A method for measuring the thermal resistance of solid-liquid interface based on nano-heat wire

Abstract

The present invention belongs to the field of microscale heat transfer, and particularly relates to a method for measuring the thermal resistance of a solid-liquid interface based on a nano-heater wire. The method includes: (1) depositing gold electrodes on a silicon substrate covered with a silicon dioxide insulating layer, etching grooves between the electrodes, and using ion beam deposition of metal to weld the metal nano-heater wire on the gold electrodes, so that it is suspended above the grooves; (2) passing a constant heating current through the heater wire for heating, and obtaining the heat flux density passing through the solid-liquid interface from the electric heating power; (3) solving the cylindrical coordinate heat conduction equation to obtain the temperature rise of the liquid at the solid-liquid interface; (4) measuring the resistance of the heating wire, and obtaining the temperature rise of the heater wire according to the resistance-temperature relationship of the heating wire; (5) obtaining the thermal resistance of the solid-liquid interface through the calculated interface heat flux, the temperature rise of the solid at the interface, and the temperature rise of the liquid at the interface. The method disclosed by the present invention can measure the thermal resistance of the solid-liquid interface between a metal and a liquid in a short time.

Description

Technical Field

[0001] The present invention belongs to the field of microscale heat transfer, and particularly relates to a method for measuring the thermal resistance of a solid-liquid interface based on a nano-heater wire. Background Art

[0002] Low-dimensional nanomaterials are increasingly widely used in scientific fields such as energy development and utilization, micro-nano electronic systems, and photothermal medicine. The heat transfer characteristics at the nano-scale interface have become an important parameter for system thermal design. In recent years, the research on the thermal resistance of the solid-liquid interface has mainly focused on simulation calculation methods. Compared with theoretical and simulation studies, due to the difficulty in preparing the nano-scale solid-liquid interface and measuring the interface thermal resistance, the experimental progress has been slow. For the measurement of heat transfer characteristics, currently only the extrapolation method of contact temperature distribution measurement, femtosecond laser, and Raman spectroscopy have experimentally studied the heat transfer characteristics of solid-solid, solid-liquid, and nano-scale solid-solid interfaces at the macroscopic scale. However, the research on the heat transfer characteristics of the nano-scale solid-liquid interface is still a difficult problem. Compared with the Raman measurement system for measuring the thermal resistance of the solid-liquid interface, the optical measurement has a large error and the measurement method is relatively complex. Therefore, developing a method for measuring the heat transfer characteristics of the solid-liquid interface is an urgent problem to be solved. Summary of the Invention

[0003] The purpose of the present invention is to provide a method for measuring the thermal resistance of a solid-liquid interface based on current heating of a nano-heater wire.

[0004] The technical solution for achieving the purpose of the present invention is as follows: A method for measuring the thermal resistance of a solid-liquid interface based on a nano-heater wire includes the following steps:

[0005] Step (1): Prepare a measurement sample: Deposit four gold electrodes on a silicon substrate, etch a groove between the two inner gold electrodes, record the depth of the groove as d, deposit a metal nano-heater wire on the four gold electrodes, suspend the middle of the metal nano-heater wire above the groove, and weld the two ends to the two gold electrodes respectively. After the sample is prepared, place it in deionized water;

[0006] Step (2): Pass a constant current through the heater wire for heating, and obtain the heat flux density passing through the solid-liquid interface from the electric heating power;

[0007] Step (3): Solve the cylindrical coordinate heat conduction equation to obtain the temperature rise of the liquid at the solid-liquid interface;

[0008] Step (4): Assume the thermal resistance of the solid-liquid interface, perform a finite element analysis on the temperature of the solid-liquid interface, and judge the rationality of the experimental parameters;

[0009] Step (5): Measure the resistance of the heating wire, obtain the relationship between the temperature rise of the heater wire according to the resistance-temperature relationship of the heating wire, and obtain the temperature rise of the solid at the interface; Through the heat flux density of the interface that has been calculated, the temperature rise of the solid at the interface, and the temperature rise of the liquid at the interface, obtain the thermal resistance of the solid-liquid interface.

[0010] Further, in step (1), let the radius of the metal nano-heat wire be r0, the length be l, and the calculation formula for the groove etching depth is as follows:

[0011] d 2 / at>5.783

[0012] where a is the thermal diffusivity of water and t is the heating time.

[0013] Further, step (2) "Apply a constant current to the heat wire for heating, and obtain the heat flux density through the solid-liquid interface from the electro-heating power" is specifically:

[0014] 2πr0lq = I 2 R

[0015] R = ρl / (πr0 2 )

[0016] where q is the interfacial heat flux, I is the applied constant current, R is the resistance of the heat wire, ρ is the resistivity of the heat wire, r0 is the radius of the heat wire, and l is the length of the heat wire.

[0017] Further, step (3) "Solve the cylindrical coordinate heat conduction equation to obtain the temperature rise of the liquid at the solid-liquid interface" is specifically:

[0018] The heat wire and the liquid are in thermal equilibrium at the initial moment, and the equilibrium temperature is T0. Define the temperature of the liquid at a distance r from the heat wire as T(r, t), and take the excess temperature θ(r, t) = T(r, t) - T0, which represents the temperature rise of the liquid; the conduction process between the heat wire and the liquid is heat diffusion, which can be expressed by the cylindrical coordinate heat diffusion equation as:

[0019]

[0020] where θ(r, t) is the temperature rise of the liquid, a is the thermal diffusivity of water, and t is the heating time;

[0021] The expression for the temperature rise of the water at the interface is as follows:

[0022]

[0023] where C = exp(γ), γ is the Euler constant, γ = 0.5772, E1(x) is the exponential integral, and λ is the thermal conductivity of the liquid.

[0024] Further, the formula for calculating the solid-liquid interface thermal resistance in step (5) is as follows:

[0025] R 20 = R t / [1 + β(T - 20)]

[0026] where R t is the resistance of the heat wire, R20 where \(R_0\) is the resistance of the hot wire at 20°C, \(T\) is the temperature of the hot wire, and \(\beta\) is the temperature coefficient of resistance;

[0027]

[0028] Among them, \(R'\) is the thermal resistance at the solid-liquid interface, \(\Delta T'\) is the temperature difference at the solid-liquid interface, and \(q\) is the heat flux at the solid-liquid interface.

[0029] Furthermore, the metal nano hot wire is a silver nanowire or a platinum nanowire.

[0030] Furthermore, ethylene glycol is used instead of deionized water.

[0031] Compared with the prior art, the significant advantages of the present invention are as follows:

[0032] The present invention constructs a model of an electro-heated nano hot wire, obtains the temperature change of the hot wire by measuring the resistance change of the hot wire, and combines the numerical solution of the interfacial liquid to obtain the thermal resistance at the solid-liquid interface. This method is simple to operate and applicable to nano hot wires of different materials and different liquid environments.

[0033] The method of the present invention has a wide range of applications and can obtain the interfacial thermal resistance between different materials.

[0034] The present invention analyzes the temperature distribution at the solid-liquid interface by finite element method and verifies the feasibility of this method. Description of the Drawings

[0035] Figure 1 is the flow chart for measuring the thermal resistance at the solid-liquid interface of the present invention.

[0036] Figure 2 is the schematic diagram for building the experimental sample.

[0037] Figure 3 is the etching depth - heating time curve.

[0038] Figure 4 is the current - interfacial heat flux curve.

[0039] Figure 5 is the interfacial water temperature rise - heating time curve.

[0040] Figure 6 is the temperature distribution curves in the solid, at the solid-liquid interface, and in the liquid.

[0041] Description of the Reference Numerals:

[0042] 1 - silicon substrate, 2 - gold electrode, 3 - groove, 4 - nano hot wire. Detailed Embodiments

[0043] The present invention will be further described in detail below with reference to the drawings.

[0044] The specific steps to implement the technical solution of the present invention are as follows: Step 1, prepare a measurement sample, determine the radius r0 and length l of the hot wire to be used, as well as the hot wire material, and etch the groove depth d on the substrate. As Figure 2 shown, weld the nanowire hot wire on the gold electrode so that it is suspended above the groove. The welding point is the contact point between the hot wire and the gold electrode. The outermost electrodes 1 and 4 are connected to an external current source, and the inner electrodes 2 and 3 are connected to a voltmeter. The present invention uses silver nanowires as the hot wire, and deposits gold electrodes on the substrate for heating. To maintain the infinite heat transfer condition in the liquid, the calculation formula for the groove etching depth is as follows:

[0045] d 2 / at>5.783 (1)

[0046] where a is the thermal diffusivity of the liquid and t is the heating time.

[0047] Step 2, calculate the interfacial heat flux. The calculation process is as follows:

[0048] 2πr0lq = I 2 R (2)

[0049] R = ρl / (πr0 2 ) (3)

[0050] where q is the interfacial heat flux density, I is the applied constant current, R is the hot wire resistance, ρ is the hot wire resistivity, r0 is the hot wire radius, and l is the hot wire length.

[0051] Step 3, calculate the interfacial liquid temperature rise. The calculation process is as follows:

[0052] The nanowire and the liquid are in thermal equilibrium at the initial moment, and the initial temperature is T0. Define the liquid temperature at a distance r from the hot wire as T(r,t), and take the excess temperature θ(r,t) = T(r,t) - T0, which represents the liquid temperature rise. The conduction process between the nanowire and the liquid is heat diffusion, which can be expressed by the cylindrical coordinate heat diffusion equation as:

[0053]

[0054] where θ(r,t) is the liquid temperature rise, a is the liquid thermal diffusivity, and t is the heating time.

[0055] Before applying the heat flux, the liquid temperature and the nanowire temperature are in equilibrium. The initial value condition is:

[0056] t = 0, θ(r,t) = 0 (5)

[0057] Boundary condition when r = r0:

[0058]

[0059] where q is the heat flux of the nanowire per unit area and λ is the thermal conductivity of the liquid.

[0060] When the boundary r→∞, the temperature rise is 0:

[0061] r→∞, θ(r,t) = 0 (7)

[0062] Solve this equation:

[0063]

[0064] where E1(x) is the exponential integral, and the expression is as follows:

[0065]

[0066] where γ is the Euler constant, γ = 0.5772

[0067] The radius of the hot wire is small enough, and r 2 / 4at is small enough, then the distribution of the interfacial water temperature is expressed as follows:

[0068]

[0069] where C = exp(γ).

[0070] Step 4: Take the typical solid-liquid interface thermal resistance, use the analytical formula of the temperature rise distribution to find the temperature distribution, and draw the curve of the solid-liquid interface temperature changing with the heating time. As Figure 6 shown, the temperature distribution inside the hot wire is uniform, and there is a temperature jump between the solid-liquid interfaces, indicating that this measurement theory is feasible.

[0071] Step 5: Calculate the interface thermal resistance, and the calculation process is as follows:

[0072] Record the voltage of the voltmeter, denoted as U, and it is known that the current is constant, denoted as I, then the resistance R of the hot wire t The calculation formula is as follows:

[0073] R t = U / I (11)

[0074] The relationship between the resistance of the hot wire and the temperature change is as follows:

[0075] R 20 = R t / [1 + β(T - 20)] (12)

[0076] where R 20 is the resistance of the hot wire at 20°C, T is the temperature of the hot wire, and β is the temperature coefficient of resistance

[0077] The respective temperatures of the solid-liquid interface have been obtained. Denote the solid-liquid temperature difference as △T', and the interfacial heat flux density as q. The calculation formula for the solid-liquid interface thermal resistance R′ is as follows:

[0078]

Claims

1. A method for measuring the thermal resistance of a solid-liquid interface based on a metal nano-heater wire, characterized in that It includes the following steps: Step (1): Prepare a measurement sample: Deposit four gold electrodes on a silicon substrate, etch a groove between the two inner gold electrodes, record the depth of the groove as d, deposit metal nanowires on the four gold electrodes, suspend the middle part of the metal nanowires above the groove, and weld the two ends to the two gold electrodes respectively. After the sample is prepared, put it into deionized water; Step (2): Pass a constant current through the metal nanowires to heat them, and obtain the heat flux density through the solid-liquid interface from the electrothermal power; Step (3): Solve the cylindrical coordinate heat conduction equation to obtain the temperature rise of the liquid at the solid-liquid interface; Step (4): Assume the solid-liquid interface thermal resistance, perform a finite element analysis on the solid-liquid interface temperature, and judge the rationality of the experimental parameters; Step (5): Measure the resistance of the metal nanowires, obtain the temperature rise relationship of the metal nanowires according to the resistance-temperature relationship of the metal nanowires, and obtain the temperature rise of the solid at the solid-liquid interface; Obtain the solid-liquid interface thermal resistance through the calculated heat flux density at the solid-liquid interface, the temperature rise of the solid at the solid-liquid interface, and the temperature rise of the liquid at the solid-liquid interface; In step (2), when passing a constant current through the metal nanowires to heat them, the specific method for obtaining the heat flux density through the solid-liquid interface from the electrothermal power is as follows: 2πr0lq = I 2 R R = ρl / (πr0 2 ) Where q is the heat flux at the solid-liquid interface, I is the applied constant current, R is the resistance of the metal nanowires, ρ is the resistivity of the metal nanowires, r0 is the radius of the metal nanowires, and l is the length of the metal nanowires; In step (3), when solving the cylindrical coordinate heat conduction equation to obtain the temperature rise of the liquid at the solid-liquid interface, the specific method is as follows: The metal nanowires and the liquid are in thermal equilibrium at the initial moment, and the equilibrium temperature is T0. Define the liquid temperature at a distance r from the metal nanowires as T(r,t), and take the excess temperature θ(r,t)=T(r,t)-T0 to represent the temperature rise of the liquid. The conduction process between the metal nanowires and the liquid is heat diffusion, which can be represented by the cylindrical coordinate heat diffusion equation as follows: Where θ(r,t) is the temperature rise of the liquid, a is the thermal diffusivity of water, and t is the heating time; The expression for the temperature rise of the interface water temperature is as follows: Where C = exp(γ), γ is the Euler constant, γ = 0.5772, E1(x) is the exponential integral, and λ is the thermal conductivity of the liquid; The formula for calculating the solid-liquid interface thermal resistance in step (5) is as follows: R 20 = R t / [1 + β(T - 20)] where R t is the resistance of the metal nano - hot - wire, R 20 is the resistance of the metal nano - hot - wire at 20 °C, T is the temperature of the metal nano - hot - wire, and β is the temperature - resistance coefficient; Where R′ is the solid-liquid interface thermal resistance, △T' is the temperature difference at the solid-liquid interface, and q is the heat flux at the solid-liquid interface.

2. The measurement method according to claim 1, wherein In step (1), record the radius r0 and length l of the metal nanowires, and the calculation formula for the groove etching depth is as follows: d 2 / at>5.783 Where a is the thermal diffusivity of water and t is the heating time.

3. The method according to claim 1, wherein The metal nanowires are silver nanowires or platinum nanowires.

4. The method according to claim 1, wherein Use ethylene glycol instead of deionized water.

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