The validity of the cubic law for laminar flow of fluids through open fractures consisting of parallel planar plates has been established by others over a wide range of conditions with apertures ranging down to a minimum of 0.2 µm. The law may be given in simplified form by Q/Δh = C(2b)3, where Q is the flow rate, Δh is the difference in hydraulic head, C is a constant that depends on the flow geometry and fluid properties, and 2b is the fracture aperture. The validity of this law for flow in a closed fracture where the surfaces are in contact and the aperture is being decreased under stress has been investigated at room temperature by using homogeneous samples of granite, basalt, and marble. Tension fractures were artificially induced, and the laboratory setup used radial as well as straight flow geometries. Apertures ranged from 250 down to 4µm, which was the minimum size that could be attained under a normal stress of 20 MPa. The cubic law was found to be valid whether the fracture surfaces were held open or were being closed under stress, and the results are not dependent on rock type. Permeability was uniquely defined by fracture aperture and was independent of the stress history used in these investigations. The effects of deviations from the ideal parallel plate concept only cause an apparent reduction in flow and may be incorporated into the cubic law by replacing C by C/ƒ. The factor ƒ varied from 1.04 to 1.65 in these investigations. The model of a fracture that is being closed under normal stress is visualized as being controlled by the strength of the asperities that are in contact. These contact areas are able to withstand significant stresses while maintaining space for fluids to continue to flow as the fracture aperture decreases. The controlling factor is the magnitude of the aperture, and since flow depends on (2b)3, a slight change in aperture evidently can easily dominate any other change in the geometry of the flow field. Thus one does not see any noticeable shift in the correlations of our experimental results in passing from a condition where the fracture surfaces were held open to one where the surfaces were being closed under stress.

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VALIDITY OF CUBIC LAW FOR FLUID FLOW IN A DEFORMABLE ROCK FRACTURE - eScholarship

Ultra-thin minichannel LCP for EV battery thermal management

Thermal management for high power lithium-ion battery by minichannel aluminum tubes

Prevent thermal runaway of lithium-ion batteries with minichannel cooling

Numerical investigation on a lithium ion battery thermal management utilizing a serpentine-channel liquid cooling plate exchanger

Thermal performance study of integrated cold plate with power module

Study on coupled heat transfer and seepage in large sparsely fractured surrounding rocks in deep underground spaces

The study of fluid-heat coupling in deep fractured surrounding rock is the basis of design, safety, and extraction of geothermal energy of deep underground spaces. The heat transfer and fractured media seepage theories were employed to establish a three-dimensional unsteady model for fluid-heat coupling heat transfer in fractured surrounding rock. Using COMSOL multiphysics simulation software, the temperature field of the fractured surrounding rock was determined. Furthermore, the influences of ventilation time, Darcy’s velocity, fracture aperture, and thermal conductivity coefficient of the surrounding rock on the fractured surrounding rock temperature field distribution were investigated. The results of the numerical simulation show that the ventilation time and fracture have a major impact on the temperature field distribution of the fractured surrounding rock. As ventilation time is 200 days, an average water temperature in centerline of the fracture decreases 9.4 K as Darcy’s velocity increased from 3e-4m/s to 2e-3m/s. As ventilation time is 200 days, an average water temperature in centerline of the fracture decreases 5.3 K as fracture aperture increased from 3 mm to 9 mm. A set of experimental devices for fluid-heat coupling heat transfer in surrounding rock with a single fracture was designed and built to validate the numerical simulation results. Numerical simulation results are, in general, in agreement with the experimental results.

/pdf/analysis-of-heat-transfer-characteristics-of-fractured-55d1rhwwq5.pdf

Analysis of Heat Transfer Characteristics of Fractured Surrounding Rock in Deep Underground Spaces

This paper presents an integrated power electronics module with a vapor chamber (VC) acting as a heat spreader to transfer the heat from the insulated gate bipolar transistor (IGBT) module to the base of the heat-sink. The novel VC integrated in a power module instead of a metal substrate is proposed. Compared with a conventional metal heat spreader, the VC significantly diffuses the concentrated heat source to a larger condensing area. The experimental results indicate that the VC based heat-sink will maintain the IGBT junction temperature 20°C cooler than a non-VC based heat-sink with high power density. The junction-to-case thermal resistance of the power module based on the VC is about 50% less than that of the power module based on a copper substrate with the same weight. The chip overshooting temperature of the copper substrate module with the same weight goes beyond 10°C against the junction temperature of the VC module at a given impulse power of 225 W. Consequently, thanks to a longer time duration to reach the same temperature, a power surge for the chip can be avoided and the ability to resist thermal impact during the VC module startup can be improved as well. The investigation shows that the VC power module is an excellent candidate for the original metal substrate, especially for an integrated power module with high power density.

Vapor Chamber Acting as a Heat Spreader for Power Module Cooling

With the development of society, the economy, and national security, the exploitation of deep underground space has become an inevitable trend in human society. However, high-temperature-related problems occur in deep underground spaces. The high temperature of deep underground space is essentially influenced by the thermal characteristics of the surrounding rock. According to the mathematical model of heat transfer of the surrounding rock in deep underground space, similar criteria numbers are established. Experiments were carried out to investigate the thermal characteristics of the surrounding rock. The distribution characteristics of temperature were determined by the Fourier number (Fo) and Biot number (Bi), and the effects of heat transfer time, airflow velocities, and air temperature and radial displacement on the distribution characteristics of temperature were studied. The results indicate that the surrounding rock temperature decreases with long heat transfer times, high airflow velocities, and low air temperatures.

/pdf/analysis-of-the-thermal-characteristics-of-surrounding-rock-1chrn44qo5.pdf

Yu Zhang

Papers

Thermal performance study of integrated cold plate with power module

Study on coupled heat transfer and seepage in large sparsely fractured surrounding rocks in deep underground spaces

Analysis of Heat Transfer Characteristics of Fractured Surrounding Rock in Deep Underground Spaces

Vapor Chamber Acting as a Heat Spreader for Power Module Cooling

Analysis of the Thermal Characteristics of Surrounding Rock in Deep Underground Space