A method for designing a thermostat for porous media thermal convection environments based on phase change materials

By designing a thermostat for a porous medium thermal convection environment based on phase change materials, and using a double-layer structure and Logistic function to adjust the thermal conductivity and permeability, the problem of temperature and flow field control in the convection environment was solved, achieving an internal thermostat effect without energy input, reducing energy consumption and complexity.

CN122133369APending Publication Date: 2026-06-02SHANGHAI SECOND POLYTECHNIC UNIVERSITY

Patent Information

Authority / Receiving Office
CN · China
Patent Type
Applications(China)
Current Assignee / Owner
SHANGHAI SECOND POLYTECHNIC UNIVERSITY
Filing Date
2026-01-20
Publication Date
2026-06-02

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Abstract

This invention discloses a method for designing a thermostat in a porous medium thermal convection environment based on phase change materials. The thermostat employs a double-layer structure. Under the background of uniform flow and linear temperature change, three concentric circles are set in the middle of the background region, with the small circle forming the central region. The inner annular region, outer annular region, and background region are all covered with isotropic porous media. The inner annular region is the functional region, which uses a phase change material with asymmetric thermal conductivity and permeability. The changes in thermal conductivity and permeability with temperature satisfy the temperature trapping condition to maintain a constant temperature in the central region. The ratio of thermal conductivity and permeability of the media between the outer annular region and the background region is governed by the same geometric relationship, satisfying the dual stealth conditions of thermal field and flow field. This invention provides a new thermal control scheme for porous medium systems, microfluidic systems, and other fields.
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Description

Technical Field

[0001] This invention relates to the field of metamaterials technology, and more specifically, to a method for designing a thermostat for a porous medium under thermal convection environment based on phase change materials. Background Technology

[0002] Isothermal control is of great significance in industries, biomedicine, microelectronics and other fields. Traditional isothermal methods (such as PID temperature control, thermoelectric refrigeration, etc.) rely on external energy input and active feedback, which have problems such as high energy consumption, slow response and complex structure. In recent years, passive temperature control technology based on phase change materials (PCM) has attracted attention because it does not require external energy, but its isothermal range is narrow, the response is not adjustable, and it is difficult to adapt to dynamic thermal environments. Thermal cloaking technology aims to control the heat flow path and make the object "invisible" in the thermal field. Early studies were mostly based on transformation thermodynamics, which required non-uniform anisotropic materials and were difficult to prepare. Among the existing technologies, Han et al. (Han, T. , Bai, X. , Gao, D. , Thong, JTL , Li, B. , & Qiu, CW. (2014). Experimental demonstration of a bilayer thermal cloak. PhysicalReview Letters,112(5), 054302) proposed the bilayer thermal cloak theory, which only requires two isotropic materials, which greatly simplifies the implementation path. However, existing thermal stealth structures are mostly designed for pure thermal conduction conditions, and it is difficult to control the temperature field and flow field simultaneously in convective heat transfer environments.

[0003] In recent years, Dai et al. (S. Dai, J. Shang, and J. Huang..2018, Theory of transformation thermal convection for creeping flow in porous media: Cloaking, concentrating, and camouflage, Phys.Rev.E 97,022129.) proposed a cloaking cloak under convection conditions based on transformation thermodynamics, but the required material parameters are complex and difficult to fabricate. Yeung et al. (Yeung, WS, Mai,VP, & Yang, RJ.(2020). Cloaking: controlling thermal and hydrodynamic fields simultaneously. Physical Review Applied,13(6.)) further proposed a double-layer convection cloaking structure, using porous media to achieve isotropic cloaking, providing a feasible solution for cloaking design in convection environments. However, this structure only achieves "cloaking" and does not integrate "temperature control" function, and cannot maintain a constant internal temperature in a dynamic thermal field. Shen et al. (Shen, X. , Li, Y. , Jiang, C. , & Huang, J..(2016). Temperature trapping: energy-free maintenance of constant temperatures as ambient temperature gradients change. Physical Review Letters, 117(5), 055501.) proposed a temperature trapping theory that utilizes thermally responsive materials (such as shape memory alloys) to achieve constant temperature without energy input. This theory designs materials whose thermal conductivity changes with temperature to form a "heat trap" near the target temperature, ensuring that the temperature in the central region remains constant even when the ambient temperature changes. This technology has been applied to thermal stealth structures, achieving "constant-temperature stealth," but it is still limited to purely thermally conductive conditions. Summary of the Invention

[0004] To address the shortcomings of the existing technology, the present invention aims to provide a method for designing a thermostat for a porous medium under thermal convection environment based on phase change materials. This thermostat can autonomously maintain an internal constant temperature without interfering with the external thermal and flow fields under uniform flow and linear temperature gradient conditions. It features no energy input, simple structure, and suitability for convection environments.

[0005] The technical solution of the present invention is described in detail below.

[0006] A method for designing a thermostat for porous media under thermal convection environment based on phase change materials is disclosed. The thermostat has a circular double-layer structure. Under the background of uniform flow and linear temperature change, three concentric circles are set in the middle of the background region, with the small circle as the central region. The inner annular region, the outer annular region, and the background region are all covered with isotropic porous media. The inner annular region is the functional region, which uses a phase change material with asymmetric thermal conductivity and permeability. Its thermal conductivity and permeability change with temperature to meet the temperature trapping condition, so as to maintain a constant temperature in the central region. The ratio of thermal conductivity and permeability of the medium between the outer annular region and the background region is governed by the same geometric relationship, which satisfies the dual stealth conditions of thermal field and flow field, and is used to protect the inner layer from the interference of external flow field and temperature field.

[0007] In this invention, within the functional region, the thermal conductivity of the asymmetric phase change material varies with temperature according to a Logistic function; the thermal conductivity is extremely high near the target temperature and extremely low away from it. Even with significant changes in ambient temperature, the material maintains its thermal conductivity at the phase change temperature T. C A "heat trap" is formed at the center, where the temperature remains almost constant.

[0008] In this invention, the left and right sides of the concentric circles serve as heat and cold sources, creating a pressure difference between the top and bottom. Based on left-right symmetry, the functional area is divided into three regions: inner region I, inner region II, and inner region III. Inner region I is responsible for controlling the high-temperature heat flow, inner region II is responsible for controlling the low-temperature heat flow, and inner region III uses an insulating and impermeable material to ensure that the temperature field inside the concealed object is completely unaffected by the external linear temperature gradient field, and also prevents external flow from entering the concealed area, resulting in zero flow within this region. The material of inner region III can be polydimethylsiloxane (PDMS), silicone rubber, etc.

[0009] In this invention, based on the temperature trapping theory of asymmetric phase change materials with thermally responsive thermal conductivity, the thermal conductivity of the functional region must satisfy the following to maintain a constant temperature in the central region:

[0010] (2)

[0011] in: This is the effective thermal conductivity value of inner region I. This is the effective thermal conductivity value of the inner region II. It is a given phase transition temperature. The thermal conductivity of the substrate ensures that the material always has a minimum thermal conductivity. It is the amplitude of the thermal conductivity jump, which controls the difference in thermal conductivity between high and low temperatures, where The permeability formulas for each region of the inner layer satisfy:

[0012] (3)

[0013] in: This is the effective permeability value of inner region I. This is the effective permeability value of the inner region II. The substrate permeability ensures that the material always has a minimum permeability. It controls the permeability jump range, and the permeability difference between high and low pressure states. , It is a given phase transition temperature.

[0014] In this invention, the flow is at a low Reynolds number. , number, It satisfies Darcy's law, the convection term is negligible, and both the temperature and pressure fields satisfy Laplace's equation:

[0015] (4)

[0016] in: It is the effective thermal conductivity of the porous medium in the outer annular region. It is the effective thermal conductivity of the porous medium in the background region. It is the effective permeability of the porous medium in the outer annular region. R1 is the thermal conductivity of the porous medium in the background region, and R2 are the radii of the inner and outer rings, respectively.

[0017] In this invention, for porous media composed of a solid framework and fluid-filled pores, the porosity is changed. Alternatively, different solid framework thermal conductivity can be selected. Material adjustment of effective thermal conductivity .

[0018] In this invention, the fluid used in the applicable flow field is selected from any one of polydimethylsiloxane, water, polyethylene glycol aqueous solution, or polyurethane prepolymer.

[0019] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0020] This invention provides a double-layer thermostat that achieves self-sustaining constant temperature in a convective heat transfer environment without consuming energy. It utilizes the temperature-dependent characteristics of thermally responsive phase change materials to form a "heat trap" near the target temperature, achieving completely passive, energy-input-free thermostating, significantly reducing system energy consumption and complexity. The invention was verified using finite element method (FEM) software. Results show that this invention can simultaneously exhibit different functional effects on the same thermal device in both thermal and flow fields, saving materials and reducing experimental fabrication difficulty. The invention is fully achievable in steady-state conditions and can be extended to transient and other physical fields to achieve the same functionality. Attached Figure Description

[0021] Figure 1 This is a schematic diagram of the simulated structure of the present invention.

[0022] Figure 2 This is a conceptual schematic diagram of the present invention. The ratio of thermal conductivity to permeability of the medium between the outer annular region and the background region is governed by the same geometric relationship, satisfying dual stealth conditions for both thermal and flow fields. This protects the inner layer from interference from external flow and temperature fields. The inner layer is a phase-change porous medium material, whose thermal conductivity and permeability change drastically near the phase-change temperature, switching between high and low thermal conductivity / permeability to ensure a constant internal temperature.

[0023] Figure 3 A three-dimensional comparison diagram of the thermal conductivity of the functional areas.

[0024] Figure 4 Figures (a)-(c) show the temperature of the central region of the reference model (i.e., without considering the design of the inner functional areas) as a function of the heat source T. H The additional simulation results show heat sources of 323K, 338K, and 353K, with gray lines representing isotherms; (d)-(f) show the temperature of the simulated material's central region as a function of heat source T, respectively. H The increased simulation results show that the heat source T H At 323K, 338K, and 353K respectively, the gray lines represent isotherms, and the simulation results show that T H The effect of increasing the approximate isothermal temperature in the central region is enhanced; (g)-(i) represent the simulation of the central region of the material as a function of the inlet pressure P. H The added simulation results show that when the inlet pressure (PH) of the background material is 200 Pa, 500 Pa, and 1000 Pa, the gray lines are isotherms. The simulation results show that the central region is approximately at a constant temperature when the inlet pressure increases.

[0025] Figure 5 This is a comparison diagram showing the temperature distribution changes at the center of the simulated material and the reference model.

[0026] Figure 6 This invention relates to a thermostat designed with phase change materials in a porous medium thermal convection environment, showing the temperature distribution along the centerline of the thermal field. The horizontal axis represents the background dimensions calculated using finite element analysis, and the vertical axis represents the temperature value.

[0027] Figure 7 The image shows the temperature distribution of the isothermal metamaterial of this invention along the centerline of the flow field; the horizontal axis represents the background size calculated by the finite element simulation, and the vertical axis represents the temperature value. Detailed Implementation

[0028] The present invention will now be described clearly and completely with reference to the accompanying drawings and embodiments.

[0029] The thermostat of this invention adopts a double-layer structure. The inner ring is a phase change porous medium material, whose thermal conductivity and permeability change drastically near the phase change temperature, switching between high and low thermal conductivity / permeability to maintain the central constant temperature functional area. The outer layer is an isotropic porous medium, whose effective thermal conductivity and permeability meet the double-layer stealth conditions, ensuring that the external flow and temperature field are not disturbed. Figure 1 This is a schematic diagram of the simulated structure of the present invention. The structure is designed with heat and cold sources on the left and right sides, creating a pressure difference between the top and bottom. The inner and outer circular regions are divided into three functional areas: based on left-right symmetry, the functional areas are divided into three regions: inner region I, inner region II, and inner region III. The outer ring and the background region have constant effective permeability and effective thermal conductivity. The central region is made of a high thermal conductivity material with constant parameters. A higher thermal conductivity value is set during the simulation to demonstrate that the central constant temperature is achieved through the inner functional regions, without relying on the insulation of the concealed area itself. The high thermal conductivity material can be a pure metal, alloy, etc. Figure 2 This is a conceptual schematic diagram of the present invention. The ratio of thermal conductivity to permeability of the medium between the outer annular region and the background region is governed by the same geometric relationship, satisfying dual stealth conditions for both thermal and flow fields. This protects the inner layer from interference from external flow and temperature fields. The inner layer is a phase-change porous medium material, whose thermal conductivity and permeability change drastically near the phase-change temperature, switching between high and low thermal conductivity / permeability to ensure a constant internal temperature.

[0030] The main scientific principles of the present invention, which is based on phase change materials, for designing a thermostat in a porous medium thermal convection environment, will be described in detail below:

[0031] 1. Thermally responsive phase change materials

[0032] Thermally responsive phase change materials (PCCs) are materials whose physical properties (such as thermal conductivity, volume, and shape) undergo significant abrupt changes near a specific temperature (phase change temperature). In this design, the inner layer is a PCC, whose thermal conductivity changes with temperature according to a Logistic function. It can autonomously maintain a constant core temperature even when the ambient temperature gradient changes. The standard Logistic function is:

[0033] (1)

[0034] In this design, to describe the thermal conductivity at T C The nearby S-shaped changes are corrected using the following form:

[0035] (2)

[0036] in, It is the thermal conductivity of the substrate that ensures the material always has a minimum thermal conductivity. It is the amplitude of the thermal conductivity jump, controlling the difference in thermal conductivity between high and low temperatures. It is the phase transition temperature. This indicates the thermal conductivity of inner region I. This is the thermal conductivity of the inner region II. From the above equation, it can be seen that... = The derivative is at its maximum at this point, indicating the most drastic change in thermal conductivity, which is beneficial for temperature stability. The corresponding permeability formulas for inner regions I and II are:

[0037] (3)

[0038] in, This is the permeability value for region I. This is the permeability value for Region II. Substrate permeability ensures that the material always has a minimum permeability. It is the magnitude of the permeability jump, controlling the permeability difference between high and low pressure states, among which , It is a given phase transition temperature.

[0039] The inner region III is made of a nearly thermally insulating and impermeable material, ensuring that the internal objects neither exchange heat with the external thermal field nor interfere with the external flow field. The inner region III can be made of materials such as polydimethylsiloxane (PDMS) or silicone rubber.

[0040] 2. Effective thermal conductivity and permeability of porous media

[0041] The outer layer first considers the thermal field. The steady-state energy equation for incompressible flow with no heat source and negligible viscous dissipation in the background is determined by the advection-diffusion equation:

[0042] (4)

[0043] In the formula For fluid density, For specific heat of fluid, Where is the thermal conductivity of the fluid, and T is the fluid temperature.

[0044] The temperature of the porous outer layer is also determined by the advection diffusion equation. Within the outer layer, both u and v are non-zero; therefore, the parameters used for the background are not applicable to the outer layer. However, for smaller... The advection term can be ignored, and the temperature of the porous outer layer is controlled by the Laplace equation:

[0045] (5)

[0046] in, It is the effective thermal conductivity of the outer layer medium. R1 and R2 are the effective thermal conductivity of the background medium, and R1 and R2 are the radii of the inner and outer layers, respectively.

[0047] For porous media consisting of a solid framework and fluid-filled pores, the effective thermal conductivity of the outer layer is... Commonly used volume-weighted average model description:

[0048] (6)

[0049] in, It is porosity (the proportion of pore volume). It refers to the thermal conductivity of a solid skeleton (such as the thermal conductivity of metallic materials in a metal foam). Porosity is the thermal conductivity of the fluid (such as air or water) within the pores. By changing the porosity... Or choose different Materials can be used to adjust the effective thermal conductivity of the porous outer layer. .

[0050] Permeability s is used to describe the ability of porous media to allow fluid to pass through, and it satisfies Darcy's Law:

[0051] (7)

[0052] in, Let μ be the pressure, s be the dynamic viscosity, s be the permeability, and v be the fluid velocity. From the above equation, we can see that when the flow velocity is low and the dynamic viscosity remains constant, the pressure gradient and permeability are linearly related. That is, theoretically, the pressure gradient can be changed to increase the permeability. To change the corresponding parameters of the penetration rate.

[0053] To achieve fluid stealth, the outer layer permeability Must meet:

[0054] (8)

[0055] in, Since it is the background permeability, the streamlines governed by Darcy's law are equivalent to the heat flux lines governed by Fourier's law. This perspective decisively verifies the hydrodynamic stealth function of our proposed two-layer structure.

[0056] The flow is low Reynolds number ( ) and low number( The system satisfies Darcy's law, the convection term is negligible, and both the temperature and pressure fields satisfy Laplace's equations.

[0057] (9)

[0058] Combining equations (5) and (8) ensures that the inner constant temperature zone is not affected by external flow and temperature field, while the outer porous medium must simultaneously meet the conditions of thermal stealth and fluid stealth.

[0059] 3. Heat convection transport

[0060] In summary, to achieve the desired functionality, this invention utilizes porous media for heat transfer, allowing conduction and convection to share the same space. When considering steady-state heat transport in metamaterials, the total heat flux is governed by a conservation equation, specifically as follows:

[0061] (10)

[0062] in, For conduction heat flow based on Fourier's law, This is the convective heat flux based on Darcy's law. The above equation holds when convection reaches local stability.

[0063] In summary, the above theoretical methods are scientifically feasible. We further extended them to finite element simulation to verify their feasibility through numerical simulation. We analyzed the simulation results by applying them to flow and thermal fields, and compared the calculated pressure, velocity, and thermal flow fields with the corresponding fields under the reference model to verify the feasibility of the invention. Through formula derivation and verification, the functional temperature control effect of the thermal functional device was finally obtained.

[0064] This invention uses COMSOL Multiphysics finite element simulation to design a thermal superstructure material model. The structural geometry is set as follows: the background material region is square, with concentric circles in the center; the smaller circle is the central region, and the inner annular region is the functional region. The thermal conductivity and permeability ratio between the outer annular region and the background are governed by the same geometric relationship. The thermal functional material device structure of this invention is laid out as a fluid material structure, with high and low pressures set at 1000 Pa, 500 Pa, and 200 Pa, respectively, and low pressure set at 0 Pa; high temperatures are set at 353 K, 338 K, and 323 K, respectively, and low temperature is set at 273 K. Under high and low temperature design conditions, this invention uses passive temperature control technology of phase change material (PCM) to modulate the effective thermal conductivity and permeability of the porous medium to verify the effect of the heat flux dual field. Under high and low pressure design conditions, this invention uses modulation of the spatial distribution of the effective permeability of the porous medium to verify the effect of the heat flux dual field.

[0065] Firstly, for simple fluid mass transfer, the Darcy's law module under porous media is used for its design: the background size is 80×80. 2 The radius of the central circle is 8. Inner circle radius 10 The outer circle radius is 20. The thermal conductivity of the background region is The background penetration rate is 1.0 × 10⁻⁶. -12 m 2 The formulas for the thermal conductivity and permeability of the outer ring satisfy formula (9), and the thermal conductivity and permeability settings for regions I and II of the inner ring satisfy formulas (2) and (3) respectively. Region III of the inner ring is an almost thermally adiabatic and impermeable material. The inlet pressure at the lower boundary of the material is set to P. H The upper boundary sets the outlet pressure to 0 Pa, and the left boundary sets the heat source to T. H The cold source on the right boundary is 273K.

[0066] Figure 3 The three-dimensional comparison diagram shows the thermal conductivity of the three parts of the inner functional region. The three-dimensional data diagrams are the thermal conductivity comparison diagrams of regions I, II, and III of the isothermal metamaterial device under isothermal conditions.

[0067] To further analyze the isothermal properties of metamaterials and explore the validity of the simulation results, Figure 4 Analyze and plot the temperature values ​​of the simulated material and the reference model in the central regions of different temperature differences and different pressure differences.

[0068] The material inlet pressure P was calculated using parametric scans. H All integer values ​​between 0 Pa and 1000 Pa, heat source temperature T H Integer values ​​between 323K and 353K. Without affecting the background material, the simulation results show that the central region remains at the phase transition temperature, and the metamaterial functions as a stealth state.

[0069] Figure 5 Analysis revealed that, under steady-state conditions, the temperature at the center of the reference model is related to the temperature at the heat source T. H The values ​​of (323K, 330K, 338K, 345K, and 353K) are positively correlated; and after setting the functional area parameters that satisfy formulas (2) and (3), as T... H As the value increases, the temperature at the center point remains approximately constant (temperature difference less than 3K).

[0070] Figure 6 Analyzing the temperature changes across the entire region under different thermal conditions, it is clear that the temperatures of the background and annular regions are constantly changing, while the central circular region remains around the phase transition temperature.

[0071] Figure 7The temperature variations across the entire region under different flow field conditions were analyzed, and the differences between the simulated material and the reference model in the central region under pressure differences were examined. It can be clearly seen that the temperature in the background and annular regions continuously changes, while the temperature in the central circular region remains around the phase transition temperature.

[0072] Considering the coupled simulation of conduction and convection, this invention uses a porous medium heat transfer module for design: the thermal conductivity of the background region is... The background penetration rate is 1.0 × 10⁻⁶. -12 m 2 The formulas for the thermal conductivity and permeability of the outer ring satisfy formula (9). Let the inlet pressure be P at the lower boundary of the material. H =200Pa, 500Pa, 1000Pa, let the outlet pressure be P at the upper boundary. L =0Pa, let the heat source on the left boundary be T. H =323K, 338K, 353K, right boundary cold source T L =273K. The feasibility and scalability of this invention were verified from different perspectives.

[0073] In summary, this invention is based on a two-layer structure. The inner ring is a phase-change porous medium material whose thermal conductivity and permeability change drastically near the phase-change temperature. Switching between high and low thermal conductivity / permeability allows it to autonomously maintain a nearly constant core temperature despite changes in ambient temperature gradients. The outer layer is an isotropic porous medium whose effective thermal conductivity and permeability satisfy the two-layer stealth condition, ensuring that external flow and temperature fields remain undisturbed. This invention provides a method that, under uniform flow and linear temperature conditions, achieves both internal temperature stability and simultaneous thermal and flow field stealth. The feasibility of the design method is then verified through finite element simulation. This invention can greatly simplify the fabrication of porous metamaterials. The Darcy thermal convection considered in this invention is a simple, unidirectionally coupled multiphysics process, thus naturally applicable to other unidirectionally coupled thermal convection processes. It also exhibits similar control effects for other thermal convection models, such as peristaltic flow between two plates.

Claims

1. A method for designing a thermostat for porous media thermal convection environments based on phase change materials, characterized in that, The thermostat has a circular double-layer structure. Under the background of uniform flow and linear temperature change, three concentric circles are set in the middle of the background area. The small circle is the central area. The inner ring area, the outer ring area, and the background area are all covered with isotropic porous media. The inner ring area is the functional area. The functional area uses asymmetric phase change material with thermal conductivity and permeability. Its thermal conductivity and permeability change with temperature to meet the temperature capture condition, so as to maintain a constant temperature in the central area. The ratio of thermal conductivity and permeability of the medium between the outer ring area and the background area is governed by the same geometric relationship, which meets the dual stealth conditions of thermal field and flow field, and is used to protect the inner layer from the interference of external flow field and temperature field.

2. The method for designing a thermostat for porous media thermal convection environments based on phase change materials according to claim 1, characterized in that, Within the functional region, the thermal conductivity of the asymmetric phase change material changes with temperature according to the Logistic function.

3. The method for designing a thermostat for porous media thermal convection environments based on phase change materials according to claim 1, characterized in that, The concentric circles are hot and cold sources on the left and right sides, creating a pressure difference between the top and bottom. Based on the left-right symmetry, the functional area is divided into three regions: inner region I, inner region II, and inner region III. Inner region I is responsible for high-temperature heat flow control, inner region II is responsible for low-temperature heat flow control, and inner region III uses heat-insulating and impermeable materials to ensure that the temperature field inside the cloaked object is completely unaffected by the external linear temperature gradient field, and also prevents external flow from entering the cloaked area, making the flow inside this region zero.

4. The method for designing a thermostat for porous media thermal convection environments based on phase change materials according to claim 3, characterized in that, According to the temperature trapping theory of asymmetric phase change materials with thermally responsive thermal conductivity, in order to maintain a constant temperature in the central region, the thermal conductivity of the functional region must satisfy: (2) in: This is the effective thermal conductivity value of inner region I. This is the effective thermal conductivity value of the inner region II. It is a given phase transition temperature. The thermal conductivity of the substrate ensures that the material always has a minimum thermal conductivity. It is the amplitude of the thermal conductivity jump, which controls the difference in thermal conductivity between high and low temperatures, where ; The permeability formulas for each region of the inner layer satisfy: (3) in: This is the effective permeability value of inner region I. This is the effective permeability value of the inner region II. The substrate permeability ensures that the material always has a minimum permeability. It controls the permeability jump range, and the permeability difference between high and low pressure states. , It is a given phase transition temperature.

5. The method for designing a thermostat for porous media thermal convection environments based on phase change materials according to claim 1, characterized in that, The flow is at a low Reynolds number. , number, It satisfies Darcy's law, the convection term is negligible, and both the temperature and pressure fields satisfy Laplace's equation: (4) in: It is the effective thermal conductivity of the porous medium in the outer annular region. It is the effective thermal conductivity of the porous medium in the background region. It is the effective permeability of the porous medium in the outer annular region. R1 is the thermal conductivity of the porous medium in the background region, and R2 are the radii of the inner and outer rings, respectively.

6. The method for designing a thermostat for porous media thermal convection environments based on phase change materials according to claim 5, characterized in that, For porous media composed of a solid framework and fluid-filled pores, by changing the porosity Alternatively, different solid framework thermal conductivity can be selected. Material adjustment of effective thermal conductivity .

7. The method for designing a thermostat for porous media thermal convection environments based on phase change materials according to claim 1, characterized in that, The fluid used in the applicable flow field is selected from any one of polydimethylsiloxane, water, polyethylene glycol aqueous solution, or polyurethane prepolymer.