Measurement Method for Convective Heat Transfer Coefficient between Elastic Card Solid Refrigerant and Heat Transfer Fluid
Through the lumped parameter method and assumption conditions, the volume average temperature change of the solid state refrigerant of the solid state refrigerant of the solid state refrigerant and the heat transfer fluid was measured, which solved the problem of large measurement errors in the prior art and achieved high reliability of the heat transfer coefficient characterization.
Patent Information
- Application Number
- CN202211667896.X
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2022-12-23
- Publication Date
- 2025-07-29
- Estimated Expiration
- 2042-12-23
AI Technical Summary
The prior art cannot accurately characterize the convection heat transfer coefficient between the solid state refrigerant of the cylindrical solid state refrigerant and the heat transfer fluid. Especially in complex structures and operating conditions, it leads to large measurement errors and cannot meet the needs of the green cylindrical refrigeration device.
Using the lumped parameter method and assumption conditions, the heat transfer model is established by measuring the volume average temperature change history of the solid state refrigerant of the solid state refrigerant of the solid state refrigerant of the solid state refrigerant and the heat transfer fluid.
It significantly improves the reliability of the characterization of convection heat transfer coefficients, fills the gap in the characterization of convection heat transfer coefficients in green e-crack refrigeration technology, and improves the accuracy and reliability of measurements.
Smart Images
Figure CN116242877B_ABST
Abstract
Description
Technical Field
[0001] The present invention relates to the technical field of refrigeration, and more specifically, to a method for measuring the convective heat transfer coefficient between a snap - fit solid refrigerant and a heat transfer fluid. Background Art
[0002] With the intensification of global climate change, reducing greenhouse gas emissions has attracted more and more attention. The new snap - fit refrigeration technology uses a snap - fit solid refrigerant mainly based on nickel - titanium shape memory alloy, and there is no greenhouse gas emission during operation, showing great application prospects in domestic refrigeration and industrial heat dissipation.
[0003] One of the key problems in the research and development of snap - fit refrigerators is the accurate characterization of the convective heat transfer coefficient between the snap - fit solid refrigerant and the heat transfer fluid. The reasons are as follows: (1) During the operation of the snap - fit refrigerator, there are temperature gradients in the length and thickness directions of the snap - fit solid refrigerant and they change with time, so the classical heat transfer correlation formulas for flow in pipes and channels are no longer applicable; (2) The internal flow channel size of the snap - fit solid refrigerant with an advanced cross - section design is extremely small, resulting in difficulties in measuring the temperature of the heat transfer fluid inside the flow channel and great difficulty in accurate measurement; (3) The temperature of the heat transfer fluid inside the flow channel is non - linearly distributed along the flow direction, and using the average value of the inlet and outlet heat transfer fluid temperatures to represent the average temperature of the heat transfer fluid will introduce a large systematic error. Scholars at home and abroad have been seeking methods to accurately characterize the convective heat transfer coefficient between the snap - fit solid refrigerant and the heat transfer fluid.
[0004] Currently, the characterization devices and methods for the convective heat transfer coefficient between the snap - fit solid refrigerant and the heat transfer fluid are mostly used in a narrow range and cannot fully meet the needs of characterizing the convective heat transfer coefficient in snap - fit refrigeration devices with diverse structures and working conditions. There is no systematic solution for the online characterization of the convective heat transfer coefficient between the snap - fit solid refrigerant and the heat transfer fluid during the operation of the snap - fit refrigerator. Summary of the Invention
[0005] In order to overcome the deficiencies of the prior art, the present invention provides a method for measuring the convective heat transfer coefficient between a snap - fit solid refrigerant and a heat transfer fluid.
[0006] The technical solution adopted by the present invention to solve its technical problems is: a method for measuring the convective heat transfer coefficient between a snap - fit solid refrigerant and a heat transfer fluid, which is improved in that the method includes the following steps:
[0007] S10. For an object with volume V and outer surface S, according to the energy balance at any position x, a differential - form heat transfer control equation can be obtained;
[0008] S20. Apply the lumped parameter method to the snap - fit solid refrigerant and the heat transfer fluid to obtain an expression for the change of the volume - average temperature with time;
[0009] S30. By assuming conditions, make both the hysteresis heat and the release rate positive during the loading / unloading process; calculate the expression for the total heat of the outer surface S.
[0010] S40. During the loading / unloading process, measure the variation history of the volume-average temperature of the cartridge solid refrigerant with time to inversely deduce the average equivalent convective heat transfer coefficient between the cartridge solid refrigerant and the heat transfer fluid.
[0011] Further, in step S10, the differential form of the control equations for the cartridge solid refrigerant and the heat transfer fluid are respectively:
[0012]
[0013]
[0014] where λ is the heat capacity per unit volume, λ = ρc, ρ and c respectively represent density and specific heat, k is the thermal conductivity, g(x,t) is the heat source term. is the symbol of partial derivative. is the symbol of gradient operator, and the subscripts s and f respectively represent the cartridge solid refrigerant and the heat transfer fluid.
[0015] Further, in step S20, the volume-average temperature within the volume V defines a time function representing the spatially averaged temperature of the two. Transform equations (1) and (2) into:
[0016]
[0017]
[0018] where
[0019]
[0020]
[0021] A cartridge solid refrigerant material with an effective length L and a thickness t1, and a thickness t2 and a flow velocity u0, undergoes a displacement-controlled Brayton cycle deformation loading with a frequency f. The shape memory alloy is loaded / unloaded, and then the highest / lowest strain holding time t0 = 1 / 2t p , period t p = 1 / f.
[0022] Further, in step S30, the said assumed conditions include:
[0023] Condition 1: The heat release / absorption caused by phase change and the release of hysteresis heat are two internal heat sources of the snap-fit solid refrigerant material, and their intensities are proportional to the strain rate and the square of the strain rate applied to the snap-fit solid refrigerant material, respectively.
[0024] Step S30 includes the following steps:
[0025] S301. The volume-averaged heat source g(t) = 1 / V ∫ V g(x,t)dv in formulas (5) and (6) includes latent heat and hysteresis heat, where the total sum of latent heat per unit volume is l0, and the total amount of hysteresis heat per unit volume is D; the latent heat comes from the phase change of the refrigerant, so the release rate of latent heat is assumed to be proportional to the phase change rate or the strain rate, which is positive during the loading process and negative during the unloading process.
[0026] S302. According to Assumption 1, the release of latent heat can be written as (l0ω / 2)sin(ωt), so the integrals of the latent heat release rate with respect to time during the loading and unloading processes are l0 and -l0, respectively; simultaneously with the phase change, hysteresis heat is released by internal friction inside the refrigerant, and its magnitude increases with the increase of the strain rate and is positive during both the loading and unloading processes; the release rate of hysteresis heat is assumed to be proportional to the square of the strain rate, i.e., (Dω / π)sin 2 (ωt);
[0027] S303. It is necessary to ensure that the total release amount of hysteresis heat in a loading-unloading cycle is D, that is
[0028]
[0029] Set the time for loading, heat dissipation, unloading, and heat absorption to each account for one-quarter of the period t p The following expression represents the process of 0 < t < t p / 4:
[0030]
[0031] S304. Apply the divergence theorem to convert the volume integrals in formulas (3) and (4) into surface integrals:
[0032]
[0033] The surface integral includes the heat convection through the contact surface between the snap-fit solid refrigerant and the heat transfer fluid, and the heat flux is where h is the convective heat transfer coefficient between the inner surface of the refrigerant and the fluid, which depends on the temperature difference between the inner surface of the refrigerant and the fluid, the fluid flow rate, and the inherent properties of the fluid, and the heat conduction through the two cross-sections at the ends of the snap-fit solid refrigerant, and the heat flux is Qcond(=-2kA end|dT / dx| = -2α s k s dt1(T s (T - T0) / L), where k is the thermal conductivity of the refrigerant and α is a constant.
[0034] Furthermore, step S30 further includes the steps:
[0035] S305. The total heat flux through the outer surface S can be expressed as:
[0036]
[0037]
[0038] In equations (9) and (10), is the effective convective heat transfer coefficient between the lumped inner surface of the refrigerant and the fluid, and it is assumed that i.e., it already includes the contribution of heat conduction at the two cross-sections at the ends of the refrigerant. Therefore, as L0 increases gradually decreases, and when there is
[0039] S306. According to equations (9) and (10), during the heat release and heat absorption processes after loading / unloading, equations (1) and (2) are expressed as:
[0040]
[0041]
[0042] At each loading frequency and D both depend on the temperature and the temperature change history over time. Equations (11) and (12) are a system of nonlinear ordinary differential equations;
[0043] S307. Take and D as the steady-state values for each loading process; when the loading speed is fast enough, according to the initial conditions T s (t = 0) = T s,0 and T f (t = 0) = T f,0 , there is:
[0044] T s (t) = T m +(T s,0 -T m )exp(-t / τ0) (13);
[0045] T f (t) = T m+(T f,0 -T m )exp(-t / τ0) (14);
[0046]
[0047]
[0048] T s (t) = T m (t) + [T s,0 -T m (t)]exp[-t / τ0(t)] (17);
[0049] T f (t) = T m (t) + [T f,0 -T m (t)]exp[-t / τ0(t)] (18);
[0050]
[0051]
[0052] Based on formulas (19) and (20), during the loading / unloading process, it is only necessary to measure the change history of the volume-average temperature of the solid-state refrigerant in the cartridge over time, and then the average equivalent convective heat transfer coefficient between the solid-state refrigerant in the cartridge and the heat transfer fluid can be deduced backwards. And based on A comprehensive analysis model of the working process of the refrigerant in the cartridge refrigerator is established.
[0053] Furthermore, in step S30, the assumed conditions further include:
[0054] Condition 2: The heat flowing through the pressure heads at both ends of the solid-state refrigerant material in the cartridge is considered as the heat conduction through the two end cross-sections of the phase-change refrigerant undergoing cyclic phase change over the effective length L0.
[0055] Condition 3: The change in the volume-average temperature of the fluid caused by the transport of the heat transfer fluid is expressed using the difference between the constant fluid temperature at the inlet of the flow channel and the fluid temperature at the outlet of the flow channel related to the volume-average temperature.
[0056] The beneficial effects of the present invention are as follows: By establishing a heat transfer model coupling the solid-state refrigerant and the heat transfer fluid, the present invention can realize the convective heat transfer coefficient between the solid-state refrigerant in the cartridge and the heat transfer fluid only by extracting the temperature of the solid-state refrigerant in the cartridge during the cyclic loading in the operation of the cartridge refrigerator, significantly improving the reliability of the characterization of the convective heat transfer coefficient. BRIEF DESCRIPTION OF THE DRAWINGS
[0057] Figure 1This is a schematic structural diagram of the measuring device for the convective heat transfer coefficient between the bullet clip solid refrigerant and the heat transfer fluid in the present invention. Detailed implementation manners
[0058] The present invention will be further described below in conjunction with the accompanying drawings and embodiments.
[0059] Hereinafter, the concept, specific structure and technical effects of the present invention will be clearly and completely described in conjunction with the embodiments and the accompanying drawings, so as to fully understand the purpose, features and effects of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. Based on the embodiments of the present invention, other embodiments obtained by those skilled in the art without creative efforts shall fall within the scope of protection of the present invention. In addition, all the connection / linkage relationships involved in the patent do not simply refer to the direct connection of components, but refer to the more optimal connection structure that can be formed by adding or reducing connection accessories according to the specific implementation situation. Each technical feature in the present invention can be interactively combined without conflicting with each other.
[0060] Referring to Figure 1 As shown, the present invention discloses a measuring device for the convective heat transfer coefficient between the bullet clip solid refrigerant and the heat transfer fluid. Specifically, the measuring device includes a bullet clip solid refrigerant 1, a heat insulation layer 2, an anti-buckling sleeve 3, an upper pressing head 4, a lower pressing head 5, a linear bearing 6, a fixing member 7, an upper plate 8, a lower plate 9, a threaded column 10, a locking nut 11, an anti-buckling member 12 and a force sensor 13. The heat insulation layer 2 is installed outside the bullet clip solid refrigerant 1, the anti-buckling sleeve 3 is installed outside the heat insulation layer 2, both ends of the bullet clip solid refrigerant 1 are connected to the upper pressing head 4 and the lower pressing head 5, the upper pressing head 4 is matched with the linear bearing 6 to ensure coaxiality with the bullet clip solid refrigerant 1, and the lower pressing head 5 is installed in the fixing member 7 to ensure coaxiality with the bullet clip solid refrigerant 1. The linear bearing 6 is installed on the upper plate 8, the fixing member 7 is installed on the lower plate 9, the upper plate 8 and the lower plate 9 are locked and fixed by a set of four threaded columns 10 and locking nuts 11, an anti-buckling member 12 is installed between the linear bearing 6 and the anti-buckling sleeve 3, and a force sensor 13 is connected between the lower pressing head 5 and the lower plate 9.
[0061] Based on the above-mentioned measuring device for the convective heat transfer coefficient between the bullet clip solid refrigerant and the heat transfer fluid, the present invention also provides a measuring method for the convective heat transfer coefficient between the bullet clip solid refrigerant and the heat transfer fluid, and the method includes the following steps:
[0062] S10. For an object with a volume V and an outer surface S, according to the energy balance at any position x, a differential form of the heat transfer control equation can be obtained;
[0063] In step S10, the differential form of the control equations of the bullet clip solid refrigerant and the heat transfer fluid are respectively:
[0064]
[0065]
[0066] Among them, λ is the heat capacity per unit volume, λ = ρc, where ρ and c represent density and specific heat respectively, k is the thermal conductivity, and g(x,t) is the heat source term. is the symbol of partial derivative, ▽ is the symbol of gradient operator, and the subscripts s and f represent the elastocaloric solid refrigerant and the heat transfer fluid respectively.
[0067] S20. Apply the lumped parameter method to the elastocaloric solid refrigerant and the heat transfer fluid to obtain an expression for the variation of the volume-averaged temperature with time.
[0068] In the step S20, the volume-averaged temperature within the volume V defines a time function, representing the spatially averaged temperature of the two. Transform equations (1) and (2) into:
[0069]
[0070]
[0071] Among them,
[0072]
[0073]
[0074] An elastocaloric solid refrigerant material with an effective length L and a thickness t1 is subjected to displacement control and a Brayton cycle deformation load with a frequency f on an elastocaloric solid refrigerant material with a thickness t2 and a flow velocity u0. The shape memory alloy is loaded / unloaded, and then the highest / lowest strain holding time t0 = 1 / 2t p , cycle t p = 1 / f.
[0075] S30. By assuming conditions, make both the hysteresis heat and the release rate positive during the loading / unloading process; calculate the expression for the total heat of the outer surface S.
[0076] In this embodiment, in the step S30, for the sake of simplifying the model, the assumed conditions include:
[0077] Condition 1: The heat release / absorption caused by phase change and the release of hysteresis heat are two internal heat sources of the elastocaloric solid refrigerant material, and their intensities are proportional to the strain rate and the square of the strain rate applied to the elastocaloric solid refrigerant material respectively.
[0078] Condition 2: The heat flowing through the two end punches of the elastocaloric solid refrigerant material is considered as the heat conduction through the two end cross-sections of the refrigerant undergoing cyclic phase change with an effective length L0.
[0079] Condition 3. The change in the volume-averaged temperature of the heat transfer fluid due to fluid transport is expressed using the difference between the constant fluid temperature at the inlet of the flow channel and the fluid temperature at the outlet of the flow channel related to the volume-averaged temperature.
[0080] Step S30 includes the following steps:
[0081] S301. The volume-averaged heat source g(t) = 1 / V in equations (5) and (6) ∫ V g(x,t)dv includes latent heat and hysteresis heat, where the total sum of latent heat per unit volume is l0 and the total amount of hysteresis heat per unit volume is D; the latent heat comes from the phase change of the refrigerant, so the release rate of latent heat is assumed to be proportional to the phase change rate or strain rate, which is positive during the loading process and negative during the unloading process;
[0082] S302. According to Assumption 1, the release of latent heat can be written as (l0ω / 2)sin(ωt), so the integrals of the latent heat release rate with respect to time during the loading and unloading processes are l0 and -l0 respectively; simultaneously with the phase change, hysteresis heat is released due to internal friction within the refrigerant, and its magnitude increases with the increase in the strain rate and is positive during both the loading and unloading processes; the release rate of hysteresis heat is assumed to be proportional to the square of the strain rate, i.e., (Dω / π)sin 2 (ωt);
[0083] S303. It is necessary to ensure that the total release amount of hysteresis heat in one loading-unloading cycle is D, that is
[0084]
[0085] Set the time for loading, heat dissipation, unloading, and heat absorption to each account for one-quarter of the period t p The following expression represents the process of 0 < t < t p / 4:
[0086]
[0087] S304. Apply the divergence theorem to convert the volume integrals in equations (3) and (4) into surface integrals:
[0088]
[0089] The surface integral includes the heat convection through the contact surface between the elastic card solid refrigerant and the heat transfer fluid, and the heat flux is where h is the convective heat transfer coefficient between the inner surface of the refrigerant and the fluid, which depends on the temperature difference between the inner surface of the refrigerant and the fluid, the fluid flow rate, and the inherent properties of the fluid, and the heat conduction through the two cross-sections at the ends of the elastic card solid refrigerant, and the heat flux is Qcond (= -2kAend |dT / dx| = -2α s k s dt1(T s - T0) / L), where k is the thermal conductivity of the refrigerant and α is a constant.
[0090] S305, The total heat flux through the outer surface S can be expressed as:
[0091]
[0092]
[0093]
[0094] In equations (9) and (10), is the effective convective heat transfer coefficient between the inner surface of the lumped refrigerant and the fluid, and it is assumed that i.e., it already includes the contribution of heat conduction at the two cross-sections at the ends of the refrigerant. Therefore, as L0 increases gradually decreases. When there is
[0095] S306, According to equations (9) and (10), during the heat release and heat absorption processes after loading / unloading, equations (1) and (2) are expressed as:
[0096]
[0097]
[0098] At each loading frequency and D both depend on the temperature and the history of temperature change with time. Equations (11) and (12) are a system of non-linear ordinary differential equations;
[0099] S307, Take and D as the steady-state values for each loading process; when the loading speed is fast enough, according to the initial conditions T s (t = 0) = T s,0 and T f (t = 0) = T f,0 , there is:
[0100] T s (t) = T m +(T s,0 - T m )exp(-t / τ0) (13);
[0101] T f (t) = Tm +(T f,0 -T m )exp(-t / τ0) (14);
[0102]
[0103]
[0104] T s (t) = T m (t) + [T s,0 -T m (t)]exp[-t / τ0(t)] (17);
[0105] T f (t) = T m (t) + [T f,0 -T m (t)]exp[-t / τ0(t)] (18);
[0106]
[0107]
[0108] S40. During the loading / unloading process, measure the variation history of the volume average temperature of the elastic card solid refrigerant with time to inversely deduce the average equivalent convective heat transfer coefficient between the elastic card solid refrigerant and the heat transfer fluid
[0109] Based on formula (19) and formula (20), during the loading / unloading process, only by measuring the variation history of the volume average temperature of the elastic card solid refrigerant with time, the average equivalent convective heat transfer coefficient between the elastic card solid refrigerant and the heat transfer fluid can be inversely deduced And based on Establish a comprehensive analysis model for the working process of the refrigerant in the elastic card refrigerator
[0110] Compared with the prior art, by establishing a heat transfer model coupling the solid refrigerant and the heat transfer fluid, the present invention can realize the convective heat transfer coefficient between the elastic card solid refrigerant and the heat transfer fluid only by extracting the temperature of the elastic card solid refrigerant under cyclic loading during the operation of the elastic card refrigerator, significantly improving the reliability of the characterization of the convective heat transfer coefficient. It fills the blank of the characterization technology of the convective heat transfer coefficient between the elastic card solid refrigerant and the heat transfer fluid in the green elastic card refrigeration technology
[0111] The above is a specific description of the preferred embodiment of the present invention, but the present invention is not limited to the described embodiment. Those skilled in the art can make various equivalent deformations or substitutions without departing from the spirit of the present invention, and these equivalent deformations or substitutions are all included in the scope defined by the claims of this application
Claims
1. A method for measuring the convective heat transfer coefficient between a snap-in solid refrigerant and a heat transfer fluid, characterized in that, The method includes the following steps: S10. For an object with a volume V and an outer surface S, according to the energy balance at any position x, a differential form of the heat transfer control equation can be obtained. S20. Apply the lumped parameter method to the elastic card solid-state refrigerant and the heat transfer fluid to obtain an expression for the variation of the volume-average temperature with time. S30. Through assumed conditions, make both the hysteresis heat and the release rate positive during the loading / unloading process. Calculate the expression for the total heat of the outer surface S. In step S30, the assumed conditions include: Condition 1: The heat release / absorption caused by phase change and the release of hysteresis heat are two internal heat sources of the elastic card solid-state refrigerant material, and their intensities are respectively proportional to the strain rate and the square of the strain rate applied to the elastic card solid-state refrigerant material. Condition 2: The heat flowing through the tips at both ends of the elastic card solid-state refrigerant material is considered as the heat conduction through the two end cross-sections of the phase change refrigerant undergoing cyclic phase change with an effective length L0. Condition 3: The change in the fluid volume-average temperature caused by the transport of the heat transfer fluid is expressed using the difference between the constant fluid temperature at the inlet of the flow channel and the fluid temperature at the outlet of the flow channel related to the volume-average temperature. S40. During the loading / unloading process, measure the variation history of the volume average temperature of the spring clip solid refrigerant over time to back-calculate the average equivalent convective heat transfer coefficient between the spring clip solid refrigerant and the heat transfer fluid.
2. The measurement method of the convective heat transfer coefficient between the elastic card solid refrigerant and the heat transfer fluid according to claim 1, characterized in that In step S10, the differential form of the control equations for the elastic card solid-state refrigerant and the heat transfer fluid are respectively: where, λ is the heat capacity per unit volume, λ = ρc, ρ and c represent density and specific heat respectively, k is the thermal conductivity, g(x,t) is the heat source term, is the symbol of partial derivative, is the symbol of gradient operator, and the subscripts s and f represent the elastic solid refrigerant and the heat transfer fluid respectively.
3. The measurement method of the convective heat transfer coefficient between the spring clip solid refrigerant and the heat transfer fluid according to claim 2, characterized in that, In step S20, the volume-average temperature within the volume V defines a time function, representing the spatially averaged temperature of the two. Convert equations (1) and (2) to: Where, A spring-loaded solid refrigerant material with an effective length L, thickness t1 and thickness t2, and a flow rate of u0 is subjected to displacement control and Brayton cycle deformation loading with a frequency of f. The shape memory alloy is loaded / unloaded, and then the maximum / minimum strain is maintained for a time t0 = 1 / 2t p , period t p =1 / f.
4. The method for measuring the convective heat transfer coefficient between the elastic card solid refrigerant and the heat transfer fluid according to claim 3, wherein Step S30 includes the following steps: S301. In formulas (5) and (6), the volume-averaged heat source \(g(t)=\frac{1}{V}\int\) V \(g(x,t)dv\) includes latent heat and hysteretic heat, where the total sum of latent heat per unit volume is \(l_0\), and the total amount of hysteretic heat per unit volume is \(D\); the latent heat comes from the phase change of the refrigerant, so the release rate of the latent heat is assumed to be proportional to the phase change rate or strain rate, which is positive during the loading process and negative during the unloading process; S302. According to Assumption 1, the release of latent heat can be written as (l0ω / 2)sin(ωt). Thus, the integrals of the latent heat release rate with respect to time during the loading and unloading processes are l0 and -l0, respectively. Simultaneously with the phase change, internal friction in the refrigerant releases hysteresis heat, the magnitude of which increases with the increase in the strain rate and is positive during both the loading and unloading processes. Assume that the hysteresis heat release rate is proportional to the square of the strain rate, i.e., (Dω / π)sin 2 (ωt); S303. It is necessary to ensure that the total release amount of hysteresis heat in a loading / unloading cycle is D, that is Set the time for loading, heat dissipation, unloading, and heat absorption to each account for one-quarter of the cycle t p The following expression represents the process of 0 < t < t p / 4: S304. Apply the divergence theorem to convert the volume integrals of equations (3) and (4) into surface integrals: Surface integral includes heat convection through the contact surface between the snap-in solid refrigerant and the heat transfer fluid, and the heat flux is where h is the convective heat transfer coefficient between the inner surface of the refrigerant and the fluid, which depends on the temperature difference between the inner surface of the refrigerant and the fluid, the fluid velocity, and the inherent properties of the fluid, and the heat conduction through two cross-sections at the ends of the snap-in solid refrigerant, and the heat flux is Qcond(=-2kA end |dT / dx|=-2α s k s dt1(T s -T0) / L), where k is the thermal conductivity of the refrigerant and α is a constant.
5. The measurement method of the convective heat transfer coefficient between the elastic card solid refrigerant and the heat transfer fluid according to claim 4, characterized in that, Step S30 also includes the step: S305, Total heat flux through the outer surface S Can be expressed as: In Formula (9) and Formula (10), is the effective convective heat transfer coefficient between the lumped refrigerant inner surface and the fluid, and it is assumed that i.e., the contribution of heat conduction through the two cross-sections at the refrigerant end is already included, Therefore, as L0 increases gradually decreases. When there is S306. According to equations (9) and (10), during the heat release and absorption processes after loading / unloading, equations (1) and (2) are expressed as: At each loading frequency Both and D depend on temperature and the temperature history over time. Equations (11) and (12) are a system of non-linear ordinary differential equations; S307. Take and D as the steady-state values for each loading process; when the loading speed is fast enough, according to the initial conditions T s (t = 0) = T s,0 and T f (t = 0) = T f,0 , there is: T s \(T(t)=T\) m +(T s,0 -T m )exp(-t / τ0) (13); T f x(t) = T m + (T f,0 - T m ) exp(-t / τ0) (14); T s (t) = T m (t) + [T s,0 -T m (t)] exp[-t / τ0(t)] (17); T f \(T(t)=T\) m \((t)+[T\) f,0 \(-T\) m \((t)]\text{exp}[{-t} / {\tau_0(t)}] \ (18);\) Based on Equation (19) and Equation (20), during the loading / unloading process, only the variation history of the volume-average temperature of the elastic card solid refrigerant with time needs to be measured, and the average equivalent convective heat transfer coefficient between the elastic card solid refrigerant and the heat transfer fluid can be deduced inversely. And based on A comprehensive analysis model of the refrigerant working process in the elastic card refrigerator is established.