Parallel-serial-parallel calculation method of equivalent thermal conductivity of graphene composite insulation board

Abstract

The present application relates to the field of new thermal insulation energy-saving materials, especially to a kind of parallel-serial-parallel connection calculation method for equivalent thermal conductivity of graphene composite insulation board, comprising the following steps: S1, establishing the parallel-serial-parallel connection calculation model of graphene composite insulation board;S2, determining the mass ratio and volume ratio of graphene composite insulation board matrix material and three kinds of impurity materials;S3, calculating the thermal resistance of secondary subunit, the thermal resistance of secondary subunit matrix material and the thermal resistance of secondary subunit inclusion material;S4, calculating the overall unit thermal resistance, the thermal resistance of primary subunit and the thermal resistance of primary subunit matrix material;S5, calculating the equivalent thermal conductivity of secondary subunit;S6, calculating the equivalent thermal conductivity of primary subunit;S7, calculating the equivalent thermal conductivity of overall thermal unit.The present application can accurately solve the equivalent thermal conductivity, greatly improve the calculation accuracy compared with traditional calculation model, and provide effective basis for the optimization and improvement of graphene composite material insulation board.

Description

Technical Field

[0001] This invention relates to the field of new thermal insulation and energy-saving materials, and in particular to a method for calculating the equivalent thermal conductivity of a graphene composite insulation board. Background Technology

[0002] In recent years, energy expenditure in global industrial and residential construction has become one of the most critical issues. To achieve sustainable national and societal development, it is necessary to utilize insulation materials for better energy conservation and strengthen sustainable energy strategies in the building sector. The construction industry continuously develops new insulation materials to improve energy efficiency. The insulation efficiency of insulation materials primarily depends on their thermal conductivity and their ability to maintain their thermal properties over a period of time. Thermal conductivity is one of the main characteristics of insulation materials in the building industry, and the most accurate method to obtain the thermal conductivity of composite insulation boards is measurement according to standard testing methods. Building envelope insulation is crucial for energy conservation and a comfortable indoor environment. For the building envelope, the lower the thermal conductivity, the better the insulation performance of the material, and the higher the building's energy efficiency. However, many insulation materials are flammable, and improving insulation performance will reduce the fire resistance of the building structure. Therefore, while ensuring the fire resistance requirements of building envelope materials, adjusting and improving the thermal conductivity of the insulation material components in the envelope has become key to improving the insulation performance of the building structure.

[0003] Thermal conductivity is a crucial parameter for quantitatively characterizing the thermal insulation performance of insulation materials. Studies have shown that graphene composite insulation boards reduce density and thermal conductivity without compromising combustion and mechanical properties. Currently, research on material thermal conductivity both domestically and internationally focuses on theoretical calculations, indoor experiments, and numerical simulations. Theoretical calculations can significantly improve efficiency and reduce the tediousness and resource waste of experimental measurements and numerical simulations. However, traditional parallel and series prediction models cannot accurately predict the thermal conductivity of graphene composite insulation boards. Therefore, addressing the challenge of low accuracy in theoretical predictions of the thermal conductivity of graphene composite insulation boards, an accurate prediction method for the thermal conductivity of graphene composite insulation boards is urgently needed to provide a basis for its optimized design. Summary of the Invention

[0004] In view of this, in order to solve the problem of low theoretical accuracy of the thermal conductivity of graphene composite insulation board, this invention provides a parallel-series-parallel calculation method for the equivalent thermal conductivity of graphene composite insulation board.

[0005] An embodiment of the present invention provides a method for calculating the equivalent thermal conductivity of a graphene composite insulation board, comprising the following steps:

[0006] S1. Based on the minimum thermal resistance rule and the equal equivalent thermal conductivity rule, a parallel-series-parallel calculation model for graphene composite insulation board is established. The parallel-series-parallel calculation model includes several cubic overall units. Each overall unit includes three first-level sub-units connected in parallel along the vertical direction. Each first-level sub-unit includes a left-side first-level sub-unit matrix material, a diode sub-unit, and a right-side first-level sub-unit matrix material connected in series. Each second-level sub-unit matrix includes a front-side diode sub-unit matrix material, a diode sub-unit impurity material, and a rear-side diode sub-unit matrix material connected in parallel.

[0007] S2. Determine the mass proportions of the graphene composite insulation board matrix material (graphite polystyrene particles) and the three impurity materials (cement, vitrified microspheres, and silica fume) as ω1, ω2, ω3, and ω4, respectively. Calculate the volume proportions of the matrix material and the three impurity materials as Ф1, Ф2, Ф3, and Ф4. Further determine the side lengths a, b, and c of the dipole unit inclusion material in the calculation model.

[0008] S3. Based on Fourier's law of thermal conduction, calculate the thermal resistances RDm, REm, and RFm of the second-level sub-unit, the thermal resistances RADD, RBEE, and RCFF of the matrix material of the second-level sub-unit, and the thermal resistances RD, RE, and RF of the inclusion material of the second-level sub-unit.

[0009] S4. Based on Fourier's law of thermal conduction, calculate the overall unit thermal resistance Rm, the thermal resistances RA, RB, and RC of the first-level sub-unit, and the thermal resistances RAD, RBE, and RCF of the matrix material of the first-level sub-unit.

[0010] S5. Based on the minimum thermal resistance rule and the equal equivalent thermal conductivity rule, establish a parallel model of the matrix material and the inclusion material of the second-level sub-unit, and calculate the equivalent thermal conductivity λDm, λEm, and λFm of the second-level sub-unit.

[0011] S6. Based on the minimum thermal resistance rule and the equal equivalent thermal conductivity rule, establish a series model of the first-level sub-unit matrix material and the second-level sub-unit, and calculate the equivalent thermal conductivity λA, λB, and λC of the first-level sub-unit.

[0012] S7. Based on the principle of minimum thermal resistance and the principle of equal equivalent thermal conductivity, establish a parallel model of the first-level sub-units in the overall unit, and calculate the equivalent thermal conductivity λ of the overall thermally conductive unit. m .

[0013] In step S2, the formula for calculating the volume percentage of the matrix material and the three impurity materials is as follows:

[0014]

[0015] In the formula, ρ iLet be the density of the matrix material and the three impurity materials, and i = 1, 2, 3, 4 represent graphite polystyrene particles, cement, vitrified microspheres, and silica fume, respectively.

[0016] The formulas for calculating the side lengths a, b, and c of the dipole unit inclusion material in the computational model are as follows:

[0017]

[0018] In step S3, the formula for calculating the thermal resistance of the insulation material is:

[0019]

[0020] In the formula, Q i The power of the heat source transferred between the inner and outer sides of the i-th material in the graphite composite insulation board, expressed in W; ΔT i R represents the temperature difference between the inner and outer surfaces of the i-th material, expressed in K. i δ represents the thermal resistance of the i-th material, expressed in K / W. i λ represents the thickness of the i-th material in the heat transfer direction, in meters (m). i Let be the thermal conductivity of the i-th material, expressed in W·(m·K). -1 A i The heat transfer cross-sectional area of ​​the i-th material is expressed in m². 2 .

[0021] In step S3, the formula for calculating the thermal resistance of the secondary sub-unit is:

[0022]

[0023]

[0024]

[0025] In the formula, λ Dm The equivalent thermal conductivity of the second-order subunit;

[0026] The formula for calculating the thermal resistance of the matrix material of the second-level subunit is as follows:

[0027]

[0028]

[0029]

[0030] In the formula, λ1 is the thermal conductivity of the graphene polystyrene particle matrix material;

[0031] The formula for calculating the thermal resistance of the inclusion material in the second-level subunit is as follows:

[0032]

[0033]

[0034]

[0035] In the formula, λ2, λ3 and λ4 are the thermal conductivity coefficients of the inclusion materials in the second-order subunit, respectively.

[0036] In step S4, the formula for calculating the overall unit thermal resistance is:

[0037]

[0038] In the formula, λ m The equivalent thermal conductivity of the entire unit;

[0039] The formula for calculating the thermal resistance of the first-level subunit is as follows:

[0040]

[0041]

[0042]

[0043] In the formula, λ A , λ B and λ C The equivalent thermal conductivity of the first-order subunit;

[0044] The formula for calculating the thermal resistance of the matrix material of the first-level subunit is as follows:

[0045]

[0046]

[0047]

[0048] In the formula, λ1 is the thermal conductivity of the matrix material of the first-order subunit.

[0049] In step S5, the calculation formula for the parallel model of the secondary sub-unit matrix material and the secondary sub-unit inclusion material is as follows:

[0050]

[0051]

[0052] The formula for calculating the equivalent thermal conductivity of the second-level subunit is as follows:

[0053]

[0054]

[0055]

[0056] In step S6, the calculation formula for the series model of the first-level sub-unit matrix material and the second-level sub-unit is as follows:

[0057]

[0058]

[0059]

[0060] The formula for calculating the equivalent thermal conductivity of the first-level subunit is as follows:

[0061]

[0062]

[0063]

[0064] In step S7, the calculation formula for the parallel model of the first-level sub-units in the overall unit is:

[0065] Attached Figure Description

[0066] Figure 1 This is a flowchart of a parallel-series-parallel calculation method for the equivalent thermal conductivity of a graphene composite insulation board according to the present invention;

[0067] Figure 2 This is the theoretical model of the graphene composite insulation board of the present invention;

[0068] Figure 3 This is a simplified parallel-series-parallel model of the graphene composite insulation board of the present invention;

[0069] Figure 4 This is the theoretical model of the parallel-series-parallel heat-conducting cell of the present invention;

[0070] Figure 5 This refers to the basic dimensions of the parallel-series-parallel heat-conducting cell of the present invention;

[0071] Figure 6 This is a comparison between the results of different calculation models of the present invention and the experimental results. Detailed Implementation

[0072] To make the objectives, technical solutions, and advantages of the present invention clearer, the embodiments of the present invention will be further described below with reference to the accompanying drawings.

[0073] Please refer to Figures 1 to 6 The present invention provides a parallel-series-parallel calculation method for the equivalent thermal conductivity of a graphene composite insulation board. Based on the minimum thermal resistance rule and the equality rule of specific equivalent thermal conductivity, a parallel-series-parallel calculation model for the graphene composite insulation board is established to calculate the equivalent thermal conductivity of the insulation board. The method specifically includes the following steps:

[0074] S1、 Figures 2 to 4 Based on the minimum thermal resistance rule and the equality rule of equivalent thermal conductivity, a parallel-series-parallel theoretical calculation model for graphene composite insulation boards was established. The parallel-series-parallel calculation model includes several cubic overall units. Each overall unit includes three first-level sub-units A, B, and C connected in parallel along the vertical direction. Each first-level sub-unit includes the matrix material of the left first-level sub-unit, the diode sub-unit, and the matrix material AD, BE, and CF of the right first-level sub-unit connected in series. The second-level sub-units include the matrix material of the front diode sub-unit, the impurity materials D, E, and F of the diode sub-unit, and the matrix material ADD, BEE, and CFF of the rear diode sub-unit connected in parallel.

[0075] S2. Based on the design parameters, further determine the mass proportions of the graphene composite insulation board matrix material (graphite polystyrene particles) and the three impurity materials (cement, vitrified microspheres, and silica fume) as ω1, ω2, ω3, and ω4, respectively. Calculate the volume proportions of the matrix material and the three impurity materials as Ф1, Ф2, Ф3, and Ф4. Further determine the side lengths a, b, and c of the inclusion materials in the dipole unit in the calculation model, with dimensions as shown in the figure. Figure 5 As shown, the overall unit has a side length of L = 1 and is divided into three parallel thermally conductive first-level sub-units A, B, and C. The thickness of the three thermally conductive first-level sub-units is δ = 1 / 3. The matrix material and inclusion material in the three sub-units are combined in a series-parallel manner. The inclusion materials D, E, and F of the two-pole sub-units are cuboids, with side lengths a, b, and c in the three first-level sub-units, respectively. The thermally conductive surfaces are rectangular with dimensions of δ×a, δ×b, and δ×c, respectively.

[0076] The formulas for calculating the volume percentages of the matrix material and the three impurity materials are as follows:

[0077]

[0078] In the formula, ρ i Let be the density of the matrix material and the three impurity materials, and i = 1, 2, 3, 4 represent graphite polystyrene particles, cement, vitrified microspheres, and silica fume, respectively.

[0079] The formulas for calculating the side lengths a, b, and c of the inclusion material in the dipole unit of the computational model are as follows:

[0080]

[0081] S3 Figure 4 and Figure 5 A parallel-series-parallel calculation model for the thermal conductivity of graphene composite insulation board was determined. Based on Fourier's law of heat conduction, the thermal resistances RDm, REm, and RFm of the second-level sub-unit, the thermal resistances RADD, RBEE, and RCFF of the matrix material of the second-level sub-unit, and the thermal resistances RD, RE, and RF of the inclusion material of the second-level sub-unit were calculated.

[0082] The formula for calculating the thermal resistance of the insulation material is as follows:

[0083]

[0084] In the formula, Q i The power of the heat source transferred between the inner and outer sides of the i-th material in the graphite composite insulation board, expressed in W; T i R represents the temperature difference between the inner and outer surfaces of the i-th material, expressed in K. i δ represents the thermal resistance of the i-th material, expressed in K / W. i λ represents the thickness of the i-th material in the heat transfer direction, in meters (m). i Let be the thermal conductivity of the i-th material, expressed in W·(m·K). -1 A i The heat transfer cross-sectional area of ​​the i-th material is expressed in m². 2 .

[0085] Figure 4 In the parallel-series-parallel computing model shown, D m E m and F m As a second-level subunit, according to formula (3), the thermal resistance of the second-level subunit is obtained as follows:

[0086]

[0087]

[0088]

[0089] In the formula, λ Dm The equivalent thermal conductivity of the second-order subunit;

[0090] The calculation formulas for the thermal resistance of the matrix materials ADD, BEE, and CFF of the second-level subunit are as follows:

[0091]

[0092]

[0093]

[0094] In the formula, λ1 is the thermal conductivity of the graphene polystyrene particle matrix material;

[0095] The formulas for calculating the thermal resistance of the inclusion materials D, E, and F in the secondary subunit are as follows:

[0096]

[0097]

[0098]

[0099] In the formula, λ2, λ3 and λ4 are the thermal conductivity coefficients of the inclusion materials in the second-order subunit, respectively;

[0100] S4. Based on Fourier's law of thermal conduction, calculate the overall unit thermal resistance Rm, the thermal resistances RA, RB, and RC of the first-level sub-unit, and the thermal resistances RAD, RBE, and RCF of the matrix material of the first-level sub-unit.

[0101] exist Figure 4 In the prediction model shown, the equivalent thermal resistance of the cubic heat-conducting cell is:

[0102]

[0103] In the formula, λ m The equivalent thermal conductivity of the entire unit;

[0104] The formulas for calculating the thermal resistance of the first-level subunits A, B, and C are as follows:

[0105]

[0106]

[0107]

[0108] In the formula, λ A , λ B and λ C The equivalent thermal conductivity of the first-order subunit;

[0109] The calculation formulas for the thermal resistances of the first-level subunit matrix materials AD, BE, and CF are as follows:

[0110]

[0111]

[0112]

[0113] In the formula, λ1 is the thermal conductivity of the matrix material of the first-order subunit;

[0114] S5. Based on the minimum thermal resistance rule and the equal equivalent thermal conductivity rule, establish a parallel model of the matrix material and the inclusion material of the second-level sub-unit, and calculate the equivalent thermal conductivity λDm, λEm, and λFm of the second-level sub-unit.

[0115] In first-level subunits A, B, and C, second-level subunit D m E m and F m The matrix material and inclusion materials are combined in parallel. Figure 5 D m E m and F m The partial parallel model calculation formula is as follows:

[0116]

[0117]

[0118]

[0119] According to formulas (4), (7), (10) and (20), we obtain D. m The formula for calculating the equivalent thermal conductivity is:

[0120]

[0121] According to formulas (5), (8), (11) and (21), E is obtained. m The formula for calculating the equivalent thermal conductivity is:

[0122]

[0123] According to formulas (6), (9), (12) and (22), we obtain F m The formula for calculating the equivalent thermal conductivity is:

[0124]

[0125] S6. Based on the minimum thermal resistance rule and the equal equivalent thermal conductivity rule, establish a series model of the first-level sub-unit matrix material and the second-level sub-unit, and calculate the equivalent thermal conductivity λA, λB, and λC of the first-level sub-unit.

[0126] First-level subunits A, B, and C are composed of a first-level subunit matrix material and second-level subunits connected in series. The thermal resistance of first-level subunits A, B, and C can be expressed as:

[0127]

[0128]

[0129]

[0130] According to formulas (4), (14), (17), (23) and (26), the formula for calculating the equivalent thermal conductivity of first-order subunit A is as follows:

[0131]

[0132] According to formulas (5), (15), (18), (24) and (27), the formula for calculating the equivalent thermal conductivity of first-level subunit B is as follows:

[0133]

[0134] According to formulas (6), (16), (19), (25) and (28), the formula for calculating the equivalent thermal conductivity of the first-order subunit C is as follows:

[0135]

[0136] S7. Based on the principle of minimum thermal resistance and the principle of equal equivalent thermal conductivity, establish a parallel model of the first-level sub-units in the overall unit, and calculate the equivalent thermal conductivity λ of the overall thermally conductive unit. m ;

[0137] The cubic heat-conducting cell is composed of parallel connections of first-level sub-units A, B, and C. Therefore, the thermal resistance of the cubic heat-conducting cell can be expressed as:

[0138]

[0139] According to formulas (13)-(16) and (29)-(32), the equivalent thermal conductivity of the thermally conductive cell of the cube can be obtained.

[0140] The calculation results of the series model, parallel model, series-parallel model, finite element model, and parallel-series-parallel model are compared with the experimental test results, such as... Figure 6 As shown, the calculation results of the parallel-series-parallel model are closer to the experimental results, with an error of less than 3%. It accurately solves the equivalent thermal conductivity and greatly improves the calculation accuracy compared with the traditional calculation model, providing an effective basis for the optimization and improvement of graphene composite insulation boards.

Claims

1. A parallel-series-parallel calculation method for the equivalent thermal conductivity of a graphene composite insulation board, characterized in that, Includes the following steps: S1. Based on the minimum thermal resistance rule and the equal equivalent thermal conductivity rule, a parallel-series-parallel calculation model for graphene composite insulation board is established. The parallel-series-parallel calculation model includes several cubic overall units. Each overall unit includes three first-level sub-units connected in parallel along the vertical direction. Each first-level sub-unit includes the matrix material of the left first-level sub-unit, the diode sub-unit, and the matrix material of the right first-level sub-unit connected in series. Each second-level sub-unit includes the matrix material of the front diode sub-unit, the impurity material of the diode sub-unit, and the matrix material of the rear diode sub-unit connected in parallel. S2. Determine the mass proportions of the graphene composite insulation board matrix material (graphite polystyrene particles) and the three impurity materials (cement, vitrified microspheres, and silica fume) as ω1, ω2, ω3, and ω4, respectively. Calculate the volume proportions of the matrix material and the three impurity materials as Ф1, Ф2, Ф3, and Ф4. Further determine the side lengths a, b, and c of the dipole unit inclusion material in the calculation model. S3. Based on Fourier's law of thermal conduction, calculate the thermal resistances RDm, REm, and RFm of the second-level sub-unit, the thermal resistances RADD, RBEE, and RCFF of the matrix material of the second-level sub-unit, and the thermal resistances RD, RE, and RF of the inclusion material of the second-level sub-unit. S4. Based on Fourier's law of thermal conduction, calculate the overall unit thermal resistance Rm, the thermal resistances RA, RB, and RC of the first-level sub-unit, and the thermal resistances RAD, RBE, and RCF of the matrix material of the first-level sub-unit. S5. Based on the minimum thermal resistance rule and the equal equivalent thermal conductivity rule, establish a parallel model of the matrix material and the inclusion material of the second-level sub-unit, and calculate the equivalent thermal conductivity λDm, λEm, and λFm of the second-level sub-unit. S6. Based on the minimum thermal resistance rule and the equal equivalent thermal conductivity rule, establish a series model of the first-level sub-unit matrix material and the second-level sub-unit, and calculate the equivalent thermal conductivity λA, λB, and λC of the first-level sub-unit. S7. Based on the principle of minimum thermal resistance and the principle of equal equivalent thermal conductivity, establish a parallel model of the first-level sub-units in the overall unit, and calculate the equivalent thermal conductivity λ of the overall thermally conductive unit. m .

2. The parallel-series-parallel calculation method for the equivalent thermal conductivity of a graphene composite insulation board as described in claim 1, characterized in that: In step S2, the formula for calculating the volume percentage of the matrix material and the three impurity materials is as follows: In the formula, ρ i Let be the density of the matrix material and the three impurity materials, and i = 1, 2, 3, 4 represent graphite polystyrene particles, cement, vitrified microspheres, and silica fume, respectively. The formulas for calculating the side lengths a, b, and c of the dipole unit inclusion material in the computational model are as follows:

3. The parallel-series-parallel calculation method for the equivalent thermal conductivity of a graphene composite insulation board as described in claim 1, characterized in that: In step S3, the formula for calculating the thermal resistance of the insulation material is: In the formula, Q i The power of the heat source transferred between the inner and outer sides of the i-th material in the graphite composite insulation board, expressed in W; △T i R represents the temperature difference between the inner and outer surfaces of the i-th material, expressed in K. i δ represents the thermal resistance of the i-th material, expressed in K / W. i The thickness of the i-th material in the heat transfer direction is expressed in meters (m). λ i Let be the thermal conductivity of the i-th material, expressed in W·(m·K). -1 ; A i The heat transfer cross-sectional area of ​​the i-th material is expressed in m². 2 .

4. The parallel-series-parallel calculation method for the equivalent thermal conductivity of a graphene composite insulation board as described in claim 3, characterized in that: In step S3, the formula for calculating the thermal resistance of the secondary sub-unit is: In the formula, λ Dm The equivalent thermal conductivity of the second-order subunit; The formula for calculating the thermal resistance of the matrix material of the second-level subunit is as follows: In the formula, λ1 is the thermal conductivity of the graphene polystyrene particle matrix material; The formula for calculating the thermal resistance of the inclusion material in the second-level subunit is as follows: In the formula, λ2, λ3 and λ4 are the thermal conductivity coefficients of the inclusion materials in the second-order subunit, respectively.

5. The parallel-series-parallel calculation method for the equivalent thermal conductivity of a graphene composite insulation board as described in claim 1, characterized in that: In step S4, the formula for calculating the overall unit thermal resistance is: In the formula, λ m The equivalent thermal conductivity of the entire unit; The formula for calculating the thermal resistance of the first-level subunit is as follows: In the formula, λ A , λ B and λ C The equivalent thermal conductivity of the first-order subunit; The formula for calculating the thermal resistance of the matrix material of the first-level subunit is as follows: In the formula, λ1 is the thermal conductivity of the matrix material of the first-order subunit.

6. The parallel-series-parallel calculation method for the equivalent thermal conductivity of a graphene composite insulation board as described in claim 1, characterized in that: In step S5, the calculation formula for the parallel model of the secondary sub-unit matrix material and the secondary sub-unit inclusion material is as follows: The formula for calculating the equivalent thermal conductivity of the second-level subunit is as follows: Wherein, λ1 is the thermal conductivity of the graphene polyphenylene particle matrix material, and λ2, λ3 and λ4 are the thermal conductivity of the inclusion materials in the secondary subunits, respectively.

7. The parallel-series-parallel calculation method for the equivalent thermal conductivity of a graphene composite insulation board as described in claim 1, characterized in that: In step S6, the calculation formula for the series model of the first-level sub-unit matrix material and the second-level sub-unit is as follows: The formula for calculating the equivalent thermal conductivity of the first-level subunit is as follows: Wherein, λ1 is the thermal conductivity of the graphene polyphenylene particle matrix material, and λ2, λ3 and λ4 are the thermal conductivity of the inclusion materials in the secondary subunits, respectively.

8. The parallel-series-parallel calculation method for the equivalent thermal conductivity of a graphene composite insulation board as described in claim 1, characterized in that: In step S7, the calculation formula for the parallel model of the first-level sub-units in the overall unit is:

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