Heating plate and method based on Cantor fractal structure and efficient heat transfer experimental device

Abstract

The invention discloses a heating plate based on a Cantor fractal structure, a method and an efficient heat transfer experimental device. A coarse structure generated through Cantor fractal is arranged on the surface, making contact with experimental fluid, of the heating plate based on the Cantor fractal structure. The rough structure generates multi-layer tiny protrusions with self-similar characteristics in a limited plane area through multiple iterations, equivalently, under the same projection area, the actual contact surface area of the heating plate and fluid is greatly increased, and more channels are provided for heat transfer.

Description

Technical Field

[0001] This invention belongs to the field of thermal convection simulation experiment technology, specifically relating to a heating plate, method, and high-efficiency heat transfer experimental device based on Cantor fractal structure. Background Technology

[0002] Existing Rayleigh-Bradley convection experimental setups are primarily designed around the core requirement of "thermal convection simulation," but they have significant shortcomings in structural design, functional implementation, and experimental adaptability, as detailed below: 1. Core component design (heating / cooling plate + measurement structure + cooling method + temperature control) The surface structure of the heating / cooling plate is either a "smooth plane" or a "single-scale rough structure". The single-scale structure is mostly a "replication of regular geometry" (such as small cubes, rectangular blocks, etc.), with completely consistent size and spacing. There is no iterative generation process, and "roughening" is achieved only through simple repetition, without following the fractal law of natural roughness.

[0003] Measurement structure: The cavity is designed with only a "single-hole measurement port", which can only insert one temperature probe. Each experiment can only obtain temperature and flow state data at a single location (such as the center or the side wall).

[0004] Cooling structure: Cooling plates mostly use "single-pass water pipes" or "simple water tanks", with cooling water flowing through the cooling plate in only one direction, resulting in a short heat exchange path; some use double-pass pipes, but without surface structure optimization, and only perform conventional cooling functions.

[0005] Temperature control method: The temperature difference is controlled only by "basic heating / cooling elements" (such as heating wires and ordinary cold water circulation), without real-time temperature monitoring and feedback adjustment mechanism, and the parameters are adjusted by human experience.

[0006] 1. Auxiliary structure design: The "simple fixing plate + bolt" combination is adopted, which only meets the basic cavity fixing requirements. It does not optimize for issues such as circulating water sealing and cavity deformation during the experiment. The reinforcement and leak prevention design is relatively crude.

[0007] (ii) Deficiencies in existing technology 1. Poor realism and low efficiency in heat transfer simulation: The single-scale rough structure differs greatly from the "multi-scale fractal roughness" in the natural environment (such as the atmospheric boundary layer and river surface), making it impossible to realistically reproduce the natural characteristics of heat convection; at the same time, the single-scale contact area is limited, resulting in low heat exchange efficiency and a large deviation between experimental results and actual natural phenomena.

[0008] 2. Incomplete and inefficient experimental data acquisition: The single-hole design can only acquire data from a single area. Multiple adjustments to the probe position and repeated experiments are required to cover key areas such as the "sidewall-semi-center-center". This is not only time-consuming, but also prone to data incomparability due to changes in experimental conditions (such as temperature difference and fluid state).

[0009] 3. Insufficient cooling efficiency and temperature control accuracy: Insufficient heat exchange in single-pipe water supply and uneven temperature distribution on cooling plate; temperature control without PID feedback cannot correct temperature deviation in real time, resulting in large temperature fluctuations (e.g., ±2℃ or more) and poor experimental repeatability (high deviation rate of results under the same conditions).

[0010] 4. Weak stability and practicality of the device: The auxiliary structure is not leak-proof or reinforced enough, and the circulating water is prone to leakage during the experiment, or the cavity may deform due to uneven stress, which directly affects the stability of the flow field and thus interferes with the accuracy of the experimental data. Summary of the Invention

[0011] In view of this, the main objective of the present invention is to provide a heating plate, method and high-efficiency heat transfer experimental device based on Cantor fractal structure.

[0012] To achieve the above objectives, the technical solution of the present invention is implemented as follows: A heating plate based on a Cantor fractal structure, wherein the surface of the heating plate in contact with the experimental fluid is provided with a rough structure generated by Cantor fractal.

[0013] Preferably, the rough structure is generated by n iterations, where n≥2.

[0014] An efficient heat transfer experimental apparatus, comprising: The Ruili-Bernard convection chamber is used to contain experimental fluids. A heating plate, located at the bottom of the Ruili-Bernard convection cavity, is used to heat the experimental fluid; A cooling plate, located at the top of the Ruili-Bernard convection cavity, is used to cool the experimental fluid.

[0015] Preferably, the device further includes a cover plate that covers the water channel of the cooling plate to prevent water leakage.

[0016] Preferably, the Ruili-Bernard convection cavity is formed by side plates; the side plates include a left side plate, a right side plate, a first side plate, and a second side plate that are sequentially enclosed.

[0017] Preferably, the device further includes a fixing component that secures the Ruili-Bernard convection cavity from both sides.

[0018] Preferably, the fixing assembly includes a left fixing plate and a right fixing plate, which are used to press and fix the Ruili-Bernard convection cavity with multiple bolts to prevent water leakage.

[0019] Preferably, the device further includes an insulating base that encloses the heating plate to prevent heat loss.

[0020] Preferably, the device further includes a base support frame and a base for supporting the entire device and keeping it horizontal; the base is located at the bottom of the heat-insulating base; the base support frame is located on both sides of the left and right fixed plates and its bottom surface is fixed to the base.

[0021] A method for generating a heating plate based on the Cantor fractal structure, comprising the following steps: A heating plate substrate is provided, the heating plate substrate having a flat heat transfer surface to be processed; Based on the Cantor fractal algorithm, the number of iterations n of the target coarse structure and the generation rule of each iteration are determined, where n≥2; Based on the target rough structure, a material removal process is performed sequentially on the flat heat transfer surface. n Through repeated processing iterations, a raised structure is formed, thereby generating a Cantor fractal rough structure with self-similar properties.

[0022] Compared with the prior art, the beneficial effects of the present invention are as follows: Through multiple iterations, the rough structure of this invention generates multi-layered micro-protrusions with self-similar properties within a limited planar area. This is equivalent to significantly increasing the actual surface area of ​​the heating plate in contact with the fluid under the same projected area, providing more channels for heat transfer. Attached Figure Description

[0023] The accompanying drawings, which are included to provide a further understanding of the invention and form part of this invention, illustrate exemplary embodiments of the invention and, together with their descriptions, serve to explain the invention and do not constitute an undue limitation thereof. In the drawings: Figure 1 A perspective view of a heating plate based on a Cantor fractal structure is provided for an embodiment of the present invention; Figure 2 A top view of a heating plate based on a Cantor fractal structure is provided in an embodiment of the present invention; Figure 3 A side view of a heating plate based on a Cantor fractal structure is provided for an embodiment of the present invention; Figure 4 A perspective view of a high-efficiency heat transfer experimental device is also provided as an embodiment of the present invention; Figure 5 Another perspective view of the high-efficiency heat transfer experimental device is also provided as an embodiment of the present invention; Figure 6 A side sectional view of a high-efficiency heat transfer experimental device is also provided as an embodiment of the present invention; Figure 7 The present invention also provides a flowchart of the method for generating a heating plate based on the Cantor fractal structure; Figure 8 The present invention also provides a schematic diagram of a line segment iterated n times in the method for generating a heating plate based on the Cantor fractal structure. Figure 9 An embodiment of the present invention also provides a schematic diagram of the heating plate after four iterations in the method for generating a heating plate based on the Cantor fractal structure. Detailed Implementation

[0024] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0025] In the accompanying drawings of this embodiment, the same or similar reference numerals correspond to the same or similar components. In the description of this invention, it should be understood that the terms "upper," "lower," "left," "right," "inner," "outer," etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings. They are only for the convenience of describing this invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, the terms used to describe positional relationships in the accompanying drawings are only for illustrative purposes and should not be construed as limiting this patent. For those skilled in the art, the specific meaning of the above terms can be understood according to the specific circumstances.

[0026] It should be noted that, in this document, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, article, or apparatus. Without further limitation, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, article, or apparatus that includes that element.

[0027] This invention provides a heating plate based on a Cantor fractal structure, such as... Figure 1-3As shown, the surface of the heating plate 1 that is in contact with the experimental fluid is provided with a rough structure 11 generated by Cantor fractal.

[0028] Through multiple iterations, the rough structure 11 of the present invention generates multi-layered micro-protrusions with self-similar properties within a limited planar area. This is equivalent to significantly increasing the actual surface area of ​​the heating plate in contact with the fluid under the same projected area, providing more channels for heat transfer.

[0029] In the Rayleigh-Bernard convection experiment, the fluid near the heated surface forms a relatively static "thermal boundary layer," which is the main resistance to heat transfer. The protrusions created by the rough structure can interfere with and disrupt the laminar boundary layer, prompting the fluid to generate more tiny eddies and mixing, bringing the cold fluid to the hot surface while carrying the hot fluid away, thus greatly enhancing convective heat transfer. If the experiment involves boiling heat transfer (such as when a liquid is heated to boiling), the protrusions can serve as ideal vaporization nuclei, promoting the formation and release of bubbles, and boiling heat transfer is a highly efficient heat transfer method.

[0030] In some embodiments, the coarse structure 11 is generated by n iterations, where n≥2.

[0031] For specific fluid and thermal conditions, a rough structure 11 is designed in a customized manner to find the optimal point for heat transfer efficiency, rather than simply increasing the roughness. The design based on a mathematical fractal model makes the performance improvement predictable and repeatable.

[0032] The rough structure has a bulge height of h1 after the first iteration and a bulge height of h2 after the second iteration, where h1 > h2 and the ratio of h1 to h2 is between 1.5 and 4.

[0033] This invention also provides a high-efficiency heat transfer experimental device, such as... Figure 4-6 As shown, the device includes: The Ruili-Bernard convection chamber is used to contain experimental fluids. The heating plate 1 described in the above embodiment is disposed at the bottom of the Ruili-Bernard convection cavity and is used to heat the experimental fluid; Cooling plate 2 is disposed at the top of the Ruili-Bernard convection cavity and is used to cool the experimental fluid.

[0034] This invention significantly improves the heat transfer efficiency of the experimental device by using a heating plate 1 with a Cantor fractal rough structure. Its fractal structure greatly increases the heat exchange area and can effectively destroy the thermal boundary layer and promote fluid disturbance and turbulence development, thereby achieving faster and more efficient heat exchange in the experiment. At the same time, this structure provides an excellent experimental platform for studying complex turbulence and thermal convection phenomena.

[0035] In some embodiments, the device further includes a cover plate 3 that covers the water channel of the cooling plate 2 to prevent water leakage.

[0036] The cover plate 3 is precision machined from stainless steel sheet, and its dimensions perfectly match the water channel on the cooling plate 2. The cover plate 3 is fastened to the cooling plate 2 by M4 countersunk head screws evenly distributed around its perimeter. A rectangular cross-section sealing groove is machined on the contact surface between the cover plate 3 and the cooling plate 2. A high-temperature resistant and anti-aging silicone sealing ring is embedded in the groove. The pressure generated by tightening the screws causes the sealing ring to elastically deform, thereby achieving a reliable seal for the entire water channel and completely preventing leakage of cooling water under pressure circulation.

[0037] In some embodiments, the Ruili-Bernard convection cavity is formed by side plates; the side plates include a left side plate 15, a first side plate 13, a right side plate 12, and a second side plate 14 arranged sequentially.

[0038] The Ruili-Bernard convection cavity consists of a rectangular frame assembled from four transparent acrylic sheets (polymethyl methacrylate) through precision milling. The contact surfaces of the left side plate 15, right side plate 12, first side plate 13, and second side plate 14 are all milled with high-precision right-angle steps. After being positioned using a specialized fixture, they are seamlessly bonded using chloroform solvent, forming a sealed cavity with precise internal dimensions, high optical transparency, and excellent thermal insulation properties, used to contain experimental fluids and observe their flow patterns.

[0039] In some embodiments, the device further includes a fixing component 4 that fixes the Ruili-Bernard convection cavity from both sides.

[0040] The fixing assembly 4 includes a left fixing plate 41 and a right fixing plate 42. The left fixing plate 41 and the right fixing plate 42 are used to press and fix the Ruili-Bernard convection cavity with multiple bolts to prevent water leakage.

[0041] Both the left fixing plate 41 and the right fixing plate 42 are heavy-duty plates made of stainless steel, with a rigidity far exceeding that of the acrylic cavity side plates. The left fixing plate 41 and the right fixing plate 42 are clamped from both sides of the cavity by at least four high-strength double-ended studs (e.g., M10 size) and matching nuts. By tightening the nuts sequentially diagonally using a torque wrench, a uniform and controllable normal clamping force can be applied to the cavity side plates. This pressure is transmitted through the side plates to the sealing surfaces of the heating plate 1 and the cooling plate 2, ensuring that all static seals (such as O-rings) are fully compressed, thereby effectively preventing leakage of the experimental fluid within the cavity throughout the experiment.

[0042] In some embodiments, the device further includes an insulating base 5 that encloses the heating plate 1 to prevent heat loss.

[0043] The insulating base 5 is made of low thermal conductivity bakelite (phenolic resin laminate) machined by a CNC milling machine. Its structure is a box with openings at the top and front. The internal cavity dimensions match the shape of the heating plate 1 (including its associated heating element and temperature sensor), completely enclosing the five sides of the heating plate 1 except for the upper heat transfer surface. This minimizes convective and radiative heat loss from the heating plate 1 to the surrounding air, ensuring that the input heat can be efficiently used to heat the experimental fluid, thus improving the thermal efficiency and temperature control accuracy of the experiment.

[0044] In some embodiments, the device further includes a base support frame 6 and a base 7 for supporting the entire device and keeping it horizontal; the base 7 is disposed at the bottom of the heat-insulating base 5; the base support frame 6 is disposed on both sides of the left fixing plate 41 and the right fixing plate 42 and its bottom surface is fixed to the base 7.

[0045] The base 7 is a thick low-carbon steel plate with four adjustable anchor bolts on its bottom surface, which are used to precisely adjust the level of the entire device to ensure that the temperature field and flow field inside the experimental chamber are symmetrical.

[0046] The base support frame 6 is a column structure made of four stainless steel square tubes welded together. Its bottom is firmly connected to the base 7 by bolts, and its upper part is connected to the lateral lugs of the left fixing plate 41 and the right fixing plate 42 by bolts. The weight of the Ruili-Bernard convection cavity and the fixing component 4 is directly transferred to the heat insulation base 5 through the sturdy support frame, forming a stable and rigid overall frame, which effectively avoids the adverse effects on sealing performance caused by component deformation.

[0047] This invention also provides a method for generating a heating plate based on the Cantor fractal structure, such as... Figure 7 As shown, it includes the following steps: S101. A heating plate substrate is provided, wherein the heating substrate has a flat heat transfer surface to be processed; S102. Based on the Cantor fractal algorithm, determine the number of iterations n of the target coarse structure and the generation rule for each iteration, where n≥2; Specifically, the generation rules include: pre-setting an initial length. L 0 and height h 0, and the horizontal scale factor f x With longitudinal scale factor f y ; Among them, the n After the first iteration, the characteristic length of a single protrusion structure L n With initial length L 0 satisfies the relation: .

[0048] No. n After the next iteration, the feature height of a single protrusion structure h n With initial height h 0 satisfies the relation: .

[0049] Assuming in the first n The feature length and feature height obtained in the second iteration are respectively L n and h n Then in the first n+1 In this iteration, they satisfy the following scaling relationship:

[0050]

[0051] in, h 0 is the initial height. h 0 represents the initial height.

[0052] It should be noted that, to ensure the stability and manufacturability of the structure, the characteristic height of adjacent protrusions must meet the following requirements. h k >h k+1 ; where k belongs to any iteration number within the range of n.

[0053] No. n After the iteration, the total number of protrusions formed N n for: , s The number of segments to retain after each iteration.

[0054] S103. Based on the target rough structure, a material removal process is performed sequentially on the flat heat transfer surface. n Through repeated processing iterations, a raised structure is formed, thereby generating a Cantor fractal rough structure 11 with self-similar properties.

[0055] Specifically, in the initial stage (n=0), the initial processing plane is defined as a complete, undivided initial line segment (which can be considered a rectangular region on a two-dimensional plane). This line segment possesses an initial characteristic length. L 0. This state represents the flat surface of the heating plate substrate to be processed.

[0056] In the first iteration, the initial line segment with n=0 is divided into... 2s-1 Each segment is divided into segments, with the middle segment serving as the initial feature height of the convex shape. h The length is 0, and the remaining segments are retained to form a trench.

[0057] In the second iteration, the line segment with n=1 is divided into... 2s-1 Each segment is divided into segments, with the middle segment serving as the initial feature height of the convex shape. h The length is 0, and the remaining segments are retained to form a trench.

[0058] In the third iteration, the line segment with n=2 is divided into... 2s-1 Each segment is divided into segments, with the middle segment serving as the initial feature height of the convex shape. h The length is 0, and the remaining segments are retained to form a trench.

[0059] In the fourth iteration, the line segments with n=3 are divided into... 2s-1 Each segment is divided into segments, with the middle segment serving as the initial feature height of the convex shape. h The length is 0, and the remaining segments are retained to form a trench.

[0060] Among them, in the first n In the nth iteration, for the th n-1 Perform the following operations on each protrusion structure formed after the next iteration: Divide the length direction of the current line segment into equal parts. 2s-1 Each segment.

[0061] Canter sets belong to self-affine fractals, and their fractal dimension is... D It can be given by the following formula:

[0062] Among them, 1< D <2. Fractal dimension D The surface morphology complexity determines the roughness; the larger the complexity, the more complex the rough morphology and the larger the surface area occupied by the rough unit.

[0063] According to the generation rules, remove the material corresponding to at least one specific segment to form a trench.

[0064] The remaining segments are retained to form a new convex structure after the nth iteration.

[0065] Furthermore, the step of dividing the length direction of the current line segment into s segments specifically involves dividing the length of the top surface of the current protrusion structure or the area to be processed into s consecutive virtual segments of equal length.

[0066] The segmentation process is first completed in a digital model using computer algorithms to generate a precise processing path. Subsequently, during physical processing, coordinate positioning or an optical positioning system is used to accurately define and identify each segmented region.

[0067] For example, the value of s is 2.

[0068] For example, such as Figure 8 , 9 As shown, when n=0, the initial stage is a single line segment, a complete and undivided initial line segment, representing the starting point of processing, i.e., a flat heating plate substrate surface. Its length is defined as the initial characteristic length. L 0; When n=1, taking the classic Cantor set as an example, the line segment with n=0 is divided into three equal parts, and the middle 1 / 3 is removed. At this point, the originally continuous line segment is divided into two discrete line segments, and the length of each segment becomes... L 1 =L 0 / 3 In the processing of heated plates, this corresponds to the first etching or milling, which creates the first level (also the largest size) of grooves and protrusions on the plane.

[0069] When n=2, repeat the same operation for each of the remaining two line segments from n=1: divide them into three equal parts and remove the middle segment. At this point, the total number of line segments becomes 2×2=4, and the length of each line segment becomes... L 2 =L 1 / 3 =L 0 / 9 This means that a second, finer process is carried out on the large protrusion formed in the first stage to depict a smaller-scale secondary structure.

[0070] When n=3, the remaining 4 line segments from n=2 are trisected and intermediate segments are removed one by one. The number of line segments increases to 2×4=8, and the length of each line segment is shortened to... L 3 =L 2 / 3=L 0 / 27 This represents the third iteration of processing, which introduces a third level of finer roughness structure.

[0071] When n=4, after processing the 8 line segments of n=3, 2×8=16 line segments are generated, each with a length of only [missing information]. L 4 =L 3 / 3 =L 0 / 81 This represents the fourth iteration of processing, which introduces a fourth level of finer roughness structure.

[0072] After four iterations, the result is as follows: Figure 9 The heating plate substrate shown, through four iterations, shows that both its length and height systematically decrease with increasing iteration number, starting from the initial length. L Within the projected area of ​​0, 15 independent protrusions are formed, which greatly increases the actual heat transfer area in contact with the fluid. The multi-scale structure, from macroscopic (n=1) to microscopic (n=4), can effectively destroy the thermal boundary layer at different scales, synergistically enhance turbulence and mixing, and thus maximize heat transfer efficiency.

[0073] The above description is merely a preferred embodiment of the present invention and is not intended to limit the scope of protection of the present invention.

Claims

1. A heating plate based on a Cantor fractal structure, characterized in that, The surface of the heating plate that comes into contact with the experimental fluid has a rough structure generated by Cantor fractals.

2. The heating plate based on the Cantor fractal structure according to claim 1, characterized in that, The coarse structure is generated by n iterations, where n ≥ 2.

3. A high-efficiency heat transfer experimental device, characterized in that, The device includes: The Ruili-Bernard convection chamber is used to contain experimental fluids. The heating plate as described in claim 1 or 2 is disposed at the bottom of the Ruili-Bernard convection cavity for heating the experimental fluid; A cooling plate, located at the top of the Ruili-Bernard convection cavity, is used to cool the experimental fluid.

4. The high-efficiency heat transfer experimental apparatus according to claim 3, characterized in that, The device also includes a cover plate that covers the water channel of the cooling plate to prevent water leakage.

5. The high-efficiency heat transfer experimental apparatus according to claim 3, characterized in that, The Ruili-Bernard convection cavity is formed by side plates; the side plates include a left side plate, a right side plate, a first side plate, and a second side plate, which are sequentially enclosed.

6. The high-efficiency heat transfer experimental apparatus according to claim 3, characterized in that, The device also includes a fixing assembly that secures the Ruili-Bernard convection cavity from both sides.

7. The high-efficiency heat transfer experimental apparatus according to claim 6, characterized in that, The fixing assembly includes a left fixing plate and a right fixing plate, which are used to press and fix the Ruili-Bernard convection cavity with multiple bolts to prevent water leakage.

8. The high-efficiency heat transfer experimental apparatus according to claim 7, characterized in that, The device also includes an insulated base that encloses the heating plate to prevent heat loss.

9. The high-efficiency heat transfer experimental apparatus according to claim 8, characterized in that, The device also includes a base support frame and a base for supporting the entire device and keeping it level; the base is located at the bottom of the insulated base; the base support frame is located on both sides of the left and right fixed plates and its bottom surface is fixed to the base.

10. A method for generating a heating plate based on a Cantor fractal structure as described in claim 1 or 2, characterized in that, Includes the following steps: A heating plate substrate is provided, the heating plate substrate having a flat heat transfer surface to be processed; Based on the Cantor fractal algorithm, the number of iterations n of the target coarse structure and the generation rule of each iteration are determined, where n≥2; Based on the target rough structure, a material removal process is performed sequentially on the flat heat transfer surface. n Through repeated processing iterations, a raised structure is formed, thereby generating a Cantor fractal rough structure with self-similar properties.

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