Two-phase flow in high-heat-flux micro-channel heat sink for refrigeration cooling applications: Part II—heat transfer characteristics

This paper is the second of a two-part study concerning two-phase flow and heat transfer characteristics of R134a in a micro-channel heat sink incorporated as an evaporator in a refrigeration cycle. Boiling heat transfer coefficients were measured by controlling heat flux (q″ = 15.9 − 93.8 W/cm²) and vapor quality (x_e = 0.26 − 0.87) over a broad range of mass velocity. While prior studies point to either nucleate boiling or annular film evaporation (convective flow boiling) as dominant heat transfer mechanisms in small channels, the present study shows heat transfer is associated with different mechanisms for low, medium and high qualities. Nucleate boiling occurs only at low qualities (x_e < 0.05) corresponding to very low heat fluxes, and high fluxes produce medium quality (0.05 < x_e < 0.55) or high quality (x_e > 0.55) flows dominated by annular film evaporation. Because of the large differences in heat transfer mechanism between the three quality regions, better predictions are possible by dividing the quality range into smaller ranges corresponding to these flow transitions. A new heat transfer coefficient correlation is recommended which shows excellent predictions for both R134a and water.     

Fluid flow in micro-channels

We consider the problem of liquid and gas flow in micro-channels under conditions of a small Knudsen and Mach numbers, that correspond to continuum model. Data from the literature on pressure drop in circular, rectangle, triangular and trapezoidal micro-channels with hydrodynamic diameter ranging from 1.01 μm to 4010 μm are analyzed. The Reynolds number at transition from laminar to turbulent flow is considered. Attention is paid to comparison between predictions of the conventional theory and experimental data, obtained during the last decade, as well as to discussion of possible sources of unexpected effects which were revealed by a number of previous investigations.     

Three-dimensional thermal analysis of heat sinks with circular cooling micro-channels

The pressure drop and thermal characteristics of heat sinks with circular micro-channels are investigated using the continuum model consisting of the conventional Navier-Stokes equations and the energy conservation equation. Developing flow (both hydrodynamically and thermally) is assumed in the fluid region and three-dimensional conjugate heat transfer is assumed in the solid region. Thermal results based on this approach are shown to be in good agreement with existing experimental data. Effects of various geometrical parameters, material properties, and Reynolds number on the thermal performance of the sink were investigated. A comparison between circular and rectangular channels at the same Reynolds number and hydraulic diameter showed that sinks with rectangular channels have lower thermal resistance, while sinks with circular channels dissipate more heat per unit pumping power.     

Investigation of size effects on material behavior of thin sheet metals using hydraulic bulge testing at micro/meso-scales

Reliable material models are necessary for accurate analysis of micro-forming and micro-manufacturing processes. The grain-to-feature size ratio (d/D_c) in micro-forming processes is predicted to have a critical impact on the material behavior in addition to the well-known effect of the grain size (d) itself as manifested by the Hall–Petch relation. In this study, we investigated the “size effects” on the material flow curve of thin sheet metals under hydraulic bulge testing conditions. The ratio of the sheet thickness to the material grain size (N=t₀/d) was used as a parameter to characterize the interactive effects between the specimen and the grain sizes at the micro-scales, while the ratio of the bulge die diameter to the sheet thickness (M=D_c/t₀) was used to represent the effect of the feature size in the bulge test. Thin sheets of stainless steel 304 (SS304) with an initial thickness (t₀) of 51 μm and three different grain sizes (d) of 9.3, 10.6, and 17 μm were tested using five bulge diameters (D_c) of 2.5, 5, 10, 20, and 100 mm. A systematic approach for determining the flow curve of thin sheet metals in bulge testing was discussed and presented. The results of the bulge tests at different scales showed a decrease in the material flow curve with decreasing N value from 5.5 to 3.0, and with decreasing M value from 1961 to 191. However, as M value was decreased further from 191 to 49, an inversed relation between the flow curve and M value was observed; that is, the flow curve was found to increase with decreasing M value from 191 to 49, a new observed phenomenon that has never been reported in any open literature. New material models, both qualitatively and quantitatively, were developed to explain the size effects on the material flow curve by using the N and M as the characteristic parameters of relative size between the grain, the specimen (i.e., sheet thickness), and the part feature (i.e., bulge diameter). The explanation and prediction of the flow curve behavior based on these models were shown to be in good agreement with the bulge test results in this study and in the literature.     

Low-Reynolds number heat transfer enhancement in sinusoidal channels

Fully developed laminar flow and heat transfer in three-dimensional, streamwise-periodic sinusoidal channels with circular and semi-circular cross-sections are considered. Computational fluid dynamics (CFD) is used to investigate the effect of Reynolds number (5?Re?200) and amplitude to half wavelength ratio (0.222?A/L?0.667) on heat transfer enhancement and pressure drop for steady, incompressible, constant property, water (Pr=6.13) flows in geometries with L/d=4.5 for the constant wall heat flux (H2) and constant wall temperature (T) boundary conditions.The flow field in the sinusoidal geometries is increasingly dominated by secondary flow structures (Dean vortices) with increasing Reynolds number and A/L. These vortices act to promote convective heat transfer enhancement, resulting in high rates of heat transfer and low pressure loss relative to fully developed flow in a straight pipe. Heat transfer enhancement exceeds the relative pressure-drop penalty by factors as large as 1.5 and 1.8 for the circular and semi-circular cross-sections, respectively.     

Two-phase flow in high-heat-flux micro-channel heat sink for refrigeration cooling applications: Part I--pressure drop characteristics

Two-phase pressure drop was measured across a micro-channel heat sink that served as an evaporator in a refrigeration cycle. The micro-channels were formed by machining 231 μm wide × 713 μm deep grooves into the surface of a copper block. Experiments were performed with refrigerant R134a that spanned the following conditions: inlet pressure of P_in = 1.44-6.60 bar, mass velocity of G = 127-654 kg/m² s, inlet quality of x_e,in = 0.001-0.25, outlet quality of x_e,out = 0.49-superheat, and heat flux of q″ = 31.6-93.8 W/cm². Predictions of the homogeneous equilibrium flow model and prior separated flow models and correlations yielded relatively poor predictions of pressure drop. A new correlation scheme is suggested that incorporates the effect of liquid viscosity and surface tension in the separated flow model’s two-phase pressure drop multiplier. This scheme shows excellent agreement with the R134a data as well as previous micro-channel water data. An important practical finding from this study is that the throttling valve in a refrigeration cycle offers significant stiffening to the system, suppressing the large pressure oscillations common to micro-channel heat sinks.     

Effect of curing parameters and configuration on the efficacy of ultraviolet light curing self-adhesive masks used for abrasive jet micro-machining

Abrasive jet micro-machining (AJM) uses a high speed jet of particles to mechanically etch features such as micro-channels into a wide variety of target materials. Since the resulting air-particle jet is divergent, erosion resistant masks are required for patterning. Because of their ease of application, 50 and 100 μm thick commercially available ultraviolet (UV) light curing self-adhesive masks are potentially very useful in AJM. However, optimum curing parameters have until now been specified in terms of a curing time for a specific recommended curing unit, making extrapolation to other curing units impossible. Using masks to create straight 250–600 μm wide reference channels in borofloat glass, this paper quantified the optimum curing UV light energy density, and investigated the effect of differing UV exposure units (flat and cylindrical-backed), UV light energy densities, and mask configuration during curing, on the pattern transfer accuracy (before AJM), and the eroded micro-channel feature size. As expected, as long as the masks were cured at the same energy density, the pattern transfer accuracy did not depend on the curing unit. The most accurate pattern transfer to the mask film (widths within 5–7% of design) corresponded to energy densities between 516–774 and 387–516 mJ/cm² for the thick (100 μm) and thin (50 μm) masks, respectively. Under these conditions and for both exposure units, the average widths of the eroded channels after AJM were found to be within 3–9% of the intended design. Curing the masks outside this range resulted in eroded features that were approximately 15–20% and ∼5% larger than intended, for the thick and thin masks, respectively. The orientations of the channel patterns with respect to the curing cylinder axis did not affect the pattern transfer. However, when compared to the cylinder ends, curing at the midpoint along the cylinder length improved the pattern accuracy by approximately 3%, resulting in eroded features that were 10–20% closer to the design width. Finally, it was found that patterning multiple layers of masks improved the erosion resistance without compromising the feature width, enabling the AJM of higher aspect ratio features.     

Polyimide micro-channel arrays for peripheral nerve regenerative implants

Mechanical guidance is one way in which regenerating axons can be directed towards an appropriate target. In this paper, we present the design and fabrication process of a three-dimensional (3D) device comprising a bundle of parallel micro-channels, which can be used as a 3D regenerative implant for peripheral nerve repair. The skeleton of the device is entirely made of flexible polyimide films. Gold micro-electrodes and micro-channels of photosensitive polyimide are patterned directly on polyimide substrates. After fabrication, the 2D electrode channel array is rolled into a 3D channel bundle fitting the peripheral nerve.The efficiency with which axons enter the 2D channel array was evaluated in vitro as a function of channel width, spacing and pitch. Axon outgrowth is maximised when micro-channels are wide (>30 μm), and when the array transparency (the channel width to pitch ratio) is at least 50%. To ensure the metallic electrodes remain functional in the rolled device, substrate thickness and micro-channel height must also be optimized to position the metal film in the neutral plane of the rolled structure. Electrodes embedded in the implant polyimide structure are robust to rolling. Their impedance at 1 kHz in Ringer solution is of the order of 1 MΩ on flat samples, and changes little when the same samples are rolled and inserted into 1.5 mm inner diameter tube. Such 3D, electrode channel devices on polymer not only provides a novel technological approach to physical guidance of regenerating neurons in vivo but also enables the fabrication of an electrode implant with direct electrical communication with multiple groups of nerve fibres in a regenerating peripheral nerve.     

Fabrication of high aspect ratio ceramic micro-channel in diamond wire sawing as catalyst support used in micro-reactor for hydrogen production

Ceramic is an ideal material for preparing micro-channel catalyst supports with their characteristics of high temperature resistance, corrosion resistance and mechanical strength. High aspect ratio micro-channel structure has the advantages of large specific surface area, strong mass and heat transfer performance and high material utilization. However, ceramic materials are hard and brittle, and it is difficult to fabricate micro-channel structures with aspect ratio more than 1.5:1 by traditional processing methods. In this paper, a cutting method of large diameter diamond wire sawing was proposed. The micro-channels with width of 520 μm and aspect ratio of more than 4:1 was successfully fabricated by this method. Furthermore, the integrity of the micro-channel structure processed by diamond wire sawing was analyzed. And than the effect of surface morphology in different processing parameters on the catalyst loading performance were studied. The catalyst loading strength of ceramic slices with different surface morphology was tested. Finally, the ceramic micro-channel array was used as the catalyst support in micro-reactor for hydrogen production via methanol steam reforming (MSR). The methanol conversion rate and H₂ production rate could reach 87.8% and 74.6 mmol/h, respectively under GHSV 12600 ml/g·h at 300 °C. The experimental results show that the large-diameter diamond wire sawing technology can be used to process ceramic microchannels with high aspect ratio; using ceramic microchannel arrays as catalyst supports in hydrogen production can obtain better reaction performance; the feasibility of ceramic materials were broadened as microchannel catalyst supports.     

Inverse methods to gradient etch three-dimensional features with prescribed topographies using abrasive jet micro-machining: Part II—Verification with micro-machining experiments

Cross sectional shape and centerline waviness along the length of a micro-channel can affect different characteristics of microfluidic flow, including heat transfer, pressure distribution and dissipation, and separation of flow. Current existing technologies that allow such micro-machining have many limitations. The accompanying paper presented inverse techniques that can be used to predict the required non-uniform velocity to gradient etch, using abrasive jet micro-machining (AJM), micro-channels and pockets with a wide variety of prescribed textures and cross-sectional shapes. Methods to predict the final three-dimensional (3D) profiles of such features were also presented. In this paper, the velocity functions predicted using the inverse methods were used to machine micro-channels with prescribed centerline depths that varied linearly, parabolically and sinusoidally, pockets with prescribed textures in two directions, and micro-channels with prescribed W-shaped cross sections. Two different erosive efficacy sources were used, one resulting from an adjustable shadow mask and one using a maskless technique. The inverse and 3D shape prediction techniques were verified by comparing the measured feature topographies with those that were initially prescribed. The effect of process parameters such as source shape and the machined feature size on the accuracy of machined features and predictions of the models were also discussed. Overall, the inverse techniques were found to be very effective for predicting the process parameters required to machine a wide variety of desired micro-channel and pocket topographies.