RU2457471C2 - Method of determining thermal resistance of section of structural element in nonsteady heat-transfer mode - Google Patents

Abstract

FIELD: physics.

SUBSTANCE: essence of the invention lies in determining conditions for existence of a quasi-steady heat-transfer mode and criterion θ_max thereof. Based on defined quasi-steady mode conditions for a specific section, the duration of the measurement time interval τ^min is selected depending on the heat retention time of the section τⁱⁿ and the overall duration of the measurement time interval τ≥τ^min≥3τ_in. The limiting value of the quasi-steadiness criterion θ is determined. Time intervals τ_i are arbitrarily selected and from the set of values (τ_i), those time intervals τ _ij, where the quasi-steadiness criterion θ(τ_i) is less than θ, are selected. These time intervals τ _ij will be closer to steady. The non-steady mode which is difficult to diagnose and calculate is excluded and the known steady method can be used when determining thermal resistance of the section of the structure.

EFFECT: higher accuracy of determination.

2 dwg, 2 tbl

Description

The invention relates to the field of measuring technology and will find application in almost all processes of construction, production, operation and repair of various technical objects, where diagnostics, quality control, ensuring operability and safety of operation of objects and their individual units, blocks and parts are necessary.

Heat transfer through heat conduction [1-3] plays the main role in the energy balance of buildings and structures [4-6], thereby determining the level of energy loss across the entire housing and communal services of the country [4, 5]. The control of the heat transfer parameters of the enclosing external walls is therefore of particular relevance, concentrating on identifying the thermal resistance of the walls, a parameter that depends only on their internal structure and physical characteristics [4-6].

In the Russian Federation, in practice, a method is used to determine the quality of objects by analyzing their resistance to heat transfer - see GOST 26254-84. "Buildings and constructions. Methods for determining the heat transfer resistance of building envelopes. " Introduced by resolution of the USSR State Committee for Construction Affairs dated August 2, 1984 No. 127, UDC 624.01.001.006.354. The method described here consists in measuring the density of the heat flux (q) through a controlled fence and the temperature of the media near its surfaces (T _n ) and (T _c ) for at least 15 days when the controlled fencing reaches a stationary or close thermal regime. The achievement of this mode is determined by the behavior of the measured temperature of the outer (T _pn ) and inner (T _pv ) surface of the fence.

Determining the quality of the fence by its resistance to heat transfer (R ₀ ) is carried out in accordance with the formula:

where R _in , R _n - thermal resistance to heat transfer on the inner and outer surface of the fence;

R _to - thermal resistance of the design of the fence.

This method is simple and obvious, but it has a drawback that limits its scope and significantly reduces the accuracy of the results. The method is applicable only if the heat transfer process through the controlled structure is stationary (i.e., only if the heat flux entering the structure is constant) on one surface and leaving the structure on another surface: q = const.

In practice, when thermal monitoring of structures with a real change in time of the temperature of the media T _n and T _in this condition is extremely rare. Failure to comply with the condition of constant heat flux density leads to the appearance of large errors in the determination of R ₀ - up to 300-500%.

According to GOST 26254-84, in the external enclosing structures, the stationary process of heat transfer, depending on their thermal inertia, is established after 1.5-7.5 days. However, in practice, when monitoring building structures, the difference in outdoor temperature at night and daytime, for example, reaches 10-15 degrees. This causes unsteady heat transfer processes in the studied structures and makes the method inapplicable.

The solution to this problem is proposed in the monograph of Budadin ON etc. Thermal non-destructive testing of products. M .: Nauka, 2002 - S.139-145. It consists in solving the inverse problem of unsteady heat conduction in a multilayer medium.

The proposed methodology was put into the development of modern methods.

There is a method that determines the local thermal resistance of the studied areas under unsteady heat transfer (see patent No. 2219534, class G01N 25/72, 09/12/02). According to the known method determine the time interval necessary and sufficient to obtain a reliable result. Throughout the entire time interval, the temperature and heat flux density are measured periodically on the outer and inner surfaces of the object. The value of the thermal conductivity of the desired layer is arbitrarily and repeatedly set. Using the developed generalized physical and mathematical model of thermal non-destructive testing of multilayer objects with inhomogeneities and a given value of thermal conductivity, theoretically possible temperature and density of the heat flux of the external and internal surfaces, respectively, are calculated for each given value of thermal conductivity, an instant thermal imaging inspection is carried out, and temperatures and heat flux densities are measured, respectively on the inner and outer surfaces. Theoretically possible values are compared with the measured ones. For further calculations, the value of thermal conductivity is selected from among the given values, which could provide the conditions for comparison.

There is a method in which thermal resistance is determined under an unsteady heat transfer mode (see RF patent No. 2316760, class G01N 25/72, dated August 22, 2005).

According to the known method, at least two thermally homogeneous zones are isolated on the thermogram of the internal surface of the object. In the selected areas, the temperatures of their outer and inner surfaces are measured and calculated at the given values of thermal conductivity (λ). Compare these temperatures in one coordinate system. The error between the compared temperatures is set to δ ± 8.5%. The time intervals are determined and the heat transfer coefficient (α) is calculated on the selected time intervals. Select the values of thermal conductivity (λ) at which α α + Δα. Determine the thermal resistance of all areas with anomalies in the temperature field and, accordingly, the thermal transfer resistance of these areas and the reduced heat transfer resistance of the multilayer object.

The known methods are universal, but widespread use in practice is constrained by a number of circumstances, which are as follows:

- there is a significant non-linear dependence of the accuracy of the results on the error of the input data - the results of primary measurements. This leads to the need to ensure small values of the error of the results of primary measurements, which requires the use of special expensive measuring instruments, qualified operators, etc .; measurements require compliance with special climatic conditions;

- the presence of an input data error can lead to the case when the inverse problem does not converge, i.e. there will be no solution;

- the solution to the inverse problem, as a rule, is not the heat transfer resistance itself, but the value of the heat conductivity coefficient of one of the layers, usually the layer with the highest thermal resistance, for example, a heat-insulating layer of a fence.

In addition, the known methods require the necessary comparative base, the creation of which requires a long time. All of the above makes the methods expensive and time consuming.

A known method (see RF patent No. 2383008, class G01N 25/18, dated 12/19/08), which allows to determine the state of structures and their heat loss in the study of non-stationary processes. The known method includes measuring the average temperature and heat flux on the outer and inner surfaces for several time intervals, sequentially changing the magnitude and initial values of the time intervals fixing those time intervals and the measured average temperature and heat flux in which these values differ by not exceeding the value of a predetermined error, and determining the heat transfer resistance of the controlled area and determining the thermal drag across the surface of the object.

The disadvantage of this method is that it cannot be implemented, because contradicts the stationary heat equation (see, for example, [1-3]). An error was made in determining the heat transfer resistance, in addition, it is impossible in the general case to measure the average values of temperature and heat fluxes, in this case they can only be calculated.

A prototype of the proposed method can be a method (see RF patent No. 2262686, class G01N 25/72, 04/23/04), which is used for the technical diagnosis of heterogeneous structures by thermal resistance. The essence of the method lies in the fact that the density of the heat flux through the controlled fence is determined, its value (q) is measured on one of the surfaces (for example, on the inner surface - q _c ), the temperatures of the media near the opposite surfaces are measured (T _n , T _c ), temperatures of opposite surfaces (T _mon , T _pv ) and determine the quality of the controlled object by its resistance to heat transfer R ₀ in accordance with the formula:

Additionally measure the value of the heat flux density on the opposite surface (q _n ); measurements of heat flux density q _n (t), q _in (t) and temperatures T _n (t), T _in (t), T _mon (t), T _pv (t) are carried out periodically during the time interval (t) ; the error of measuring the density of heat fluxes (Δqmax), permissible for determining the quality of the object, is set, the moments of time t ₁ , t ₂ , ... t _n are determined, at which the values of flows on opposite surfaces are equal to the error Δq≤Δqmax: | q _n (tq _in (t ) | ≤Δqmax, they continue to measure the density of heat fluxes until the difference in their values exceeds the limits (Δqmax), from the obtained time instants choose the moment (t _k ) near which the values of the density of heat fluxes q _in (t _к ) and q _н (t _к ) coincide with a given error (Δqmax) during the largest interval bp Meni (Δt _k), determine the quality of the object in accordance with the above formula for q = q _n values, q _a, T _n, T _Mo, T _in, T _MF measured at time t _k.

In the known method, from the non-stationary process of heat transfer during time (t), a time interval is determined during which a quasi-stationary process is realized in the object under study. To do this, consider the heat fluxes q _n (t), q _in (t) and determine the times at which the values of the density of heat fluxes on opposite surfaces of the fence are equal with an error Δq≤Δqmax.

As practice has shown, this approach to determining the quasistationary process is not true, since there is a significant nonlinear dependence of the accuracy of the results on the error of the input data - the results of primary measurements. Measurements of the heat flux density, especially of the external one, have low accuracy, and such a comparison of q _in and q _n in the interval Δt≤Δt _{in is} not a reliable criterion, since the equality of the density of heat fluxes is only a necessary, but not sufficient condition for stationarity. Even in the case when q _in = q _n for any measurement time intervals Δt, there are solutions in which the stationary and quasi-stationary heat transfer processes are not realized.

The proposed technical solution eliminates the above drawbacks and is aimed at prompt and reliable determination of the thermal characteristics of the section of the structural element.

The technical result consists in the development of a quasi-stationary method for controlling heat transfer parameters of various kinds of heat-insulating structures and materials, including building envelopes of buildings and structures.

Common features of the prototype and the claimed method are that they determine the time interval of measurements necessary and sufficient to ensure the required level of reliability of the result. During this time interval, instantaneous values of temperatures and heat flux densities are continuously recorded on the surfaces of the investigated area, and the thermal resistance of the area is determined from the obtained values.

New in the proposed method is that by theoretical analysis and analytical solution of the linear non-stationary heat transfer equation with boundary conditions of the first kind, the conditions for the quasistationarity of the heat transfer regime, the criteria for the quasistationary heat transfer regime θ ^max and the correction of thermal resistance ΔR caused by the non-stationary heat transfer are determined.

Then, from the conditions defined above, select the minimum duration of the measurement time interval τ ^min , which depends on the thermal inertia time of the section τ _in and the total duration of the measurement time interval τ in such a way that:

τ≥τ ^min ≥3τ _in

where: τ _yn = max (τ ^to _yn, τ ^N _in) - time thermal inertia portion;

τ ⁱⁿ _Institute, τ ⁿ _in - time thermal inertia respectively, the inner and outer surfaces of the portion.

The limiting value of the quasistationary criterion of the heat transfer mode θ is determined based on the given error in determining the thermal resistance of the investigated area.

θ = θ ^max · Δ / 15,

where: θ ^max is the value of the quasistationary criterion for the heat transfer mode at 15% relative systematic error in determining the value of thermal resistance;

Δ is the relatively permissible error in determining the thermal resistance of the investigated area,%.

The duration of the time interval for determining the heat transfer resistance of the section τ is selected and the limiting value of the criterion for the quasistationarity of the heat transfer mode θ is determined so that throughout the entire time interval τ, arbitrarily identifying time gaps τ _i with a duration of at least a · τ _in

τ≥τ _i ≥ a τ _in

where: a = 2 [1 + ln (1 + θ (τ _i ))] is a dimensionless coefficient taking into account the change in the recorded surface temperatures of the site;

determine at each of these time intervals (τ _i ) the value of the quasistationarity criterion θ (τ _i )

θ (τ _i ) = | (k ^q _in T ' _in · τ ⁱⁿ _in -k ^q _n T' _n · τ ⁿ _in ) / ΔT |,

where: ΔT = T _in ^sr -T _n ^sr - the average value of the temperature difference of the surfaces of the plot in the interval τ _i ;

T ' _in , T' _n - respectively, the average value of the rate of change of temperature of the surface of the plot in the interval τ _i ;

k ^q _in , k ^q _n - the coefficients of the mutual influence of heat fluxes and rates of temperature changes on the corresponding surfaces,

and compare it with a certain limit value of the criterion of quasistationarity θ, identifying from the set of values of τ _i , those time intervals τ _ij , where the criteria of quasistationarity θ (τ _i ) is less than the limit value of the criterion of quasistationarity θ,

θ (τ _i ) ≤θ,

such time intervals τ _ij , and will contain measurements, on the basis of which the value of the thermal resistance of the section of the structural element is determined based on the dependence:

R = ΔT _ij / q _ij + ΔR,

where: ΔT _ij = (T _in ^Wed , _ij -T _n ^Wed , _ij ) is the average temperature difference of the surface of the plot;

q _ij is the average density of heat fluxes on the surfaces of the plot;

ΔR = ΔT _R (τ _in , T ' _in , T' _in , G ⁿ _in ) / q _ij - correction of thermal resistance caused by non-stationary heat transfer;

ΔТ _R is a function that takes into account the non-stationary nature of the heat transfer mode and depends on the configuration, structure, thermophysical characteristics of the materials of the studied area (parameters τ _in , G ⁿ _in ) and the rate of change of surface temperatures of the section (T ' _in , T' _in );

G ⁿ _s = 1 / G ⁱⁿ _n = τ ⁿ _yn / τ ^{in the} _in - form factor, respectively outer and inner surface areas determined by calculation based on the configuration of the structural member (a flat, cylindrical, spherical or other form of construction.), Structure and thermophysical characteristics of the composition materials.

The essence of the method is as follows: to find and systematize the conditions for the existence of quasi-stationary and non-stationary thermal states of external walls for different types of thermal disturbances.

Quasistationary are such changes in the characteristics of the medium in which the parameters of the object can be described by stationary equations, for example:

where: ΔT = Tv-Tn is the temperature difference on the corresponding surfaces of the site;

q is the heat flux density;

R is the thermal resistance of the plot.

In the extreme case of small changes in the characteristics of the medium, stationarity arises - the invariance of the thermal state of the object. Their weak changes are quasi-stationary. The measure of "weakness" is determined by the quasi-stationary criterion θ (τ _i ).

From equation (1) it follows that the implementation of this stationary equation does not require a constant temperature or a constant heat flux, but only a constant relationship is needed, slightly violating the thermal state of the object

In the quasistationary regime, the change in the thermal state can be significant, as, for example, in the case of prolonged slow heating (cooling) of the wall under boundary conditions of the first kind [9], when the requirement for the limiting value of the quasistationarity criterion θ (τ _i ) ≥θ is not fulfilled, those. when the actual value of the relative permissible error in determining the thermal resistance will exceed the specified value Δ.

These modes are also of practical interest to us, since they are close to stationary and can be used for thermal diagnostics. Such cases are characterized by a systematic error in the measurement of thermal resistance ΔR, taken into account as an amendment to formula (1):

This correction ΔR is derived from the analytical solution of the unsteady heat conduction problem [9]

ΔR = ΔT _R (τ _in , T ' _in , T' _n , G ⁿ _in ) / q,

where: ΔT _R is a function that takes into account the non-stationary mode of heat transfer and depends on the configuration, structure, thermophysical characteristics of the materials of the studied area (parameters τ _in , G ⁿ _in ) and average rates of temperature change of the surface of the site (T ' _in , T' _n )

форм-фактор соответственно наружной и внутренней поверхностей участка, определяемый расчетом исходя из конфигурации элемента конструкции (плоская, цилиндрическая, сферическая или др. форма конструкции) его структуры и теплофизических характеристик материалов состава.

the form factor of the outer and inner surfaces of the plot, respectively, determined by calculation based on the configuration of the structural element (flat, cylindrical, spherical or other design form) of its structure and thermophysical characteristics of the composition materials.

_yn τ = max (τ ^to _yn, τ ^N _in) - time plot thermal inertia.

τ ⁱⁿ _Institute, τ ⁿ _in - time thermal inertia respectively, the inner and outer surfaces of the portion.

Table 1 compares the considered characteristics of stationary and non-stationary methods for determining the thermal resistance of walls. The stationary method has an advantage of 10 points marked with a “+” sign, non-stationary method - only one, and they do not differ by 4 points.

In connection with all of the above, it is advisable to consider a more general theoretical problem of identifying stationary states in practice and mixed quasistationary and quasiperiodic conditions. The research results consisted in identifying time intervals during which the state of heat transfer is close to stationary, and a criterion for determining the presence of such states. Thus, the conditions of applicability of expressions (1) and (2) were also determined.

The detected time intervals can be used in thermal diagnostics of buildings, determining the applicability of the normative stationary method of the method [7], and make it possible to do without involving the cumbersome solution of the incorrect non-stationary problem.

Under stationary conditions, by definition, the heat fluxes outside and inside the walls are equal to each other [1-4]. To establish the presence of a stationary regime by measuring and comparing them would be most simple. However, measurements of the heat flux density, especially of the external one, have low accuracy, and such a comparison is not a reliable criterion.

In addition, even under conditions that can be considered completely stationary, external heat fluxes are so sensitive to any external factors (wind, solar radiation, precipitation, etc.) that their instantaneous values almost always differ greatly from fairly stable thermal values flows on the inner surface.

This can be seen from figure 1 - illustration of the effect of the inequality of the internal (q _in ) and external (q _n ) heat fluxes on the time course of the ratio ΔT (t) / q (t), measured in the period from 29.03.07 to 10.04.07 in brick wall (d = 91 cm) of a building located in the center of Moscow, from the ΔT (t) / q (t) relationship graphs constructed using heat fluxes measured on the inner and outer sides of the wall (q _in , q _n - respectively). The graphs intersect only at three points, and even those lie far beyond the range of acceptable values. The differences between them even in the right, most balanced part of figure 1, reach 90%, which requires additional analysis of the processes leading to such differences, and the creation of a stationary method that takes into account these differences.

So, for the experimental detection of the stationary regime and determination of thermal resistance by the formula (2), one will have to go a different way. First, it is necessary, guided by the methodology [7, 6], to measure the time dependences of temperature and heat flux inside and outside the building. The duration of the measurements, in contrast to [7, 6], where it always exceeds 15 days, should depend on the thermal inertia of the wall, exceeding the time τ _in (time of inertia).

As a result of the theoretical analysis and analytical solution of the linear non-stationary heat transfer equation [9] with boundary conditions of the first kind [9], which describe the unsteady heat transfer process in the studied section of the structural element, the conditions and criterion of quasi-stationary heat transfer θ ^{max are} determined. Then, from certain conditions for a particular section of the structural element, the minimum duration of the measurement time interval τ ^{min is} selected. The duration of the measurement time interval depends on the time of the thermal inertia of the section (τ _in ). And the total duration of the measurement time interval (τ) is determined from the condition:

τ≥τ ^min ≥3τ _in

where: τ _in - time thermal inertia of the site.

After that, determine the limit value of the criterion for the quasistationarity of the heat transfer mode θ based on a given error Δ of determining the thermal resistance of the studied area, based on the dependence:

θ = θ ^max Δ / 15

where: θ ^max is the value of the quasistationarity criterion at 15% relative systematic error in determining the value of thermal resistance,

Δ is the relatively permissible error in determining the thermal resistance,%.

Then, from these data, it is necessary to identify the time intervals for the applicability of formula (1), which are characterized by the constancy of the ratio ΔT (t) / q (t) ≈const = R, when the changes ΔT (t) and q (t) occur quasi-stationary (if they occur), without breaking this relationship.

This defines the conditions for the existence of a quasistationary thermal state, which the thermal system always strives for, and the only question is how quickly it does it. It is preserved if the external action is slower than the internal processes, and is monitored by a corresponding change in the internal parameters while maintaining the same stationary relations between them (in this case, relations (1)). These states, unlike the stationary ones, are most common in nature.

An important guideline in identifying such quasistationary conditions is the aforementioned time of thermal inertia.

Throughout the entire previously determined time interval - τ, randomly allocate time intervals τ _{i with a} duration of at least a · τ _in

τ≥τ _i ≥ a τ _in ,

where: a = 2 [1 + ln (1 + θ (τ _i ))] is a dimensionless coefficient taking into account the measurement of the recorded surface temperatures of the site.

At each of these time intervals (τ _i ), the value of the quasistationarity criterion θ (τ _i ) is determined based on the dependence:

θ (τ _i ) = | (k ^q _in · T ' _in · ⁱⁿ _in -k ^q _n · T' _n · τ ⁿ _in ) / ΔT |

where: ΔT = T _in ^sr -T _n ^sr - the average value of the temperature difference of the surfaces of the plot in the interval τ _i ,

T ' _in , T' _n - respectively, the average values of the rate of change of temperature of the surface of the plot in the interval τ _I ,

k _in , k _n - the coefficients of the mutual influence of heat fluxes and rates of temperature changes on the corresponding surfaces.

After determining θ (τ _i ), compare it with the previously determined limit value θ and identify from the set of values of τ _i those time intervals τ _ij where the criteria for quasistationarity θ (τ _i ) are less than the limit value for the criterion for quasistationary θ

θ (τ _i ) ≤θ.

These time intervals τ _ij will contain measurements, based on which the value of the thermal resistance of the section of the structural element is determined based on the dependence θ:

R = ΔT _ij / q _ij + ΔR

where: ΔT _ij = (T _in ^Wed -T _n ^Wed ) is the average temperature difference of the surface of the plot,

q _ij is the average density of heat fluxes on the surfaces of the plot,

ΔR is the correction of thermal resistance caused by non-stationary heat transfer.

Table 2 shows the values of τ _in for various types of homogeneous walls, illustrating the entire spectrum of thermal inertia of the materials from which the building envelopes of residential and industrial buildings are built. These estimates are quite universal, because the spread of τ _in values taking into account the humidity regime of the premises and the humidity zones of the location area does not exceed 20%.

From Table 2 it can be seen that measurements on walls with low thermal inertia (for example, wooden), under a favorable set of circumstances, can take no more than a day, while thick brick and concrete walls may take a week or more.

Figure 2 - determination of thermal resistance of a wall of 3.5 bricks (d = 91 cm) from the time course of the ratio ΔT (t) / q (t) for the period from 03/29/07 to 04/10/07 in buildings located in the center of Moscow . The typical time course of the ΔT (t) / q (t) ratio shown is obtained on a massive brick wall in the spring season. For the correct processing of the results, it is advisable to introduce a corridor of reliable values determined by the measurement accuracy ΔT (t) / q (t). (According to [7], this is 15%.) Within these limits, the ratio ΔT (t) / q (t) coincides with the thermal resistance of the wall R.

In figure 2, during the last, more than 3 days, the stabilization of the ratio ΔT (t) / q (t) is observed. This is a sign of quasi-stationary heat transfer, since the observed stabilization lasts longer than the thermal inertia time (in accordance with (1) and [8], t _in = 2 days), which indicates a steady state, and not a transitional state. It is important that even for such a massive, almost meter-long brick wall and at a far from the best time for measurements (April), a quasi-stationary thermal regime is established. This indicates the prospects of the claimed method for determining thermal resistance.

With this approach to the study of the mixed regime of heat transfer by non-stationary sections, we simply neglect it.

The non-stationary mode, difficult for diagnostics and calculation, is excluded from consideration, the stationary method finds its application, formula (2),

For example: for a flat one-dimensional structure:

τ ^min = τ _i = a · τ _in - the minimum duration of the measurement time interval is equal to the minimum duration of the time interval for determining the thermal resistance of the section,

a = 1 + ln (1 + θ (τ _i )) is a dimensionless coefficient that takes into account the registered changes in the temperature of the surfaces of the element on a continuous interval τ,

θ (τ _i ) = | (k ^q _in T ^' _in · τ ⁱⁿ _in -k ^q _n T' _n · τ ⁿ _in ) / ΔT | - the value of the criterion of quasistationary plot in the interval τ _i ,

Where:

ΔT = T _in ^sr -T _n ^sr - the average value of the temperature difference of the surfaces of the plot in the interval τ _i ,

T ' _in , T' _n - respectively, the average values of the rate of change of temperature of the surface of the plot in the interval τ _i ,

и

для схемы измерения теплового потока на обеих поверхностях k^q _н=k^q _в=0,5).k ^q _in , k ^q _n - coefficient of mutual influence of the rate of change of temperature and heat fluxes on the corresponding surfaces, (for a flat one-dimensional design, for the scheme of measuring the heat flux on one of the surfaces

and

circuitry for measuring the heat flux on both surfaces k ^q = _n k ^q _s = 0.5).

For the error in determining the thermal resistance ± 15%, the quasistationarity criterion is: θ ^max = 0.09 - for the heat flux measurement circuit on only one of the surfaces and θ ^max = 0.18 for the heat flux measurement circuit on both surfaces of the section.

In the case of a homogeneous flat wall and measurement scheme, providing for the measurement of heat flux density on the inner and outer surfaces of the plot:

form factor G ⁿ _vn = 1, and

ΔT _R = π ² τ _jn ΔT '/ 12, where

ΔT 'is the rate of change of the temperature difference of the inner and outer surfaces of the plot ΔT' = T ' _in -T' _n ,

τ ⁱⁿ _in = τ ⁿ _in = d ² / π ² a - respectively, the time of thermal inertia of the surfaces of the plot and the plot of the structural element,

Where:

α is the coefficient of thermal diffusivity of the material,

d is the thickness of the wall section.

Using the proposed method will allow us to estimate the quasistationary nature of the heat transfer process in heat-inertial elements of an arbitrary structure, internal structure and structure, obeying the Fourier law of thermal conductivity under conditions of unsteady heat transfer. The proposed method does not require the use of special expensive measuring instruments and skilled operators, which makes it cheaper compared to the known one. The method is not related to solving the inverse problem and therefore more accurate than existing ones.

Table 1 Comparison of the features of non-stationary and stationary models for calculating the thermal resistance of walls No. Characteristic Non-stationary model Stationary model one Measured parameters Same 2 Requirements for Measured Parameters Inconstancy Constancy 3 Applicability to external conditions (temperature pressure, etc.) Equally limited four The dependence of the measurement time on the thermal inertia of the wall Weak ~ 5 days Strong, from fractions of a minute to ~ 5 days + 5 Calculation error May be high ("rating") Always controlled + 6 Sensitivity to measurement error Very high, up to the divergence of the solution Low + 7 Degree of difficulty High Zero + 8 Development and prescription of research About the same 9 Availability of analytical solutions and their practical applicability Limited Always exist + 10 Possibility of numerical solution Limited by conditions of convergence, correctness, uniqueness Always exists + eleven Labor costs Large Moderate + 12 Applicability to laminate walls Almost not applicable Applicable + 13 Practical application Narrow Wide + fourteen Reliability degree, reliability of results Low High + fifteen Applicability Criteria Exists Are absent +

table 2 The thermal inertia time of a homogeneous wall (The range between the values in wet and dry environments is indicated) Fencing material Fencing thickness
d, m Thermal inertia time
τ _in , days Clay brick 0.65 0.9 ÷ 1.1 Concrete 0.65 0.54 ÷ 0.57 Expanded clay

0.82 ÷ 0.95 0.31 ÷ 0.36 Pine timber 0.2 0.3 ÷ 0.38 Expanded polystyrene 0.2 0.16 ÷ 0.19 Glass 2 × 0.004 18 sec

Used Books

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6. MED 01.01.00. Methodology-2-2006. Methodology for examining the condition of the external building envelopes of buildings and structures using the thermal imaging method. KP MED, Moscow, 2006.

7. GOST 26254-84. Buildings and constructions. Method for determining the heat transfer resistance of building envelopes. Enter fast. Gos. com USSR for construction. 2.08.84, No. 127. M., 1985.

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9. Kutateladze S.S. Fundamentals of the theory of heat transfer. Automizdat, 1979, p. 416.

Claims (1)

A method for determining the thermal resistance of a section of an element of a structure under an unsteady heat transfer mode, which consists in the fact that for the studied section of a structural element, the measurement time interval necessary to ensure the required level of reliability of the result is determined, instantaneous temperature values are continuously recorded on the surfaces of the studied section throughout the entire measurement interval and heat flux densities, from the obtained values determine the thermal resistance ASTK, characterized in that the determined conditions quasistationarity heat mode, criterion quasistationarity mode of heat transfer θ ^max and the correction of thermal resistance ΔR, cause non-stationary heat transfer through theoretical analysis and analytical solutions of a linear time-dependent equation heat transfer boundary conditions of the 1st kind, which describe the unsteady heat transfer process in the studied section of the structural element, from the conditions specified above for a specific section of the element design, choose the minimum duration of the time interval of measurements τ ^min , depending on the time of the thermal inertia of the plot τ _in , and the total duration of the time interval of measurements τ so that:
τ≥τ ^min ≥3τ _in ,
where τ _yn = max (τ ^to _yn, τ ^N _in) - time thermal inertia portion;
τ ⁱⁿ _Institute, τ ⁿ _in - time thermal inertia, respectively inner and outer surfaces of the portion is determined limit value quasistationarity heat mode criterion θ, based on a predetermined error calculation of thermal resistance test site:
θ = θ ^max · Δ / 15,
where θ ^max is the value of the quasistationarity criterion at a 15% relative systematic error in determining the value of thermal resistance;
Δ is the relatively permissible error in determining the thermal resistance,%,
so that throughout the entire time interval τ, arbitrarily identifying time intervals τ _{i with a} duration of at least a · τ _in
τ≥τ _i ≥aτ _in ,
where a = 2 [1 + ln (1 + θ (τ _i ))] is a dimensionless coefficient taking into account the change in the recorded surface temperatures of the plot; determine at each of these time intervals (τ _i ) the value of the quasistationarity criterion θ (τ _i )
θ (τ _i ) = | (k _in ^q T ' _in · τ ⁱⁿ _in -k _n ^q T' _n · τ ⁿ _in ) / ΔT |,
where ΔT = T _in ^avg , T _n ^av - the average value of the temperature difference of the surfaces of the plot in the interval τ _i ;
T ' _in , T' _n - respectively, the average values of the rate of change of temperature of the surface of the plot in the interval τ _i ;
k _in ^q , k _n ^q are the coefficients of the mutual influence of heat fluxes and rates of temperature change on the corresponding surfaces,
and compare it with a certain limit value of the quasistationarity criterion θ, identifying those time intervals τ _ij from the set τ _i , where the quasistationarity criterion θ (τ _i ) is less than the limit value of the quasistationarity criterion θ,
θ (τ _i ) ≤θ,
such time intervals τ _ij will contain measurements, on the basis of which the value of the thermal resistance of the section of the structural element is determined based on the dependence:
R = ΔT _ij / q _ij + ΔR,
where ΔT _ij = (T _in ^avg , _ij -T _n ^av , _ij ) is the average temperature difference of the surface of the site;
q _ij is the average density of heat fluxes on the surfaces of the plot;
ΔR = ΔT _R (τ _in , T ' _in , T' _in , G ⁿ _in ) / q _ij - correction of thermal resistance caused by non-stationary heat transfer;
ΔТ _R is a function that takes into account the non-stationary nature of the heat transfer mode and depends on the configuration, structure, thermophysical characteristics of the materials of the investigated area (parameters τ _in , G ⁿ _in ) and average rates of temperature change of the surface of the area (T ' _in , T' _in );
G ⁿ _s = 1 / G ⁱⁿ _n = τ ⁿ _yn / τ ^{in the} _in - form factor, respectively outer and inner surface areas determined by calculation, based on the configuration of the structural member (a flat, cylindrical, spherical or other shape structure.), A structure and thermophysical characteristics of the composition materials.

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