Jocelyn Bonjour

Analytical Model for Characterization of Loop Heat Pipes

The present paper proposes general equations for predicting the steady-state behavior of a loop heat pipe, linking its operating temperature to various fluidic and geometrical parameters. The closed-form solutions determined for variousloop-heat-pipe operatingmodesarededucedfromtheequationsofapreviouslydevelopednumericalmodel. This new approach of the loop-heat-pipe modeling facilitates the identification of the physical mechanisms that influence its operating behavior. In addition, the transition heat flux between variable and fixed conductance modes can also be estimated. This simplified model has been validated for each loop-heat-pipe operating mode for various geometries and operating conditions. The present model could be a useful tool for the design of loop heat pipes. Nomenclature A = cross-sectional area cp = specific heat D = diameter e = thickness f = friction factor g = gravitational acceleration h = convective heat transfer coefficient hC = condensation heat transfer coefficient K = overall heat transfer coefficient or permeability k = thermal conductivity L = length lv = latent heat of vaporization _ m = mass flow rate P = pressure Q = heat transfer rate R = thermal resistance Rp = pore radius Re = Reynolds number S = heat exchange surface area T = temperature � H = relative elevation � = wetting angle � = dynamic viscosity � = density � = surface tension Subscripts

Extension of Murray's law using a non-Newtonian model of blood flow

BackgroundSo far, none of the existing methods on Murrays law deal with the non-Newtonian behavior of blood flow although the non-Newtonian approach for blood flow modelling looks more accurate.ModelingIn the present paper, Murrays law which is applicable to an arterial bifurcation, is generalized to a non-Newtonian blood flow model (power-law model). When the vessel size reaches the capillary limitation, blood can be modeled using a non-Newtonian constitutive equation. It is assumed two different constraints in addition to the pumping power: the volume constraint or the surface constraint (related to the internal surface of the vessel). For a seek of generality, the relationships are given for an arbitrary number of daughter vessels. It is shown that for a cost function including the volume constraint, classical Murrays law remains valid (i.e. ΣRc= cste with c = 3 is verified and is independent of n, the dimensionless index in the viscosity equation; R being the radius of the vessel). On the contrary, for a cost function including the surface constraint, different values of c may be calculated depending on the value of n.ResultsWe find that c varies for blood from 2.42 to 3 depending on the constraint and the fluid properties. For the Newtonian model, the surface constraint leads to c = 2.5. The cost function (based on the surface constraint) can be related to entropy generation, by dividing it by the temperature.ConclusionIt is demonstrated that the entropy generated in all the daughter vessels is greater than the entropy generated in the parent vessel. Furthermore, it is shown that the difference of entropy generation between the parent and daughter vessels is smaller for a non-Newtonian fluid than for a Newtonian fluid.

Confocal Microscopy for Capillary Film Measurements in a Flat Plate Heat Pipe

This paper aims to show how confocal microscopy can be useful for characterizing menisci in a flat plate heat pipe made of silicon. The capillary structure is made of radial microgrooves whose width decreases from the periphery to the center of the system. A transparent plate is used to close the system and allow visualizations. The confocal method allows measuring both the liquid film shape inside the grooves and the condensate films on the fins. The film thickness is lower than 10 μm. The measurements show that the condensate film forms a drop connected to the meniscus in the grooves but their curvatures are reversed. As a result, a very thin region shall exist where the liquid formed by condensation is drained to the grooves. The drop curvature radius decreases from the condenser to the evaporator like the meniscus radius in the grooves. Therefore, a small part of the liquid is drained by the fins from the evaporator to the condenser. Furthermore, the condensate film covers a large part of the system and can also be in contact with the evaporator at high heat fluxes.

Thermohydraulic Study of a Flat Plate Heat Pipe by Means of Confocal Microscopy: Application to a 2D Capillary Structure

Thermal and hydrodynamic experimental results of a flat plate heat pipe (FPHP) are presented. The capillary structure is made of crossed grooves machined in a copper plate. The shape of the liquid-vapor interface in this type of capillary structure—that can also be viewed as an array of posts—is studied theoretically and experimentally. A confocal microscope is used to visualize the liquid-vapor interface and thus the capillary pressure field in the system. These hydrodynamic measurements, coupled to temperature measurements on the FPHP wall, are used to estimate the permeability and the equivalent thermal conductivity of the capillary structure filled with methanol or FC72. These parameters are obtained from a comparison between the experimental data and an analytical model. Finally, the model is used to compare the draining capability of crossed grooves with that of longitudinal grooves.

Effect of Local Hot Spots on the Maximum Dissipation Rates During Flow Boiling in a Microchannel

One of the most promising technologies to replace air-cooling of micro-processor chips is flow boiling in microchannels. The very high heat flux dissipation from micro-processor chips is highly non-uniform due to the presence of multiple localized hot spots usually related to the localization of bridges and gate oxide shorts. Previous studies focused on the performance of microchannels under uniform heating conditions. Recently, Revellin and Thome (see Int. J. Heat Mass Transf., vol 51, no.5-6, p. 1216-25, 2008) have proposed a new theoretical model to predict the critical heat flux (CHF) in microchannels. This model has been modified here to take into account a non-uniform axial heat flux along a microchannel. The model is used here to perform a local hot spot study to investigate the effects of fluid, saturation temperature, mass flux, microchannel diameter, heated length, size, location and number of hot spots as well as the distance between two consecutive hot spots. Based on the present simulations, to best dissipate a hot spots heat flux, microchannel heat sinks should follow the following recommendations for a channel of fixed length: determine the optimum channel diameter for the fluid (typically either very small or large is best), utilize as high of mass flux as feasible, and design with as low of saturation temperature as possible. Furthermore, the local hot spot size should be as small as possible, the number of local hot spots as few as possible and the distance between two hot spots as large as possible. Utilizing the present numerical method for individual microchannels arranged in parallel in a multi-microchannel cooling element, it is possible to simulate the entire power dissipation profile of a microprocessor die for local limits of CHF.

Integral momentum balance on a growing bubble

The integral momentum balance on a growing boiling bubble is investigated. All forces acting on the bubble are detailed, and the methods and assumptions used to calculate their integral resultants are discussed. The momentum balance computation is then performed using experimental data of bubbles growing on an artificial nucleation site in a controlled environment. The relative magnitude of each force component is compared, showing negligible dynamic forces, upwards forces composed mainly of the buoyancy and contact pressure components, and downwards forces being exclusively due to surface tension and adhesion. The difficulty encountered in measuring the apparent contact angle due to mirage effects has been highlighted; a new method, fitting numerically simulated bubble profile to the contour measurements has been proposed and used to correct the effects of refraction on the bubble profile determination. As all forces acting on the bubble were measured, it was possible to estimate the residuals of the mom...

Modeling of a Microchannel Evaporator for Space Electronics Cooling: Entropy Generation Minimization Approach

The increasing heat dissipation from electronic devices on board satellites makes it necessary to find solutions for their cooling. In the present case, 20 electronic components in series need to dissipate a heat flux of 20 kW/m2 owing to microevaporators mounted in a refrigeration system. An approach for optimizing the design of the evaporators based on the entropy generation minimization is presented here. To solve this thermal problem, a steady-state three-dimensional conduction model is combined with thermohydraulic flow boiling models valid for microchannels. The best design corresponds to an aspect ratio (ratio between height and width) around 8.8. The sensitivity of the results to the choice of the flow boiling models is also analyzed.

THERMALLY INDUCED OSCILLATORY TWO-PHASE FLOW IN A MINI-CHANNEL: TOWARDS UNDERSTANDING PULSATING HEAT PIPES

Research on Pulsating Heat Pipes (PHP) has received substantial attention in the recent past, due to its unique operating characteristics and potential applications in many passive heat transport situations. Reliable design tools can only be formulated if the nuances of its operating principles are well understood; at present, this is rather insufficient for framing comprehensive models. In this context, this paper reports experimental data on self-sustained thermally driven oscillations in a 2.0 mm ID capillary tube sub-system, consisting of only one vapor slug and one liquid plug (‘unitcell’). Understanding such a sub-system/‘unit-cell’ is vital, as it represents a primary unit of a multi-turn PHP. Experiments have been performed with two fluids, i.e. Pentane (BP = 36.1oC) and Methanol (BP = 64.7oC) at different evaporator (40oC to 65oC) and condenser temperatures (-5oC to 15oC) respectively. High speed videography and spectrum analysis reveals that self-sustained thermally driven flow oscillations are observed for both fluids, albeit the dominant periodicity is different. Oscillation frequencies vary from 1.5 Hz to 4.2 Hz approximately, depending on the fluid, operating pressure and temperature. Increasing the difference of temperature between the evaporator and condenser sections leads to enhanced driving force for creating flow oscillations. The resulting phase velocities cause interfacial instabilities, resulting in the formation of secondary bubbles which breakoff from the main meniscus. Results of this study can be compared to numerical models and will be useful to understand the physics of multi-turn PHPs.

Analysis of the Interface Curvature Evolution During Bubble Growth

This study presents an experimental investigation on the local curvature of the bubble interface and its relation to local bubble growth regimes and bubble detachment. An experimental facility has been built in order to produce bubbles by nucleating on a 180-m-diameter artificial nucleation site on a horizontal copper surface. High-speed videography was used to observe and capture the boiling phenomenon, and an image-processing code has been developed in order to determine the local curvature of the bubble interface through the two main radii of curvature. As the evolution of the curvature at the apex of the bubble reflects the evolution of the vapor pressure inside the bubble, it is shown that inertia plays a negligible role and that bubble growth is dictated by thermal diffusion considerations. The measured curvature profile along the bubble has been compared to the hydrostatic Young–Laplace curvature relation. It is observed that the curvature profile near the base diverges from the theoretical prediction as the bubble forms a neck during its growth. This observation can be related both to the successive stages or regimes of growth and to the mechanism of bubble detachment.

Curvature Ratio Effect on Two-Phase Pressure Drops in Horizontal Return Bends: Experimental Data for R134a

This article presents 154 pressure drop data points measured during two-phase flow of R-134a in horizontal return bends. The tube diameter is constant at 10.85 mm and the curvature ratio is either 7.74 or 5.53. Saturation temperature varies from 15 to 20°C, vapor quality from 0.05 and 0.95, and mass velocity ranges from 300 to 600 kg m−2 s−1. Return bend pressure drops are calculated by subtracting the straight tube pressure drop from the total measured pressure drop along the bend. The perturbations induced up- and downstream of the singularity are taken into account in the measurements. The comparison of the pressure drops for the two configurations (curvature ratio of 5.53 and 7.74) showed that they are greater (about 10%) for the larger curvature ratio. This can be attributed to the effect of the developed length on the pressure drop; on the other side the pressure gradients are larger for the lower curvature ratio, which can be explained by the effect of the centrifugal force and the perturbations up- and downstream of the return bend. The experimental data are compared against four prediction methods available in the literature. The Domanski and Hermès correlation is the best at predicting the present data.