. Furthermore, dynamic surface tension behavior of CTAB makes the bubble departure diameter a function of bubble Reynolds number (Re based on the orifice diameter and air flow rate). At low flow rates or low Re, the bubble departure diameters are smaller than those in water. As the air flow rate increases, the bubble departure diameters tend towards those in pure water. The authors gratefully acknowledge funding from AFOSR Thermal Science Program and AFRL DoD Supercomputing Resource Center for computing time and resources.

Interfacial phenomena and ebullient dynamics in saturated nucleate pool boiling of aqueous solutions of three surfactants that have different molecular weight and ionic nature are experimentally investigated. The additive molecular mobility at interfaces manifests in a dynamic surface tension behavior (surfactant adsorption–desorption at the liquid–vapor interface), and varying surface wetting (contact angle) with concentration (surfactant physisorption at the solid–liquid interface). This tends to change, enhance, and control the boiling behavior significantly, and an optimum heat transfer enhancement is obtained in solutions at or near the critical micelle concentration (CMC) of the surfactant. Furthermore, wettability (contact angle) is observed to be a function of the molecular makeup of the reagent, and shows distinct regions of change along the adsorption isotherm that are associated with the aggregation mode of adsorbed ions at the solid–water interface. This distinguishably alters the ebullience from not only that in pure water, but also between pre- and post-CMC solutions. Increased wetting tends to suppress nucleation and bubble growth, thereby weakening the boiling process.

Saturated, nucleate pool boiling on a horizontal, cylindrical heater and the associated bubble dynamics in aqueous solutions of cationic surfactants of different molecular weight and ethoxylation or ethylene oxide (EO) content, are experimentally investigated. Boiling curves qw″∝ΔTsat for different concentrations and photographic records of the salient features of the ebullient behavior are presented, along with a characterization of interfacial properties (surface tension and contact angle). The surfactant additive significantly alters the nucleate boiling in water and enhances the heat transfer. The enhancement increases with concentration, with an optimum obtained in solutions at or near the critical micelle concentration (c.m.c.) of the surfactant. The photographic and visual observations indicate a markedly different boiling behavior than that of water, as well as between pre- and post-c.m.c. solutions. A lower molecular weight surfactant tends to reduce surface tension faster, and show better enhancement performance than its higher molecular weight counterpart. With EO groups in its molecular chain the surfactant solution becomes more hydrophilic, and the higher wettability tends to suppress nucleation, thereby weakening the boiling process. Also, enhancement in pre-micellar solutions is shown to depend on the dynamic surface tension, and the number of EO groups in and molecular weight of the surfactant.

The effects of surfactant concentration on the initial short-time-scale Marangoni convection around boiling nuclei in aqueous solutions have been computationally investigated. The model consists of a hemispherical bubble (1–100 μm radius) on a downward-facing constant-temperature heated wall in a fluid pool with an initial uniform temperature gradient. Time-dependent transport of liquid mass, momentum, energy, and surfactant bulk and surface convection along with the adsorption kinetics are considered. Conditions for bubble sizes, surfactant bulk concentrations, and wall heat flux levels are represented by a range of thermocapillary and diffusocapillary Marangoni numbers (6⩽MaT⩽103,0⩽MaS⩽8.6×105) over a micro-scale time period (1 μs–1 ms). With a surfactant in solution, a surface concentration gradient develops at the bubble interface that tends to oppose the temperature gradient and reduce the overall Marangoni convection. The maximum circulation strength, which is dependent on the bubble size, corresponds to a characteristic surfactant adsorption time. This, when scaled by a ratio of bubble radius, is found to depend solely on the surfactant bulk concentration. Moreover, the interfacial surfactant adsorption does not display a stagnant cap behavior for the range of parameters and time scales covered in this study.

Saturated nucleate pool boiling of aqueous surfactant solutions on a horizontal cylindrical heater has been experimentally investigated. Sodium dodecyl or lauryl sulfate (SDS or SLS), an anionic surfactant, is employed. Boiling performance, relative to that for pure water, is found to be enhanced significantly by the presence of SDS, with an early onset of nucleate boiling. An optimum level of enhancement is observed in solutions at or near critical micelle concentration of the surfactant; the enhancement, however, decreases considerably in higher concentration solutions. The dynamic surface tension measurements indicate a substantial influence of temperature on the overall adsorption isotherm. The diffusion kinetics of surfactant molecules and micelles is, therefore, expected to be quite different at boiling temperature than at room temperature. This greatly modifies the boiling mechanism that is generally characterized by the formation of smaller-size bubbles with increased departure frequencies, and a decreased tendency to coalesce which causes considerable foaming. [S0022-1481(00)00704-0]

Steady-state heat transfer and pressure drop data for single-phase viscous fluid flows (2 ≤ Re ≤ 400) in a single-pass U-type counterflow plate heat exchanger (PHE) with chevron plates are presented. With vegetable oil as test fluid (130 < Pr < 290), three different plate arrangements are employed: two symmetric (β = 30 deg/30 deg and 60 deg/60 deg) and one mixed (β = 30 deg/60 deg). The effects of chevron angle β, corrugation aspect ratio γ, and flow conditions (Re, Pr, μ/μw on Nu and f characteristics of the PHE are delineated. The results show a rather complex influence of plate surface corrugations on the enhanced thermal-hydraulic behavior. Relative to the performance of equivalent flat-plate packs, chevron plates sustain up to 2.9 times higher heat transfer rates on a fixed geometry and constant pumping power basis, and require up to 48 percent less surface area for the fixed heat load and pressure drop constraint.

Experimental heat transfer and isothermal pressure drop data for single-phase water flows in a plate heat exchanger (PHE) with chevron plates are presented. In a single-pass U-type counterflow PHE, three different chevron plate arrangements are considered: two symmetric plate arrangements with {beta} = 30 deg/30 deg and 60 deg/60 deg, and one mixed-plate arrangement with {beta} = 30 deg/60 deg. For water (2 < Pr < 6) flow rates in the 600 < Re < 10{sup 4} regime, data for Nu and f are presented. The results show significant effects of both the chevron angle {beta} and surface area enlargement factor {phi}. As {beta} increases, and compared to a flat-plate pack, up to two to five times higher Nu are obtained; the concomitant f, however, are 13 to 44 times higher. Increasing {phi} also has a similar, though smaller effect. Based on experimental data for Re {ge} 1000 and 30 deg {le} {beta} {le} 60 deg, predictive correlations of the form Nu = C{sub 1}({beta}) D{sub 1}({phi}) Re{sup p1({beta})} Pr{sup 1/3} ({mu}/{mu}{sub w}){sup 0.14} and f = C{sub 2}({beta}) D{sub 2}({phi}) Re{sup p2({beta})} are devised. Finally, at constant pumping power, and depending upon Re, {beta}, and {phi}, the heat transfermore » is found to be enhanced by up to 2.8 times that in an equivalent flat-plate channel.« less

Fully developed laminar flows in a semicircular duct with temperature-dependent viscosity variations in the flow cross section are analyzed, where the viscosity-temperature behavior is described by the Arrhenius model. Both the T and H1 boundary conditions are considered, as they represent the most fundamental heating/cooling conditions encountered in practical compact heat exchanger applications. Numerical solutions for the flow velocity and the temperature fields have been obtained by finite difference technique. The friction factor and Nusselt number results display a strong dependence on the viscosity ratio (μw/μb), and this is correlated using the classical power-law relationship. However, results indicate that the power-law exponents are significantly different from traditional values for circular tube. They are found to be functions of the flow geometry, boundary condition, and direction of heat transfer (heating or cooling).

Thermal-hydraulic design correlations are developed to predict isothermal f and Nu for in-tube, turbulent flows with twisted-tape inserts. Experimental data taken for water and ethylene glycol, with y = 3.0, 4.5, and 6.0, are analyzed, and various mechanisms attributed to twisted tapes are identified. Tube blockage and tape-induced vortex mixing are the dominant phenomena that result in increased heat transfer and pressure drop; for loose- to snug-fitting tapes, the fin effects are insignificant. The limiting case of a straight tape insert correlates with the hydraulic-diameter-based smooth tube equation. Tape twist effects are thus isolated by normalizing the data with the asymptotic predictions for y = ∞, and the swirl effects are found to correlate with Re and l/y. The validity of the final correlations is verified by comparing the predictions with previously published data, which include both gases and liquids, under heating and cooling conditions and a wide range of tape geometries, thereby establishing a very generalized applicability. Finally, correlations for laminar (presented in the companion Part I paper) and turbulent flows are combined into single, continuous equations. For isothermal f, the correlation describes most of the available data for laminar-transition-turbulent flows within ±10 percent. For Nu, however, a family of curves is needed due to the nonunique nature of laminar-turbulent transition.

Laminar flow correlations for f and Num are developed based on experimental data for water and ethylene glycol, with tape inserts of three different twist ratios. The uniform wall temperature condition is considered, which typifies practical heat exchangers in the chemical and process industry. These and other available data are analyzed to devise flow regime maps that characterize twisted-tape effects in terms of the dominant enhancement mechanisms. Depending upon flow rates and tape geometry, the enhancement in heat transfer is due to the tube partitioning and flow blockage, longer flow path, and secondary fluid circulation; fin effects are found to be negligible in snug- to loose-fitting tapes. The onset of swirl flow and its intensity is determined by a swirl parameter, Sw=Resw/y, that defines the interaction between viscous, convective inertia, and centrifugal forces. Buoyancy-driven free convection that comes into play at low flow rates with large y and ΔTw is shown to scale as Gr/Sw2≫ 1. These parameters, along with numerical baseline solutions for laminar flows with y = ∞, are incorporated into correlations for f and Num by matching the appropriate asymptotic behavior. The correlations describe the experimental data within ±10 to 15 percent, and their generalized applicability is verified by the comparison of predictions with previously published data.

The scientific understanding of multiphase interfaces and the associated convective mass, momentum, and heat transport across and along their boundaries, provide the fundamental underpinnings of the advancement of boiling heat transfer, two-phase flows, heat pipes, spray cooling, and droplet-film coating, among many other engineering applications. Numerous studies have tried to characterize the interfacial behavior and model their mechanistic influences either directly or implicitly via parametric experimental investigations and/or simulations. The goal of advancing our understanding as well as developing generalized, perhaps “universal,” and more accurate phenomenological or mechanistic correlations, for predicting mass, momentum, and heat transfer, continues to engage the worldwide research community. A collection of some such current investigations that are representative of both basic and applied issues in the field is presented in this special issue of the Journal of Heat Transfer.

Fully developed swirling Flow in a twisted tube with an oval cross section is considered. The results shown here are for a tube with an elliptical cross section with a twist ratio of 6 and an aspect ratio of 0.7 (see equations above). The wall of the tube is held at a constant temperature. The secondary flows induced by the tube twist promote mixing in the plane normal to the bulk flow direction. This mixing works to maintain a high temperature gradient close to the tube wall and in turn increase the Nusselt number relative to that in a straight tube of the same cross section. The temperature plots show that it is indeed the case that the in‐plane mixing is effective in maintaining the temperature gradient near the tube wall. The isometric view shows flow streamlines (ribbons represent adjacent streamlines) to illustrate the swirling natur eo ft he flow.

The dynamic behavior of an air bubble, emanating from a 0.32 mm i.d., 0.64 mm o.d., vertical capillary-tube orifice with a bubble interval of 0.22–0.28 s at constant pressure and adiabatic (T=25°C) conditions, as well as droplet impact and spreading on a hydrophobic surface are characterized. Images of the mili-scale spatial-temporal evolution of bubbles (embryonic appearance at orifice tip → growth and detachment → translation) as well as droplets were acquired using a high-speed (5000 frames/s) digital video camera fitted with a 8× optical zoom lens. It was triggered through a computer interface to record continuous high-speed video from which any desired frame can be captured by digital-video-processing software; the equivalent departure diameter was estimated by area-averaging using image processing software. The impact, spreading, and recoil behaviors of ethanol and water droplets on a horizontal stainless steel surface are depicted in Fig. 1. For constant Weber number (We∼10), the spreading and recoil dynamics in the two cases are significantly different. Higher wettability of ethanol promotes greater spreading and dampens recoil in comparison with that seen in water. Figure 2 depicts the growth of an air bubble in pools of ethanol and water. While displaying similar ebullience, a bubble of smaller size and surface age is produced in low-surface-tension ethanol. Dynamic shape variations of the air bubble as it translates upwards in the pool are seen in Fig. 3. From a nearly spherical, tear-drop bubble, the shape changes to an oblate ellipsoid during translation, and surface tension effects are manifest only in the size of respective bubbles.