Device Having Enhanced Heat Transfer in Natural Convection by Means of Liquid Metals and Partitioned Domains

This application is based on, claims benefit of, and claims priority to U.S. Application No. 63/643,025 filed on May 6, 2024, which is hereby incorporated by reference herein in its entirety for all purposes.

Not Applicable.

This invention relates to a device having enhanced heat transfer in natural convection by means of liquid metals or metal alloys and partitioned domains.

Rayleigh-Benard convection (RBC) can be applied for cooling in systems with intense heat generation, such as high-performance computer chips, power electronics, or large electric batteries. In comparison to heat exchangers relying solely on conduction and forced convection, RBC offers the advantage of significant convection heat transfer not requiring an energy input.

What is needed is improved devices and methods wherein an RBC flow can be manipulated to increase the rate of heat transfer without changing the fluid volume and the temperature difference between the hot and cold walls.

The foregoing needs are met by a device according to the present disclosure having enhanced heat transfer in natural convection by means of liquid metals or liquid metal alloys and partitioned domains.

In one aspect, the present disclosure provides a heat transfer device comprising: an outer wall, a first end wall connected to a first end of the outer wall, and a second end wall connected to an opposite second end of the outer wall, wherein the outer wall, the first end wall, and the second end wall define a cavity; at least one partition wall located in the cavity, each partition wall being spaced inward from the first end wall and the second end wall; and a working fluid contained in the cavity, the working fluid being selected from liquid metals and liquid metal alloys, wherein the working fluid has a final melting point at or below an operating temperature of the heat transfer device. The heat transfer device transfers heat from a heat source adjacent the first end wall to the working fluid such that convection is induced within the working fluid that increases heat transfer from the heat source toward the second end wall.

In one embodiment of the device, the working fluid is selected from the group consisting of gallium, mercury, sodium, and eutectic alloys. In one embodiment of the device, the working fluid is selected from the group consisting of gallium, mercury, sodium, a eutectic alloy of gallium, indium, and tin, and a eutectic alloy of bismuth, lead, tin, and cadmium. In one embodiment of the device, the working fluid comprises gallium. In one embodiment of the device, the working fluid has a final melting point of 100° C. or below. In one embodiment of the device, the working fluid has a final melting point of 80° C. or below. In one embodiment of the device, the working fluid has a final melting point of 40° C. or below.

In one embodiment of the device, the at least one partition wall extends laterally between a first inner surface of the outer wall and a second inner surface of the outer wall. In one embodiment of the device, the outer wall has a cylindrical shape such that the cavity has a height and a diameter. In one embodiment of the device, a height-to-diameter ratio of the cavity is 3 or greater. In one embodiment of the device, the at least one partition wall extends laterally along the diameter of the cavity between a first inner surface of the outer wall and a second inner surface of the outer wall. In one embodiment of the device, each partition wall is spaced inward from the first end wall and the second end wall by a gap distance, and a gap distance-to-height ratio (δ) is in a range of 0.001 to 0.3. In one embodiment of the device, each partition wall is spaced inward from the first end wall and the second end wall by a gap distance, and a gap distance-to-height ratio (δ) is in a range of 0.02 to 0.6.

In one embodiment of the device, a diameter-to-height ratio (AR) of the cavity is in a range of 0.1 to 10. In one embodiment of the device, a diameter-to-height ratio (AR) of the cavity is in a range of 4 to 6. In one embodiment of the device, a Rayleigh number (Ra) of the working fluid is in a range of 105-108. In one embodiment of the device, a Rayleigh number (Ra) of the working fluid is in a range of 105-107.

In one embodiment of the device, the at least one partition wall is spaced inward from the first end wall by a first gap distance, the at least one partition wall is spaced inward from the second end wall by a second gap distance, and a gap ratio (a) of the second gap distance to the first gap distance is not 1. In one embodiment of the device, the gap ratio (a) in a range of 0.5 to 1.5. In one embodiment of the device, the gap ratio (a) in a range of 0.7 to 0.8.

In one embodiment, the device further comprises: the heat source, wherein the heat source is positioned adjacent the first end wall such that the first end wall has a first temperature higher than a second temperature of the second end wall, and the first end wall is located at a lower level than the second end wall. In one embodiment of the device, the heat source is selected from engines, electrochemical devices, power electronics, computer components, and heating, ventilation, and air conditioning systems. In one embodiment of the device, the outer wall has a polygonal shape.

In another aspect, the present disclosure provides a method for cooling a heat source. The method comprises: (a) providing a heat transfer device comprising: (i) an outer wall, a first end wall connected to a first end of the outer wall, and a second end wall connected to an opposite second end of the outer wall, wherein the outer wall, the first end wall, and the second end wall define a cavity, (ii) at least one partition wall located in the cavity, each partition wall being spaced inward from the first end wall and the second end wall; and (iii) a working fluid contained in the cavity, the working fluid being selected from liquid metals and liquid metal alloys, wherein the working fluid has a final melting point at or below an operating temperature of the heat transfer device; (b) thermally coupling the first end wall of the heat transfer device with a heat source; and (c) cooling the heat source by transferring heat from the heat source to the working fluid such that convection is induced within the working fluid that increases heat transfer from the heat source toward the second end wall.

In one embodiment of the method, the working fluid is selected from the group consisting of gallium, mercury, sodium, and eutectic alloys. In one embodiment of the method, the working fluid is selected from the group consisting of gallium, mercury, sodium, a eutectic alloy of gallium, indium, and tin, and a eutectic alloy of bismuth, lead, tin, and cadmium. In one embodiment of the method, the working fluid comprises gallium. In one embodiment of the method, the working fluid has a final melting point of 100° C. or below. In one embodiment of the method, the working fluid has a final melting point of 80° C. or below. In one embodiment of the method, the working fluid has a final melting point of 40° C. or below.

In one embodiment of the method, the at least one partition wall extends laterally between a first inner surface of the outer wall and a second inner surface of the outer wall. In one embodiment of the method, the outer wall has a cylindrical shape such that the cavity has a height and a diameter. In one embodiment of the method, a height-to-diameter ratio of the cavity is 3 or greater. In one embodiment of the method, the at least one partition wall extends laterally along the diameter of the cavity between a first inner surface of the outer wall and a second inner surface of the outer wall. In one embodiment of the method, each partition wall is spaced inward from the first end wall and the second end wall by a gap distance, and a gap distance-to-height ratio (δ) is in a range of 0.001 to 0.3. In one embodiment of the method, each partition wall is spaced inward from the first end wall and the second end wall by a gap distance, and a gap distance-to-height ratio (δ) is in a range of 0.02 to 0.6. In one embodiment of the method, a diameter-to-height ratio (AR) of the cavity is in a range of 0.1 to 10. In one embodiment of the method, a diameter-to-height ratio (AR) of the cavity is in a range of 4 to 6. In one embodiment of the method, a Rayleigh number (Ra) of the working fluid is in a range of 105-108. In one embodiment of the method, a Rayleigh number (Ra) of the working fluid is in a range of 105-107.

In one embodiment of the method, the at least one partition wall is spaced inward from the first end wall by a first gap distance, the at least one partition wall is spaced inward from the second end wall by a second gap distance, and a gap ratio (a) of the second gap distance to the first gap distance is not 1. In one embodiment of the method, the gap ratio (a) in a range of 0.5 to 1.5. In one embodiment of the method, the gap ratio (a) in a range of 0.7 to 0.8. In one embodiment of the method, the heat source is positioned adjacent the first end wall such that the first end wall has a first temperature higher than a second temperature of the second end wall, and the first end wall is located at a lower level than the second end wall. In one embodiment of the method, the heat source is selected from engines, electrochemical devices, power electronics, computer components, and heating, ventilation, and air conditioning systems. In one embodiment of the method, the outer wall has a polygonal shape.

The foregoing and other aspects and advantages of the invention will appear from the following description. In the description, reference is made to the accompanying drawings which form a part hereof, and in which there is shown by way of illustration example embodiments of the invention. Such embodiments do not necessarily represent the full scope of the invention, however, and reference is made therefore to the claims and herein for interpreting the scope of the invention.

Before any embodiments of the invention are explained in detail, it is to be understood that the invention is not limited in its application to the details of construction and the arrangement of components set forth in the following description or illustrated in the following drawings. The invention is capable of other embodiments and of being practiced or of being carried out in various ways. Also, it is to be understood that the phraseology and terminology used herein is for the purpose of description and should not be regarded as limiting. The use of “including,” “comprising,” or “having” and variations thereof herein is meant to encompass the items listed thereafter and equivalents thereof as well as additional items.

The following discussion is presented to enable a person skilled in the art to make and use embodiments of the invention. Various modifications to the illustrated embodiments will be readily apparent to those skilled in the art, and the generic principles herein can be applied to other embodiments and applications without departing from embodiments of the invention. Thus, embodiments of the invention are not intended to be limited to embodiments shown but are to be accorded the widest scope consistent with the principles and features disclosed herein. Skilled artisans will recognize the examples provided herein have many useful alternatives and fall within the scope of embodiments of the invention.

shows a heat transfer deviceaccording to one non-limiting example embodiment of the present disclosure. The heat transfer devicecomprises an outer vertical cylindrical wallof height H, a first end wallconnected to a first end of the outer wall, and a second end wallconnected to an opposite second end of the outer wall, wherein the outer wall, the first end wall, and the second end walldefine a cavity. A vertical partition wallis located in the cavity. The partition wallpasses through the cylinder's axis and extends wall-to-wall horizontally while leaving gaps of size Hbetween the partition walland the first end walland the second end wall. The width of the partition wallis 1/10 of the cylinder diameter D. A working fluid is contained in the cavity. The working fluid can be selected from liquid metals and liquid metal alloys, wherein the working fluid has a final melting point at or below an operating temperature of the heat transfer device. The heat transfer devicetransfers heat from a heat sourceadjacent the first end wallto the working fluid such that convection is induced within the working fluid that increases heat transfer from the heat sourcetoward the second end wall.

For the heat transfer deviceto function efficiently, it is preferred that there be a temperature difference between the first end walland the second end wall. Specifically, the second end wallmust have a lower temperature than the first end wall. In one embodiment, this means that the second end wallhas to have some cooling applied to it. Any kind of heat sink suitable to the specific application environment can be used. This can be an active cooling (e.g., by fan) or passive (simply exposing the outer surface of the second end wallto a cold environment). In one embodiment, fins are attached to the outer surface of the second end wallfor cooling.

In one embodiment, the first end wallhas a first temperature and the second end wallhas a second temperature wherein the second temperature is at least 20° K lower temperature than the first temperature, or the second temperature is at least 30° K lower temperature than the first temperature, or the second temperature is at least 40° K lower temperature than the first temperature, or the second temperature is at least 50° K lower temperature than the first temperature, or the second temperature is at least 60° K lower temperature than the first temperature, or the second temperature is at least 70° K lower temperature than the first temperature, or the second temperature is at least 80° K lower temperature than the first temperature. Greater differences between the first temperature and the second temperature lead to increased heat transfer in the heat transfer device. The heat transfer devicewill also work for smaller or larger temperature differences. Slight adjustments of the height of the cavity can be implemented to produce the same heat flux.

In one embodiment of the heat transfer device, the first end wallcomprises a first material having a first thermal conductivity, the second end wallcomprises a second material having a second thermal conductivity, the outer vertical cylindrical wallcomprises a third material having a third thermal conductivity, and the partition wallcomprises a fourth material having a fourth thermal conductivity. In one embodiment, the first thermal conductivity of the first material is greater than the third thermal conductivity of the third material, the first thermal conductivity of the first material is greater than the fourth thermal conductivity of the fourth material, the second thermal conductivity of the second material is greater than the third thermal conductivity of the third material, and the second thermal conductivity of the second material is greater than the fourth thermal conductivity of the fourth material. In one embodiment, the first material and the second material are independently selected from metallic materials. In one embodiment, the third material and the fourth material are independently selected from polymeric materials.

In one embodiment of the heat transfer device, the working fluid is selected from the group consisting of gallium, mercury, sodium, and eutectic alloys. In one embodiment of the heat transfer device, the working fluid is selected from the group consisting of gallium, mercury, sodium, a eutectic alloy of gallium, indium, and tin, and a eutectic alloy of bismuth, lead, tin, and cadmium. In one embodiment of the heat transfer device, the working fluid comprises gallium. One non-limiting example eutectic alloy comprises 68.5% Ga, 21.5% In, and 10.0% Sn (by weight) and is commercially available as Galinstan®. Another non-limiting example eutectic alloy comprises 50% bismuth, 26.7% lead, 13.3% tin, and 10% cadmium by mass and is commercially available as Wood's metal.

In one embodiment of the heat transfer device, the working fluid has a final melting point of 100° C. or below. In one embodiment of the heat transfer device, the working fluid has a final melting point of 80° C. or below. In one embodiment of the heat transfer device, the working fluid has a final melting point of 40° C. or below. One skilled in the art appreciates that metals and eutectic alloys have a single melting temperature and that non-eutectic alloys have melting temperature ranges wherein a final melting point is the temperature when the non-eutectic alloy is completely melted. As used herein, “a final melting point” also encompasses a single melting temperature of a metal or a eutectic alloy.

In one embodiment of the heat transfer device, the partition wallextends laterally between a first inner surface of the outer walland a second inner surface of the outer wall. In one embodiment of the heat transfer device, the outer wallhas a cylindrical shape such that the cavity has a height H and a diameter D. In one embodiment of the heat transfer device, a height-to-diameter ratio of the cavity is 3 or greater. In one embodiment of the heat transfer device, the partition wallextends laterally along the diameter of the cavitybetween a first inner surface of the outer walland a second inner surface of the outer wall.

In one embodiment of the heat transfer device, the partition wallis spaced inward from the first end walland the second end wallby a gap distance H, and a gap distance-to-height ratio (δ) is in a range of 0.001 to 0.3. In one embodiment of the heat transfer device, the gap distance-to-height ratio (δ) is in a range of 0.02 to 0.6.

In one embodiment of the heat transfer device, a diameter-to-height ratio (AR) of the cavity is in a range of 0.1 to 10. In one embodiment of the heat transfer device, the diameter-to-height ratio (AR) of the cavity is in a range of 4 to 6.

In one embodiment of the heat transfer device, a Rayleigh number (Ra) of the working fluid is in a range of 10-10. In one embodiment of the heat transfer device, the Rayleigh number (Ra) of the working fluid is in a range of 10-10.

In one embodiment of the heat transfer device, the partition wallis spaced inward from the first end wallby a first gap distance H, the partition wallis spaced inward from the second end wallby a second gap distance H, and a gap ratio (a) of the second gap distance to the first gap distance is not 1. In one embodiment of the heat transfer device, the gap ratio (a) in a range of 0.5 to 1.5. In one embodiment of the heat transfer device, the gap ratio (a) in a range of 0.7 to 0.8.

In one embodiment of the heat transfer device, the heat source is positioned adjacent the first end wallsuch that the first end wallhas a first temperature higher than a second temperature of the second end wall, and the first end wallis located at a lower level than the second end wall.

In one embodiment of the heat transfer device, the heat source is selected from engines, electrochemical devices, power electronics, computer components, and heating, ventilation, and air conditioning systems.

The outer wallis not limited to the cylindrical shape. For example, in one embodiment of the heat transfer device, the outer wallhas a polygonal shape (e.g., a cuboid).

The present invention also provides a method for cooling a heat source. The method can use any of the embodiments of the heat transfer device described herein. In a non-limiting example of the method, the first end wallof the heat transfer deviceis thermally coupled to the heat source; and the heat sourceis cooled by transferring heat from the heat sourceto the working fluid such that convection is induced within the working fluid that increases heat transfer from the heat sourcetoward the second end wall. One example role of the heat transfer deviceis to transfer the heat from the heat source to a place, where the heat can be easily dissipated into a colder environment. An example is the heat transfer from the heating elements within a computer box (a source) toward the room air. This can be achieved by a heat transfer device with the first end wallis attached to the source and the second end wallis exposed to the atmosphere.

The following Example has been presented in order to further illustrate the invention and is not intended to limit the invention in any way. The statements provided in the Example are presented without being bound by theory.

Heat generation by commonly used systems and components, such as the large batteries used for energy storage, powerful instrumentation in computing, and advanced HVAC and climate control systems, has continued to increase and is further augmented by technological advancement. Assuming progress continues, the research of heat transfer efficiency remains a meaningful and worthwhile endeavor. This Example explores possible ways to increase the effectiveness of heat transfer based on natural convection for systems at relatively low temperatures, which increases the range of applications for which it can be applied. It is hypothesized that the high energy density and high thermal conductivity of liquid metals and the effects of vertical partitions on flow organization in a fluid cavity can positively impact the heat transfer rate of a convective cell. The hypothesis is explored for a geometry of a cylindrical cavity with a single partition using Ansys Fluent CFD simulations. The aspect ratio of the cylinder, the Rayleigh number of the convective fluid flow, and the gap height between the top and bottom cylinder surfaces and a partition are considered as factors of a parametric optimization study. The results of this Example show manyfold enhancement of the heat transfer rate by a partition and indicate a strong potential in heat transfer applications.

Understanding the effects of partitioned Rayleigh-Benard convection (RBC) for a liquid metal flow requires comprehension of the factors affecting the heat transfer in RBC. Formation of a thermal boundary layer is expected for flows with a temperature difference between a surface and fluid flowing over it. This effect should be notable for fluids with a low Prandtl number fluid which dissipate heat quickly, such as liquid metals [Ref. 11]. For simulation of a vertically mounted cylindrical convective cell, thermal boundary layers are predicted to form near the cold and hot regions of the top and bottom surfaces, respectively. Identifying these thermal boundary layers, which are a source of resistance to heat transfer, provides information on the effectiveness of RBC and how much of an effect the thermal boundary layer resistance has. There exists a plethora of research investigating methods for reducing this resistance, such as deformation of the boundary layers. In one such study, boundary layer deformation of the standing-wave type, that being a combination of two waves at the same amplitude and frequency, changes global responses to convection turbulence, given that the deforming amplitude of the standing waves is close to or larger than the boundary layer thickness of the flow in RBC [Ref. 5].

The large-scale circulation caused by RBC in a convective cell also has a prominent effect on the heat rate transfer [Ref. 8]. Modifying the large-scale circulation may, therefore, be used to increase the heat transfer rate. Due to a limited number of published studies on liquid metals, value can be found in works published on more common working fluids. Research from a study on large-scale circulation used empirical data produced through experimentation to study different types of convective domains for modifying RBC bulk flow [Ref 4]. For two different flow domain setups, type 1 with a square grid suspended in a convective cell and type 2 with the grid fully extending to the top and bottoms of the convective cell, heat transfer efficiency within the type 1 domain was enhanced by up to 14%. It was opined that increased plume coherency caused this effect. Furthermore, heat transfer efficiency in the type 2 domain, with longer segments or “sub-units” of flow, increased by as much as 30%. These results confirm that the organization of the flow is a component of heat transfer optimization.

Geometry and orientation of the convective cell cavity play a significant factor in RBC heat transfer. For a cylinder, the ratio of the height to diameter, known as the aspect ratio AR, influences RBC by defining the shape in which flow can occur. Research suggests an increase in heat transfer can be observed in convective cells with a lower AR, caused by modification of large-scale circulation. In a confined geometry, the amount and intensity of hot and cold plume clusters increases and are more energetic, which has a significant influence in reducing the thickness of the thermal boundary layers [Ref. 6]. However, the organization of the flow aided by the partitions may facilitate increased heat transfer even with an increase in the surface area of a taller convective cell of the same diameter. Additionally, the effect of a smaller convective cell must also be noted, which leads to a decrease in the volume of fluid and thus reduces the amount of heat transport that can be accommodated.

Looking at the effects of just the partitions on the convective cell geometry shows promise for improved heat transfer. Partitioned RBC may lead to reduction of heat exchange between hot ascending and cold descending jets which reduce heat transfer [Ref. 5,7]. Further research shows that adding vertical partitions in a convective cell with a high-Prandtl number liquid increases convective heat transfer in a liquid medium by increasing Nusselt number Nu when compared to non-partitioned cases [Ref. 2]. Investigation of the causes of this increase suggests that partitions in a large-scale circular fluid flow within a fluid cavity create a symmetry-breaking bifurcation, causing the fluid to organize into a unidirectional flow along the partition walls. This can create a disruption of the thermal boundary layer where the partitions extend close to the top and bottom walls [Ref. 2,8]. Furthermore, it has been observed that mean velocity and temperature fields are correlated due to the increased coherency of the flow as number of partitions increases, leading to a meaningful, albeit small, improvement in heat flux. It should be noted that as the number of partitions increases, the volume of fluid within the cell decreases and impedance from the no-slip condition of the partitioned walls increases. Adding volume to the convective cell to compensate for the loss of working fluid may prove to negate these effects.

Additional investigation into the effects of partitions on a convective cell could yield an optimized configuration for increased convective heat transfer. It has been observed that the Nusselt number increases monotonically as the number of partitions aligned perpendicularly in a convective cell increase [Ref. 2]. Aided by the partitions, the working fluid is forced through the gaps at the top and bottom of the partitions and leads to a pressure distribution at the gaps that sustain flow, creating horizontal jets, which will sweep the thermal boundary layer, disturbing these layers and further increase thermal efficiency [Ref. 2]. The size of the gap height also influences the fluid flow and heat transport and may influence the flow in relation to the cell height [Ref. 7].

There are several challenges when looking at generating valuable data for liquid metal flows. Liquid metals are opaque, and so measuring velocity using optical techniques, such as PIV, is impossible. What is more, systems using liquid metal tend to operate at much higher temperatures than conventional liquids such as air or water, creating difficult working conditions and energy requirements [Ref 1]. Regardless, an advantage of liquid metals that cannot be overlooked is their high thermal conductivity that facilitates more heat transfer.

It must be stressed that the effect of partitions on heat transfer in RBC is, while evident, not very strong in conventional fluids such as water. Increase of the Nusselt number by up to 30% is reported in [Ref 2, 7, 8]. As we will see in the discussion of the results in the Results and Discussion section below, the effect is much stronger in fluids with low Prandtl numbers, e.g., liquid metals.

Understanding the advantages of partitioned RBC provides evidence that an optimized AR for increased RBC, in combination with a specific number of partitions with a given gap height, can be used to design a fluid model for which heat transfer can be optimized. The high thermal conductivity and low viscosity of the liquid gallium could potentially add to optimized heat transport, outweighing the possibility of reduced heat transfer from fluid volume reduction and increased surface area the partition will add. Thus, this Example will report on simulations combining the effects of liquid metal and partitioned flow in a convective cell.

This Section will detail methods used to set up and verify the accuracy of simulations. The results will be reported and discussed in Section 3.

An unsteady three dimensional flow in a partitioned cylindrical cavity acting as a convective cell is calculated. Several assumptions are made to simplify the model. The Oberbeck-Boussinesq approximation is assumed in which all physical properties of the fluid are assumed constant except density in the gravity force term. Density in this case is assumed to be a linear function of temperature, thus providing the buoyant force effect. The sidewalls and the wall of the partition are assumed adiabatic with heat transfer only occurring at the top and bottom walls of the cell. No-slip boundary conditions are assumed at the walls of the cavity and along the partition walls. Under these conditions, with the cylinder height H, free-fall velocity U, and ΔT as the typical scales, flow within the cavity can be represented by the governing equations:

With boundary conditions