Rémi Revellin

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.

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.

Recent Advances in Thermal Modeling of Micro-Evaporators for Cooling of Microprocessors

Note: Keynote speaker Reference LTCM-CONF-2007-007View record in Web of Science Record created on 2007-11-10, modified on 2017-05-10

Critical Heat Flux During Flow Boiling in Microchannels: A Parametric Study

The application of flow boiling in microchannels in copper cooling elements for very high heat flux dissipation from microprocessor chips is one of the promising technologies to replace air cooling and water cooling of these units, particularly in mainframes and servers. Recently, the authors have proposed a new theoretical model to predict the critical heat flux (CHF) in microchannels, and it is used here to perform a parametric study to investigate the effects of fluid, saturation temperature, mass flux, inlet subcooling, microchannel diameter, and heated length on CHF for this application. The parametric study shows that CHF is increased by: (i) decreasing channel length, (ii) lowering saturation temperature, (iii) increasing mass flux, (iv) increasing inlet subcooling, and (v) increasing microchannel diameter. The best coolant is water, but water is not feasible for the present application because of its very low saturation pressure at 30–40°C. Of the other four fluids simulated, their order of merit from best to worst is as follows: R-245fa, R-134a, R-236fa, and FC-72. FC-72, however, has a low saturation pressure (in fact, it would operate under vacuum at the saturation temperatures of 30–40°C envisioned here) and is not a candidate fluid for the flow boiling coolant here. Furthermore, the authors have also recently proposed a diabatic flow map for microchannels based on their database for R-134a and R-245fa in 0.5- and 0.8-mm channels. The new CHF model has been incorporated into their map here to predict the transition from annular flow to dry-out, which is a critical design limitation for microprocessor coolers. Importantly, this map then provides the feasible operating range of such coolers with flow boiling as the cooling process, in terms of mass flux and maximum vapor quality at the outlet to avoid CHF.

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.

Microchannel Heat Transfer Studies

One of the first studies on two-phase flow in microchannels dates back from 1964. Since then, an exponential increase of the amount of publications was observed, especially in the last decade. In 1996, the number of articles in this area was estimated to be around 20, while in 2005, more than 210 studies were published. Why this sudden infatuation with microchannels? The continuing miniaturization of electronic components and the need for compacting existing heat exchangers may explain the increasing studies on heat transfer and two-phase flow in microchannels. Micro-scale channels can endure higher operating pressures, provide much larger contact area per unit volume than large tubes, and have higher heat transfer coefficients. For these reasons, the development of extremely compact heat exchangers is favored in order to minimize the size and the amount of material used in their manufacture, as well as the coolant used in the system. This special issue of Heat Transfer Engineering is dedicated to the 6th International Conference on Boiling Heat Transfer held in Spoleto, Italy, 7–12 May 2006, where Dr. Gian Piero Celata (ENEA, Italy) was the chairman. Ten papers among those presented in the conference have been selected on the specific topic of microchannels, which is one of the hottest topics in heat transfer research and development in the past few years. Among the selected papers for this special issue of Heat Transfer Engineering, two are dedicated to the fractal-like branching channels. The advantage of this geometry is, based on predictions, a lower pressure drop penalty compared to parallel channels. Void fraction variations (Cullion et al.) and pressure drops and vapor quality distributions (Daniels et al.) in fractallike branching channels are presented. The two papers from Consolini et al. and Henning et al. address the topic of instabilities in microchannels, an aspect that is a very important and limiting parameter in two-phase flow experiments and in the operating of microchannel heat sinks. Ribatski et al. present

Asymmetry during a horizontal annular flow in a micro-channel: optical measurements and effect of dimensionless numbers

New applications of HFC refrigerants in organic Rankine cycles at high saturation temperatures and the wider use of CO2 for air-conditioning have pushed research to the characterization of two-phase heat transfer at medium/high reduced pressures and have pointed out the effect of these operating conditions on asymmetric distribution of refrigerant around tube perimeter and its indirect effect on heat transfer. Currently there is a lack of data about asymmetric distribution of liquid film at the wall, especially for refrigerants and micro-channels. In order to have a physical evidence of this asymmetry also for micro-channels and approach to a relationship between this phenomenon and dimensionless parameters, new data are here presented. The asymmetric annular flow of the refrigerant R245fa inside a horizontal, round 2.95 mm inner diameter channel is studied with pictures captured by a high speed video camera. The experimental results here presented were obtained at saturation temperatures equal to 20 °C and 40 °C at low mass velocities (50, 100 and 200 kg m-2s-1) to asymmetric distribution, enriching the database presented in previous studies. The new dimensionless parameter, eccentricity, has been related to the dimensionless groups: Froude and Bond numbers, and Martinelli parameter, showing the mutual correlation among them.

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.