CN101339149A - Test device and test method for determining early concrete thermal conductivity factor and thermal diffusivity - Google Patents

Abstract

The invention discloses a device which is used for determining the thermal conductivity and thermal diffusivity of early concrete, and a test method thereof. The determining device consists of a detachable steel test mold of 150mm multiplied by 150mm multiplied by 300mm, two resistance wires which are horizontally straightened, a connector, an ammeter, a direct-current voltage-stabilizing power supply, a thermistor, a high-precision temperature display instrument and a plurality of wires. The device has the advantages of simple structure, convenient disassembly, requirements for less materials and instruments, and high measurement accuracy. The device is not only suitable for scientific research, but also is applicable to the determination of the thermal conductivity and thermal diffusivity of early concrete on the construction site. Simultaneously, the device has a wide range of application, and can be used for measuring the thermal conductivity and thermal diffusivity of discrete materials, such as cement, sand and so on, and measuring the thermal conductivity and thermal diffusivity of clean slurry of cement and cement mortar.

Description

Measure the proving installation and the method for testing of early concrete coefficient of heat conductivity, thermal diffusivity

Technical field

The present invention relates to a kind of device and method of testing of measuring early concrete coefficient of heat conductivity, thermal diffusivity simultaneously, belong to the concrete construction field.

Background technology

In the field of civil engineering, it is very important that the heat conduction of xoncrete structure is analyzed.The hydration heat that concrete is discharged in hardening process, perhaps the thermograde to a certain degree of portion's generation within it all might cause xoncrete structure generation cracking phenomena.In order to predict the cracking trend of concrete under these factor effects accurately, and can prevent the generation of concrete cracking phenomenon timely, the just necessary concrete coefficient of heat conductivity of systematic research, thermal diffusivity and specific heat, especially in concrete stage length of time morning, more these thermal parameters of the research that should go deep into are with the rule of variation in the length of time.

The method of measuring coefficient of heat conductivity, thermal diffusivity and the specific heat of material at present mainly is divided into steady method and transient state method two big classes.

Steady method is the method for using the earliest, and its popular feature is that operating personnel set up thermograde on the wall thickness of known sample, Yi Bian and control from being delivered to the heat of another side.The most frequently used hot-fluid is an one dimension, as heat flow method or hot plate method.Adopt heat flow method to measure a kind of method and device of measuring material thermal conductivity that material thermal conductivity sees also No. 93115076.0 exposure of Chinese patent of bulletin on September 20th, 2000.The method that described patent discloses and install easy to usely, it is low to measure cost.But for liquid or gaseous matter, significantly the temperature change meeting forms convection heat transfer' heat-transfer by convection, has run counter to the fundamental starting point of steady state method, and therefore, this method is not suitable for mensuration liquid, the coefficient of heat conductivity of gaseous material.Because early concrete is in semi-liquid stage, so this method is not suitable for the coefficient of heat conductivity of measuring early concrete, and one-shot measurement can not record thermal diffusivity simultaneously.

Transient state method such as heat-pole method (Hot Wire method) are used to measure the high thermal conductivity coefficient material and/or measure under hot conditions.Heat-pole method is divided into four kinds of single line method, parallel method, hot line relative method and sonde methods again.Wherein the single line method is consistent basically with the probe ratio juris, just the device difference of test.Its principle is that the temperature rise of material (thermopair) is relevant with its coefficient of heat conductivity near the straight line (being hot line), and coefficient of heat conductivity λ can express with following formula:

λ＝qln(τ ₂/τ ₁)/4π(θ ₂-θ ₁) (1)

Wherein, q is unit length hot line thermal value W/m; τ ₁, τ ₂For measuring constantly, can determine in advance; θ ₁, θ ₂Be τ ₁, τ ₂Corresponding constantly temperature rise.But single line method, hot line relative method and sonde method can only be determined the coefficient of heat conductivity of material in measurement, and can not determine thermal diffusivity simultaneously.

Proposed among " fire resistive material coefficient of heat conductivity test method " GB/T 17106-1997 to adopt parallel method to measure the coefficient of heat conductivity of fire resistive material, though this method can be measured the coefficient of heat conductivity and the thermal diffusivity of material simultaneously, the device that proposes in this standard also is not suitable for coefficient of heat conductivity and the thermal diffusivity of measuring early concrete.

The thermal conductivity proving installation of a kind of Inorganic Non-metallic Materials that the Chinese patent of announcing on June 28th, 2000 discloses for 99214843.X number also is the coefficient of heat conductivity that adopts the heat-pole method test material.

Described heat-pole method proving installation measuring accuracy height, easy and simple to handle.But this device is not suitable for the coefficient of heat conductivity of measuring the semi-liquid stage material, and can not measure thermal diffusivity simultaneously.Therefore, be not suitable for and measure early concrete coefficient of heat conductivity, thermal diffusivity simultaneously.

Heat-pole method is widely used, can be used for the liquid substance thermal Conductivity Determination, but heat-pole method is directly to hot line energising heating, for the fluent meterial that self can conduct electricity, be transformed into heat energy fully for guaranteeing the electric energy that passes through, must do insulation to hot line and handle, in addition, must not bending in the mensuration process in the heat-pole method for accuracy requirement hot line that guarantee to measure, simultaneously the measuring accuracy of hot line heating power and temperature to be had relatively high expectations, these factors have increased the application difficulty of heat-pole method.

Summary of the invention

At above-mentioned the deficiencies in the prior art, and provide a kind of test unit and method of testing of measuring early concrete coefficient of heat conductivity, thermal diffusivity simultaneously during technical matters to be solved by this invention.

In order to solve the problems of the technologies described above, the present invention is by the following technical solutions: a kind of proving installation of measuring early concrete coefficient of heat conductivity, thermal diffusivity, comprise die trial, power supply and temperature indicator, in described die trial, be provided with two first parallel resistance wires, second resistance wire, described power supply is connected to form the loop by the lead and first resistance wire, on this loop, also be connected with a reometer, second resistance wire is provided with a thermistor, and this thermistor is connected with temperature indicator.

End plate in described die trial also is provided with connector, and described first resistance wire and second resistance wire are fixed in the die trial by connector, and described lead also is connected with first resistance wire by connector.

The material of first resistance wire is nickel-chrome, constantan wire or manganese-copper filament.

The end plate bonding of connector and die trial is fixing, and bonding agent is an alpha-cyanoacrylate fat bonding agent.

Described thermistor by heat-shrinkable T bush and alpha-cyanoacrylate fat adhesive at the resistance wire middle part.

A kind of method of testing of measuring early concrete coefficient of heat conductivity, thermal diffusivity may further comprise the steps:

The first step, gather thermistor (9) and first resistance wire (2) apart from r;

Second goes on foot, first resistance wire (2) is switched on heat, and gathers the current value I of reometer (6); And gather τ by time interval of 5～40s _iThe temperature θ of moment thermistor (9) _iObtain τ _iConstantly apart from τ _I-1Temperature difference θ constantly _Ri, τ _I+1Constantly apart from τ _iTemperature difference θ constantly _Ri+1, 10≤i≤80 wherein;

The 3rd goes on foot, makes M=θ _Ri+1/ θ _RiWhen 2≤M＜3, make x ₀=0.6, when 1≤M＜2, make x ₀=0.002;

The 4th step, iteration: make x ₀=x ₀+ 1/10 ⁷, assignment x=x ₀, ask

$R=-\mathrm{\γ}-1\mathrm{nx}-\underset{1}{\overset{\∞}{\mathrm{\Σ}}}\frac{{(-1)}^n{x}^n}{\mathrm{nn}!}/-\mathrm{\γ}-1n\left(\frac{x}{2}\right)-\underset{1}{\overset{\∞}{\mathrm{\Σ}}}\frac{{(-1)}^n{\left(\frac{x}{2}\right)}^n}{\mathrm{nn}!};$ When $|R-M|\≤\frac{1}{{10}^5}$ The time, stop iteration, output x,

In the formula, γ is Euler's constant (=0.5772156649);

The 5th step, differentiate temperature factor alpha, coefficient of heat conductivity λ;

$\mathrm{\&lambda;}=\frac{q}{4\mathrm{\&pi;}{\mathrm{\&theta;}}_{\mathrm{ri}}}\&CenterDot;(-\mathrm{\&gamma;}-1\mathrm{nx}-\underset{1}{\overset{\&infin;}{\mathrm{\&Sigma;}}}\frac{{(-1)}^n{x}^n}{\mathrm{nn}!}),$ $a=\frac{{\mathrm{<figure-callout\; id="2"\; label="r"\; filenames="A20081012292800111.png"\; state="\{\{state\}\}">r</figure-callout>}}^2}{{4\mathrm{x\&tau;}}_{i+1}}$

In the formula, the heating power of q one first resistance wire (2) per unit length, W/m.

This test unit is made according to the parallel method principle, so one-shot measurement can be measured the coefficient of heat conductivity and the thermal diffusivity of early concrete simultaneously.Heater strip selects for use effective length and diameter than greater than 150 resistance wire, therefore can be used as the ideal line thermal source to hot line fully.For guaranteeing that hot line keeps linear state in the mensuration process, so adopt the bolt of connector inside.The insulative water-proof on hot line surface is handled and is adopted the epoxy resin heat-conducting glue, and the advantage of epoxy resin heat-conducting glue is high heat-conducting property, and therefore the heat that can produce hot line fast distributes.In addition, the good water-proof effect of epoxy resin heat-conducting glue, quick solidifying and with the cohesive strength height on hot line surface.Be to guarantee the stable of hot line heating power, so adopt high-precision D.C. regulated power supply, adopting precision simultaneously is that 1/1000 reometer is measured the electric current of the hot line of flowing through, and guarantees the accuracy of hot line heating power calculating.The temperature sensor that adopts in the temperature survey is the PT100 thermistor.Thermistor is widely used in the thermometric field, and having high stability, precision, small size and temperature-responsive speed needs advantages such as cold junction compensation soon and not.The temperature display meter of combined high precision in the measurement, resolution characteristic has reached 0.01 ℃, has guaranteed the precision of measured temperature in the test process.

Compare with prior art, the present invention has following advantage:

1, proving installation of the present invention is simple in structure, and easy operating, can measure coefficient of heat conductivity and thermal diffusivity simultaneously.

2, both be applicable to discrete material (as cement, sand etc.), also be applicable to the mensuration of coefficient of heat conductivity such as early concrete, cement paste and sand-cement slurry and thermal diffusivity;

3, temperature rise is little in the method for testing test process of the present invention, the time short, and the coefficient of heat conductivity of mensuration and thermal diffusivity can be thought coefficient of heat conductivity and the thermal diffusivity under the assigned temperature;

4, the required instrument of measurement is few, assembles measurement mechanism voluntarily easily and fast, simply.

Description of drawings

Fig. 1 is the structural representation of proving installation of the present invention.

Fig. 2 is the iterative process figure of method of testing of the present invention.

The variation diagram that Fig. 3 increases with the length of time for coefficient of heat conductivity under the method for testing of the present invention.

The variation diagram that Fig. 4 increases with the length of time for thermal diffusivity under the method for testing of the present invention.

Embodiment

Below in conjunction with accompanying drawing apparatus of the present invention are further described:

Removable steel die trial 1 is of a size of 150mm * 150mm * 300mm, parallel two resistance wires 2 and 3 of being provided with in steel die trial 1, also can adopt connector 4 that above-mentioned resistance wire 2 and resistance wire 3 are fixed in the steel die trial 1, adopt connector 4 fixing methods to be, on connector 4, drill through the aperture of two certain distances in advance, to guarantee that resistance wire 2 and 3 can pass with pin.Earlier resistance wire 2 and 3 one ends are passed the aperture that drills through in advance, simultaneously lead 8 is fixed on connector 4 inside, the bolt of tightening connector 4 inside then is till being completely fixed, and employing alpha-cyanoacrylate fat bonding agent is fixed on connector 4 on the end plate of steel die trial 1.After treating that connector 4 is completely fixed, intercept a bit of heat-shrinkable T bush and pass resistance wire 3.The resistance wire 2 and 3 the other end also pass the aperture on the connector, and pass from the hole of connector 4 bottoms and to reserve a part, simultaneously lead 8 is fixed on connector 4 inside, but do not tight a bolt in advance, adopt alpha-cyanoacrylate fat bonding agent that connector 4 is fixed on another piece end plate of steel die trial 1 then.After treating that connector 4 is completely fixed on the end plate, begin to assemble steel die trial 1 and tighten all bolts.Utilize pliers to clamp the firmly tension of resistance wire of reservation then, till resistance wire 2 and 3 is tightened fully, tighten the bolt of connector 4 inside then fast, assurance resistance wire 2 and 3 is straightened fully and is fixing.Then thermistor 9 is passed heat-shrinkable T bush, and to the heat-shrinkable T bush heating, till being completely fixed thermistor.At last, utilize the epoxy resin heat-conducting glue that insulative water-proof is carried out on resistance wire 2 surfaces and handle, with silicon rubber connector periphery and wiring position are sealed simultaneously, reach the purpose of insulative water-proof with this.

Fresh concrete to be measured is packed into after the steel die trial 1, utilize the upper surface sealing of plastic sheeting,, then whole testing device is put into the fog room of temperature stabilization with scattering and disappearing of preventing that water from dividing with device.Treat to begin to measure after the temperature of inside concrete and indoor temperature reach balance.Connect 5 pairs of resistance wires 2 of D.C. regulated power supply and heat, simultaneously opening entry temperature and time corresponding.In the measuring process, utilize temperature display meter 7 to write down the temperature of a thermistor 9, in the time of 600 seconds, stop, and read the current value I of reometer 6 every 10 seconds.

Suppose at τ ₁=τ is θ apart from resistance wire 2 apart from the temperature difference that records for the r place constantly _R1At τ ₂In=2 τ moment, the temperature difference that records apart from resistance wire (2) r place is θ _R2, θ then _R1, θ _R2Can determine by following formula:

${\mathrm{\&theta;}}_{\mathrm{<figure-callout\; id="1"\; label="r"\; filenames="A20081012292800111.png"\; state="\{\{state\}\}">r</figure-callout>}1}=\frac{q}{4\mathrm{\&pi;\&lambda;}}\&CenterDot;E_i\left(\frac{{\mathrm{<figure-callout\; id="2"\; label="r"\; filenames="A20081012292800111.png"\; state="\{\{state\}\}">r</figure-callout>}}^2}{4\mathrm{\&alpha;\&tau;}}\right)---\left(2\right)$

${\mathrm{\&theta;}}_{\mathrm{<figure-callout\; id="2"\; label="r"\; filenames="A20081012292800111.png"\; state="\{\{state\}\}">r</figure-callout>}2}=\frac{q}{4\mathrm{\&pi;\&lambda;}}\&CenterDot;E_i\left(\frac{{\mathrm{<figure-callout\; id="2"\; label="r"\; filenames="A20081012292800111.png"\; state="\{\{state\}\}">r</figure-callout>}}^2}{2\&CenterDot;\left(4\mathrm{\&alpha;\&tau;}\right)}\right)---\left(3\right)$

Can get by formula (2) and (3):

$\frac{{\mathrm{\&theta;}}_{\mathrm{<figure-callout\; id="2"\; label="r"\; filenames="A20081012292800111.png"\; state="\{\{state\}\}">r</figure-callout>}2}}{{\mathrm{\&theta;}}_{\mathrm{<figure-callout\; id="1"\; label="r"\; filenames="A20081012292800111.png"\; state="\{\{state\}\}">r</figure-callout>}1}}=\frac{\frac{q}{4\mathrm{\&pi;\&lambda;}}\&CenterDot;E_i\left(\frac{{\mathrm{<figure-callout\; id="2"\; label="r"\; filenames="A20081012292800111.png"\; state="\{\{state\}\}">r</figure-callout>}}^2}{2\&CenterDot;\left(4\mathrm{\&alpha;\&tau;}\right)}\right)}{\frac{q}{4\mathrm{\&pi;\&lambda;}}\&CenterDot;E_i\left(\frac{{\mathrm{<figure-callout\; id="2"\; label="r"\; filenames="A20081012292800111.png"\; state="\{\{state\}\}">r</figure-callout>}}^2}{4\mathrm{\&alpha;\&tau;}}\right)}=M---\left(4\right)$

In the formula, λ is the coefficient of heat conductivity of medium, and α is the thermal diffusivity of medium, $E_i\left(\frac{{\mathrm{<figure-callout\; id="2"\; label="r"\; filenames="A20081012292800111.png"\; state="\{\{state\}\}">r</figure-callout>}}^2}{4\mathrm{\&alpha;\&tau;}}\right)$ Be an exponential integral, the progression of the following form of usefulness that can be similar to is determined:

Order $x=\frac{{\mathrm{<figure-callout\; id="2"\; label="r"\; filenames="A20081012292800111.png"\; state="\{\{state\}\}">r</figure-callout>}}^2}{4\mathrm{\&alpha;\&tau;}},$ Then have $E_i\left(x\right)=-\mathrm{\&gamma;}-1\mathrm{nx}-\underset{1}{\overset{\&infin;}{\mathrm{\&Sigma;}}}\frac{{(-1)}^n{x}^n}{\mathrm{nn}!}---\left(5\right)$

In the formula, γ is Euler's constant (=0.5772156649).

Then following formula can be reduced to:

$\frac{{\mathrm{\&theta;}}_{\mathrm{<figure-callout\; id="2"\; label="r"\; filenames="A20081012292800111.png"\; state="\{\{state\}\}">r</figure-callout>}2}}{{\mathrm{\&theta;}}_{\mathrm{<figure-callout\; id="1"\; label="r"\; filenames="A20081012292800111.png"\; state="\{\{state\}\}">r</figure-callout>}1}}=\frac{E_i(x/2)}{E_i\left(x\right)}=M---\left(6\right)$

According to formula (6) as can be known, if according to ratio $M=\frac{{\mathrm{\&theta;}}_{\mathrm{<figure-callout\; id="2"\; label="r"\; filenames="A20081012292800111.png"\; state="\{\{state\}\}">r</figure-callout>}2}}{{\mathrm{\&theta;}}_{\mathrm{<figure-callout\; id="1"\; label="r"\; filenames="A20081012292800111.png"\; state="\{\{state\}\}">r</figure-callout>}1}},$ Just can determine the value of x.Because E in the formula (6) _i(x/2) and E _i(x) be implicit function, can't directly solve the x value, therefore must utilize series expansion, obtain by concrete numerical evaluation.Therefore, as long as calculate the value of x, just can draw E _i(x) value, the coefficient of heat conductivity and the thermal diffusion coefficient of definite medium thus.Concrete computing formula is as follows:

$\mathrm{\&lambda;}=\frac{q}{{4\mathrm{\&pi;\&theta;}}_{\mathrm{<figure-callout\; id="1"\; label="r"\; filenames="A20081012292800111.png"\; state="\{\{state\}\}">r</figure-callout>}1}}{\&CenterDot;E}_i\left(x\right)---\left(7\right)$

$\mathrm{\&alpha;}=\frac{{\mathrm{<figure-callout\; id="2"\; label="r"\; filenames="A20081012292800111.png"\; state="\{\{state\}\}">r</figure-callout>}}^2}{{4\mathrm{x\&tau;}}_2}---\left(8\right)$

In the formula (6), λ-coefficient of heat conductivity, the W/ of unit (m ℃);

The heating power of q-resistance wire (2) per unit length, the W/m of unit;

In the formula (7), α-thermal diffusivity, the m of unit ²/ s;

R-first resistance wire 2 is apart from the distance of thermistor 9, the m of unit;

Wherein the algorithm flow block diagram of x is seen Fig. 2, makes M=θ _R2/ θ _R1When 2≤M＜3, make x ₀=0.6, when 1≤M＜2, make x ₀=0.002;

The 4th step, iteration: make x ₀=x ₀+ 1/10 ⁷, assignment x=x ₀, ask

$R=-\mathrm{\&gamma;}-1\mathrm{nx}-\underset{1}{\overset{\&infin;}{\mathrm{\&Sigma;}}}\frac{{(-1)}^n{x}^n}{\mathrm{nn}!}/-\mathrm{\&gamma;}-1n\left(\frac{x}{2}\right)-\underset{1}{\overset{\&infin;}{\mathrm{\&Sigma;}}}\frac{{(-1)}^n{\left(\frac{x}{2}\right)}^n}{\mathrm{nn}!};$ When $|R-M|\&le;\frac{1}{{10}^5}$ The time, stop iteration, output x,

In the formula, γ is Euler's constant (=0.5772156649);

Concrete assay method is: in conjunction with this device, be the mensuration that 0.4 concrete material has carried out coefficient of heat conductivity and thermal diffusivity to water cement ratio, the concrete consumption of concrete mix sees table 1 for details.Measure and carry out according to the following steps,

1, the concrete of mix is packed in the die trial 1, the fog room that whole device is put into temperature stabilization carries out maintenance then.Simultaneously, utilize aluminium-foil paper to carry out encapsulation process, to avoid ambient humidity to measuring early concrete coefficient of heat conductivity and thermal diffusivity result's influence at the die trial upper surface;

When 2, treating that concrete sample temperature inside and environment temperature reach balance, can measure.Basis for estimation when temperature reaches balance is to be not more than 0.05 ℃ inner concrete temperature inside fluctuation in 10 minutes;

3, connect high precision D.C. regulated power supply 5, utilize high-precision temperature Displaying Meter 7 opening entry temperature and time corresponding simultaneously;

4, in the one-shot measurement process, write down the temperature of a thermistor 9, in the time of 600 seconds, stop, and read the current value of reometer 6 every 10 seconds;

5, utilize time and the corresponding temperature value of self-compiling program (seeing Fig. 2 process flow diagram), calculate coefficient of heat conductivity and the thermal diffusivity of concrete in this length of time according to step 4 record;

6, to have provided this concrete be 2.5 hours in the length of time to table 2, resulting coefficient of heat conductivity of one-shot measurement and thermal diffusivity;

7, Fig. 3, Fig. 4 have provided the development and change figure of this concrete coefficient of heat conductivity and thermal diffusivity in the 180 hours length of time respectively.

Test figure

Initial temperature: t ₀=21.68 ℃

Parallel lines distance: r=0.026m

Hot line electric current: I=4.450A

The resistance value of every meter hot line: R ₀=9.92 Ω/m

Hot line unit length heating power: q=I ²R ₀=196.41379W/m

The concrete consumption of the used concrete mix of table 1 test

The test result of table 2 one-shot measurement arrangement

Claims (6)

1, a kind of proving installation of measuring early concrete coefficient of heat conductivity, thermal diffusivity, it is characterized in that: comprise die trial (1), power supply (5) and temperature indicator (7), in described die trial (1), be provided with two parallel first resistance wires (2), second resistance wire (3), described power supply (5) is connected to form the loop by lead (8) and first resistance wire (2), on this loop, also be in series with a reometer (6), second resistance wire (3) is provided with a thermistor (9), and this thermistor (9) is connected with temperature indicator (7).

2, the proving installation of mensuration early concrete coefficient of heat conductivity according to claim 1, thermal diffusivity, it is characterized in that: the end plate in described die trial (1) also is provided with connector (4), described first resistance wire (2) and second resistance wire (3) are fixed in the die trial (1) by connector (4), and described lead (8) also is connected with first resistance wire (2) by connector (4).

3, the proving installation of mensuration early concrete coefficient of heat conductivity according to claim 1, thermal diffusivity, it is characterized in that: the material of first resistance wire (2) is nickel-chrome, constantan wire or manganese-copper filament.

4, the proving installation of mensuration early concrete coefficient of heat conductivity according to claim 1, thermal diffusivity is characterized in that: connector (4) is fixing with the end plate bonding of die trial (1), and bonding agent is an alpha-cyanoacrylate fat bonding agent.

5, the proving installation of mensuration early concrete coefficient of heat conductivity according to claim 1, thermal diffusivity is characterized in that: described thermistor (9) by heat-shrinkable T bush and alpha-cyanoacrylate fat adhesive at second resistance wire (3) middle part.

6, a kind of method of testing that adopts the proving installation of the described mensuration early concrete of claim 1 coefficient of heat conductivity, thermal diffusivity is characterized in that: may further comprise the steps:

The spacing r of the first step, record thermistor (9) and first resistance wire (2);

Second goes on foot, first resistance wire (2) is switched on heat, and gathers the current value I of reometer (6); And gather τ by time interval of 5～40s _iThe temperature θ of moment thermistor (9) _iObtain τ _iConstantly apart from τ _I-1Temperature difference θ constantly _Ri, τ _I+1Constantly apart from τ _iTemperature difference θ constantly _Ri+1, 10≤i≤80 wherein;

The 3rd goes on foot, makes M=θ _Ri+1/ θ _RiWhen 2≤M＜3, make x ₀=0.6, when 1≤M＜2, make x ₀=0.002;

The 4th step, iteration: make x ₀=x ₀+ 1/10 ⁷, assignment x=x ₀, ask

$R=-\mathrm{\&gamma;}-\ln x-\underset{1}{\overset{\&infin;}{\mathrm{\&Sigma;}}}\frac{{(-1)}^n{x}^n}{\mathrm{nn}!}/-\mathrm{\&gamma;}-\ln \left(\frac{x}{2}\right)-\underset{1}{\overset{\&infin;}{\mathrm{\&Sigma;}}}\frac{{(-1)}^n{\left(\frac{x}{2}\right)}^n}{\mathrm{nn}!};$ When $|R-M|\&le;\frac{1}{{10}^5}$ The time, stop iteration, output x, in the formula, γ is Euler's constant (=0.5772156649);

The 5th step, differentiate temperature factor alpha, coefficient of heat conductivity λ:

$\mathrm{\&lambda;}=\frac{q}{4\mathrm{\&pi;}{\mathrm{\&theta;}}_{\mathrm{ri}}}.(-\mathrm{\&gamma;}-\ln x-\underset{1}{\overset{\&infin;}{\mathrm{\&Sigma;}}}\frac{{(-1)}^n{x}^n}{\mathrm{nn}!}),$ $\mathrm{\&alpha;}=\frac{r^2}{4x{\mathrm{\&tau;}}_{i+1}}$

Wherein, the heating power of q-resistance wire (2) per unit length, q=I ²R ₀, R ₀Resistance value for every meter first resistance wire (2).

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