Test

in Thermophysics No. 11

Thermal resistance of the air layer

1. Prove that the line of temperature decrease in the thickness of a multilayer fence in the coordinates “temperature - thermal resistance” is straight

2. What does the thermal resistance of the air layer depend on and why?

3. Reasons that cause a pressure difference to occur on one and the other side of the fence

temperature resistance air layer fencing

1. Prove that the line of temperature decrease in the thickness of a multilayer fence in the coordinates “temperature - thermal resistance” is straight

Using the equation for the heat transfer resistance of a fence, you can determine the thickness of one of its layers (most often insulation - a material with the lowest thermal conductivity coefficient), at which the fence will have a given (required) value of heat transfer resistance. Then the required insulation resistance can be calculated as, where is the sum of the thermal resistances of layers with known thicknesses, and minimum thickness insulation - like this: . For further calculations, the thickness of the insulation must be rounded up by a multiple of the standardized (factory) thickness values of a particular material. For example, the thickness of a brick is a multiple of half its length (60 mm), the thickness of concrete layers is a multiple of 50 mm, and the thickness of layers of other materials is a multiple of 20 or 50 mm, depending on the step with which they are manufactured in factories. When carrying out calculations, it is convenient to use resistances due to the fact that the temperature distribution over the resistances will be linear, which means that it is convenient to carry out calculations graphically. In this case, the angle of inclination of the isotherm to the horizon in each layer is the same and depends only on the ratio of the difference in design temperatures and the heat transfer resistance of the structure. And the tangent of the angle of inclination is nothing more than the density of the heat flow passing through this fence: .

At inpatient conditions The heat flux density is constant in time, and that means where R X- resistance of a part of the structure, including resistance to heat transfer inner surface and thermal resistances of the layers of the structure from the inner layer to the plane on which the temperature is sought.

Then. For example, the temperature between the second and third layers of the structure can be found as follows: .

The given resistance to heat transfer of heterogeneous enclosing structures or their sections (fragments) should be determined from the reference book; the given resistance of flat enclosing structures with heat-conducting inclusions should also be determined from the reference book.

2. What does the thermal resistance of the air layer depend on and why?

In addition to the transfer of heat by thermal conductivity and convection in the air gap, there is also direct radiation between the surfaces limiting the air gap.

Radiation heat transfer equation: , where b l - heat transfer coefficient by radiation, which largely depends on the materials of the interlayer surfaces (the lower the emissivity coefficients of the materials, the smaller and b l) and the average air temperature in the layer (with increasing temperature, the coefficient of heat transfer by radiation increases).

Thus, where l eq - equivalent thermal conductivity coefficient of the air layer. Knowing l eq, you can determine the thermal resistance of the air layer. However, resistance R VP can also be determined from a reference book. They depend on the thickness of the air layer, the air temperature in it (positive or negative) and the type of layer (vertical or horizontal). The amount of heat transferred by thermal conductivity, convection and radiation through vertical air layers can be judged from the following table.

Layer thickness, mm	Heat flux density, W/m2	Amount of heat transferred in %	Equivalent thermal conductivity coefficient, m o C/W	Thermal resistance of the interlayer, W/m 2o C
		thermal conductivity	convection	radiation




Note: the values given in the table correspond to the air temperature in the layer equal to 0 o C, the temperature difference on its surfaces is 5 o C and the emissivity of the surfaces is C = 4.4.

Thus, when designing external fences with air gaps, the following must be taken into account:

1) increasing the thickness of the air layer has little effect on reducing the amount of heat passing through it, and layers of small thickness (3-5 cm) are effective in terms of heat engineering;

2) it is more rational to make several layers of thin thickness in the fence than one layer of large thickness;

3) it is advisable to fill thick layers with materials with low thermal conductivity to increase the thermal resistance of the fence;

4) the air layer must be closed and not communicate with the outside air, that is, the vertical layers must be blocked with horizontal diaphragms at the level of the interfloor ceilings (more frequent blocking of the layers in height has no practical significance). If there is a need to install layers ventilated by outside air, then they are subject to special calculations;

5) due to the fact that the main share of heat passing through the air layer is transferred by radiation, it is advisable to place the layers closer to outside fences, which increases their thermal resistance;

6) in addition, it is recommended to cover the warmer surface of the interlayer with a material with a low emissivity (for example, aluminum foil), which significantly reduces the radiant flux. Coating both surfaces with such material practically does not reduce heat transfer.

3. Reasons that cause a pressure difference to occur on one and the other side of the fence

IN winter time the air in heated rooms has a temperature higher than outside air, and, therefore, the outside air has a higher volumetric weight (density) compared to the inside air. This difference in volumetric air weights creates differences in its pressure on both sides of the fence (thermal pressure). Air enters the room through the lower part of its external walls, and leaves it through top part. In the case of airtightness of the upper and lower fences and when closed openings the difference in air pressure reaches its maximum values at the floor and under the ceiling, and at the middle height of the room is zero (neutral zone).

Thermal protection of facades with a ventilated air gap

Part 1

Dependence of the maximum speed of air movement in the gap on the outside air temperature at different meanings thermal resistance of walls with insulation

Dependence of air speed in the air gap on the outside air temperature for different values of the gap width d

Thermal resistance dependence air gap, R ef of the gap, on the outside air temperature at different values of the thermal resistance of the wall, R pr therm. design

Dependence of the effective thermal resistance of the air gap, R ef gap, on the gap width, d, for different façade heights, L

In Fig. Figure 7 shows the dependences of the maximum air velocity in the air gap on the outside air temperature at various values of the façade height, L, and the thermal resistance of the wall with insulation, R pr term. design , and in Fig. 8 - at different values of the gap width d.

In all cases, air speed increases as the outside temperature decreases. Doubling the height of the façade results in a slight increase in air speed. A decrease in the thermal resistance of the wall leads to an increase in air speed, this is explained by an increase in heat flow, and hence the temperature difference in the gap. The gap width significantly affects the air speed; with decreasing values of d, the air speed decreases, which is explained by an increase in resistance.

In Fig. Figure 9 shows the dependences of the thermal resistance of the air gap, R eff gap, on the outside air temperature at various values of the façade height, L, and the thermal resistance of the wall with insulation, R pr therm. design .

First of all, it should be noted that the gap Reff has a weak dependence on the outside air temperature. This is easily explained, since the difference between the air temperature in the gap and the temperature of the outside air and the difference between the temperature of the internal air and the air temperature in the gap change almost proportionally with a change in t n, so their ratio, included in (3), almost does not change. Thus, when tn decreases from 0 to –40 °C R, the gap efficiency decreases from 0.17 to 0.159 m 2 °C/W. The R eff of the gap also insignificantly depends on the thermal resistance of the cladding, with an increase in R pr term. region from 0.06 to 0.14 m 2 °C/W, the R eff value of the gap changes from 0.162 to 0.174 m 2 °C/W. This example shows the ineffectiveness of insulating facade cladding. Changes in the value of the effective thermal resistance of the air gap depending on the outside air temperature and the thermal resistance of the cladding are insignificant for their practical consideration.

In Fig. Figure 10 shows the dependences of the thermal resistance of the air gap, Reff of the gap, on the gap width, d, for different values of the façade height. The dependence of R eff of the gap on the width of the gap is most clearly expressed - as the thickness of the gap decreases, the value of R eff of the gap increases. This is due to a decrease in the temperature setting height in the gap x 0 and, accordingly, with an increase in the average air temperature in the gap (Fig. 8 and 6). If for other parameters the dependence is weak, because there is an overlap various processes partially extinguishing each other, then in this case this is not the case - the thinner the gap, the faster it warms up, and the slower the air moves in the gap, the faster it heats up.

In general, the most higher value R eff of the gap can be achieved with a minimum value of d, a maximum value of L, a maximum value of R pr term. design . So, at d = 0.02 m, L = 20 m, R pr term. design = 3.4 m 2 °C/W the calculated value of R eff of the gap is 0.24 m 2 °C/W.

To calculate heat loss through the fence, the relative influence of the effective thermal resistance of the air gap is of greater importance, since it determines how much heat loss will be reduced. Despite the fact that the largest absolute value of R eff gap is achieved at maximum R pr term. design , the effective thermal resistance of the air gap has the greatest influence on heat loss at the minimum value of R pr therm. design . So, at R pr term. design = = 1 m 2 °C/W and t n = 0 °C due to the air gap, heat loss is reduced by 14%.

With horizontally located guides to which the facing elements are attached, when carrying out calculations, it is advisable to take the width of the air gap equal to the smallest distance between the guides and the surface of the thermal insulation, since these areas determine the resistance to air movement (Fig. 11).

As calculations have shown, the speed of air movement in the gap is low and is less than 1 m/s. The reasonableness of the adopted calculation model is indirectly confirmed by literature data. So, in the work it is given short review results of experimental determinations of air speed in the air gaps of various facades (see table). Unfortunately, the data contained in the article is incomplete and does not allow us to establish all the characteristics of the facades. However, they show that the air speed in the gap is close to the values obtained by the calculations described above.

The presented method for calculating temperature, air speed and other parameters in the air gap allows us to evaluate the effectiveness of a particular design measure from the point of view of increasing the operational properties of the facade. This method can be improved, first of all, this should relate to taking into account the influence of gaps between facing slabs. As follows from the calculation results and experimental data given in the literature, this improvement will not have great influence on the reduced resistance of the structure, but it may affect other parameters.

Literature

1. Batinich R. Ventilated facades of buildings: Problems of building thermal physics, microclimate systems and energy saving in buildings / Sat. report IV scientific-practical conf. M.: NIISF, 1999.

2. Ezersky V. A., Monastyrev P. V. Fastening frame of a ventilated facade and the temperature field of the outer wall // Housing Construction. 2003. No. 10.

4. SNiP II-3-79*. Construction heating engineering. M.: State Unitary Enterprise TsPP, 1998.

5. Bogoslovsky V. N. Thermal regime of the building. M., 1979.

6. Sedlbauer K., Kunzel H. M. Luftkonvektions einflusse auf den Warmedurchgang von belufteten Fassaden mit Mineralwolledammung // WKSB. 1999. Jg. 44. H.43.

To be continued.

List of symbols

с в = 1,005 J/(kg °С) - specific heat capacity of air

d - air gap width, m

L - height of the facade with a ventilated gap, m

n k - average number of brackets per m2 of wall, m–1

R pr o. design , R pr o. region - reduced resistance to heat transfer of parts of the structure from the inner surface to the air gap and from the air gap to outer surface structures, respectively, m 2 °C/W

R o pr - reduced heat transfer resistance of the entire structure, m 2 °C/W

R condition. design - resistance to heat transfer along the surface of the structure (excluding heat-conducting inclusions), m 2 °C/W

R condition - resistance to heat transfer along the surface of the structure, is defined as the sum of the thermal resistances of the layers of the structure and the heat transfer resistance of the internal (equal to 1/av) and external (equal to 1/an) surfaces

R pr SNiP - reduced heat transfer resistance of a wall structure with insulation, determined in accordance with SNiP II-3-79*, m 2 °C/W

R pr term. design - thermal resistance of a wall with insulation (from internal air to the insulation surface in the air gap), m 2 °C/W

R eff of the gap - effective thermal resistance of the air gap, m 2 °C/W

Qn - calculated heat flow through a heterogeneous structure, W

Q 0 - heat flow through a homogeneous structure of the same area, W

q - heat flux density through the structure, W/m2

q 0 - heat flux density through a homogeneous structure, W/m 2

r - coefficient of thermal uniformity

S - cross-sectional area of the bracket, m 2

t - temperature, °C

Layers, materials (item in table SP)	Thermal resistance R i =  i/l i, m 2 ×°С/W	Thermal inertia D i = R i s i	Resistance to vapor permeation R vp,i =  i/m i, m 2 ×hPa/mg
Inner boundary layer
Internal plaster made of cement-sand. solution (227)
Reinforced concrete(255)
Mineral wool slabs (50)
Air gap
External screen – porcelain stoneware
Outer boundary layer
Total ()

* – without taking into account the vapor permeability of screen seams

The thermal resistance of a closed air gap is taken according to Table 7 SP.

We accept the coefficient of thermal technical heterogeneity of the structure r= 0.85, then R req /r= 3.19/0.85 = 3.75 m 2 ×°C/W and the required insulation thickness

0.045(3.75 – 0.11 – 0.02 – 0.10 – 0.14 – 0.04) = 0.150 m.

We take the thickness of the insulation  3 = 0.15 m = 150 mm (multiples of 30 mm), and add it to the table. 4.2.

Conclusions:

In terms of heat transfer resistance, the design complies with the standards, since the reduced heat transfer resistance R 0 r above the required value R req :

R 0 r=3,760,85 = 3,19> R req= 3.19 m 2 ×°C/W.

4.6. Determination of the thermal and humidity conditions of the ventilated air layer

The calculation is carried out for winter conditions.

Determination of movement speed and air temperature in the layer

The longer (higher) the layer, the greater the speed of air movement and its consumption, and, consequently, the efficiency of moisture removal. On the other hand, the longer (higher) the layer, the greater the likelihood of unacceptable moisture accumulation in the insulation and on the screen.

The distance between the inlet and outlet ventilation holes (the height of the interlayer) is taken equal to N= 12 m.

Average air temperature in the layer t 0 is tentatively accepted as

t 0 = 0,8t ext = 0.8(-9.75) = -7.8°C.

The speed of air movement in the interlayer when the supply and exhaust openings are located on one side of the building:

where  is the sum of local aerodynamic resistance to air flow at the inlet, at turns and at the exit from the layer; depending on the design solution of the facade system= 3...7; we accept= 6.

Sectional area of the interlayer with nominal width b= 1 m and accepted (in Table 4.1) thickness = 0.05 m: F=b= 0.05 m2.

Equivalent air gap diameter:

The heat transfer coefficient of the surface of the air layer a 0 is preliminarily accepted according to clause 9.1.2 SP: a 0 = 10.8 W/(m 2 ×°C).

(m 2 ×°C)/W,

K int = 1/ R 0.int = 1/3.67 = 0.273 W/(m 2 ×°C).

(m 2 ×°C)/W,

K ext = 1/ R 0, ext = 1/0.14 = 7.470 W/(m 2 ×°C).

Odds

0.35120 + 7.198(-8.9) = -64.72 W/m2,

0.351 + 7.198 = 7.470 W/(m 2 ×°C).

Where With– specific heat air, With= 1000 J/(kg×°C).

The average air temperature in the layer differs from the previously accepted one by more than 5%, so we are clarifying the design parameters.

Speed of air movement in the interlayer:

Air density in the layer

Amount (flow) of air passing through the layer:

We clarify the heat transfer coefficient of the surface of the air layer:

W/(m 2 ×°C).

Heat transfer resistance and heat transfer coefficient of the interior of the wall:

(m 2 ×°C)/W,

K int = 1/ R 0.int = 1/3.86 = 0.259 W/(m 2 ×°C).

Heat transfer resistance and heat transfer coefficient of the outer part of the wall:

(m 2 ×°C)/W,

K ext = 1/ R 0.ext = 1/0.36 = 2.777 W/(m 2 ×°C).

Odds

0.25920 + 2.777(-9.75) = -21.89 W/m2,

0.259 + 2.777 = 3.036 W/(m 2 ×°C).

We clarify the average air temperature in the layer:

We clarify the average air temperature in the layer several more times until the values at neighboring iterations differ by more than 5% (Table 4.6).

One of the techniques that increases thermal insulation qualities fencing is the device of an air gap. It is used in the construction of external walls, ceilings, windows, and stained glass windows. It is also used in walls and ceilings to prevent waterlogging of structures.

The air gap can be sealed or ventilated.

Consider heat transfer hermetically sealed air gap.

The thermal resistance of the air layer R al cannot be defined as the thermal conductivity resistance of the air layer, since heat transfer through the layer with a temperature difference on the surfaces occurs mainly by convection and radiation (Fig. 3.14). The amount of heat,

transmitted by thermal conductivity is small, since the coefficient of thermal conductivity of air is small (0.026 W/(m·ºС)).

In the interlayers, in general, the air is in motion. In vertical ones, it moves up along the warm surface and down along the cold one. Convective heat exchange takes place, and its intensity increases with increasing layer thickness, since the friction of air jets against the walls decreases. When heat is transferred by convection, the resistance of the boundary layers of air at two surfaces is overcome, therefore, to calculate this amount of heat, the heat transfer coefficient α k should be halved.

To describe heat transfer jointly by convection and thermal conductivity, the convective heat transfer coefficient α" k is usually introduced, equal to

α" k = 0.5 α k + λ a /δ al, (3.23)

where λ a and δ al are the thermal conductivity coefficient of air and the thickness of the air layer, respectively.

This coefficient depends on geometric shape and sizes of air layers, direction of heat flow. By generalization large quantity experimental data based on the theory of similarity, M.A. Mikheev established certain patterns for α" k. Table 3.5 shows, as an example, the values of the coefficients α" k, calculated by him at an average air temperature in a vertical layer of t = + 10º C.

Table 3.5

Convective heat transfer coefficients in a vertical air layer

The coefficient of convective heat transfer in horizontal air layers depends on the direction of heat flow. If the top surface is heated more than the bottom, there will be almost no air movement, since warm air concentrated at the top, and cold at the bottom. Therefore, the equality will be satisfied quite accurately

α" k = λ a /δ al.

Consequently, convective heat transfer is significantly reduced, and the thermal resistance of the interlayer increases. Horizontal air gaps are effective, for example, when used in insulated basement floors above cold undergrounds, where the heat flow is directed from top to bottom.

If the heat flow is directed from bottom to top, then ascending and descending air flows occur. Heat transfer by convection plays a significant role, and the value of α"k increases.

To take into account the effect of thermal radiation, the coefficient of radiant heat transfer α l is introduced (Chapter 2, clause 2.5).

Using formulas (2.13), (2.17), (2.18) we determine the coefficient of heat transfer by radiation α l in the air gap between the structural layers of the brickwork. Surface temperatures: t 1 = + 15 ºС, t 2 = + 5 ºС; brick blackness degree: ε 1 = ε 2 = 0.9.

Using formula (2.13), we find that ε = 0.82. Temperature coefficientθ = 0.91. Then α l = 0.82∙5.7∙0.91 = 4.25 W/(m 2 ·ºС).

The value of α l is much greater than α "k (see Table 3.5), therefore, the main amount of heat through the layer is transferred by radiation. In order to reduce this heat flow and increase the heat transfer resistance of the air layer, it is recommended to use reflective insulation, that is, covering one or both surfaces, for example, with aluminum foil (the so-called “reinforcement”). This coating is usually placed on a warm surface to avoid moisture condensation, which impairs the reflective properties of the foil. “Reinforcement” of the surface reduces the radiant flux by about 10 times.

The thermal resistance of a sealed air layer at a constant temperature difference on its surfaces is determined by the formula

Table 3.6

Thermal resistance of closed air layers

Air layer thickness, m	R al , m 2 ·ºС/W
for horizontal layers with heat flow from bottom to top and for vertical layers	for horizontal layers with heat flow from top to bottom
summer	winter	summer	winter
0,01	0,13	0,15	0,14	0,15
0,02	0,14	0,15	0,15	0,19
0,03	0,14	0,16	0,16	0,21
0,05	0,14	0,17	0,17	0,22
0,1	0,15	0,18	0,18	0,23
0,15	0,15	0,18	0,19	0,24
0,2-0.3	0,15	0,19	0,19	0,24

The values of R al for closed flat air layers are given in Table 3.6. These include, for example, layers between layers of dense concrete, which practically does not allow air to pass through. It has been experimentally shown that in brickwork if the joints between the bricks are insufficiently filled with mortar, a violation of the tightness occurs, that is, the penetration of outside air into the layer and a sharp decrease in its resistance to heat transfer.

When covering one or both surfaces of the interlayer with aluminum foil, its thermal resistance should be doubled.

Currently, walls with ventilated air gap (walls with a ventilated facade). A suspended ventilated façade is a structure consisting of cladding materials and a sub-cladding structure, which is attached to the wall in such a way that there is an air gap between the protective and decorative cladding and the wall. For additional insulation external structures, a thermal insulation layer is installed between the wall and the cladding, so that ventilation gap left between the cladding and thermal insulation.

The design diagram of a ventilated facade is shown in Fig. 3.15. According to SP 23-101, the thickness of the air gap should be in the range from 60 to 150 mm.

The layers of the structure located between the air gap and the outer surface are not taken into account in the thermal engineering calculations. Therefore, thermal resistance external cladding is not included in the heat transfer resistance of the wall, determined by formula (3.6). As noted in paragraph 2.5, the heat transfer coefficient of the outer surface of the enclosing structure with ventilated air layers α ext for the cold period is 10.8 W/(m 2 ºС).

The design of a ventilated facade has a number of significant advantages. In section 3.2, temperature distributions in cold period in two-layer walls with internal and external insulation (Fig. 3.4). A wall with external insulation is more

“warm”, since the main temperature difference occurs in the heat-insulating layer. No condensation occurs inside the wall, its heat-shielding properties do not deteriorate, and no additional vapor barrier is required (Chapter 5).

Air flow, which occurs in the interlayer due to a pressure difference, promotes the evaporation of moisture from the surface of the insulation. It should be noted that a significant mistake is the use of a vapor barrier on the outer surface of the heat-insulating layer, since it prevents the free removal of water vapor to the outside.

AIR GAP, one of the types of insulating layers that reduce the thermal conductivity of the medium. IN Lately the importance of the air gap has especially increased due to its use in construction hollow materials. In a medium separated by an air gap, heat is transferred: 1) by radiation from surfaces adjacent to the air gap and by heat transfer between the surface and the air and 2) by heat transfer by air, if it is mobile, or by heat transfer from some air particles to others due to thermal conductivity it, if it is motionless, and Nusselt's experiments prove that thinner layers, in which the air can be considered almost motionless, have a lower thermal conductivity coefficient k than thicker layers, but with convection currents arising in them. Nusselt gives the following expression to determine the amount of heat transferred per hour by the air layer:

where F is one of the surfaces limiting the air gap; λ 0 - conditional coefficient, the numerical values of which, depending on the width of the air gap (e), expressed in m, are given in the attached plate:

s 1 and s 2 are the emissivity coefficients of both surfaces of the air gap; s is the emissivity coefficient of a completely black body, equal to 4.61; θ 1 and θ 2 are the temperatures of the surfaces limiting the air gap. By substituting the corresponding values into the formula, you can obtain the values of k (thermal conductivity coefficient) and 1/k (insulating capacity) of air layers of various thicknesses required for calculations. S. L. Prokhorov compiled diagrams based on Nusselt data (see Fig.) showing the change in the values of k and 1/k of air layers depending on their thickness, with the most advantageous area being the area from 15 to 45 mm.

Smaller air layers are practically difficult to implement, but larger ones already provide a significant thermal conductivity coefficient (about 0.07). The following table gives the values of k and 1/k for various materials, and for air several values of these quantities are given depending on the thickness of the layer.

That. It can be seen that it is often more profitable to make several thinner air layers than to use one or another insulating layers. An air layer with a thickness of up to 15 mm can be considered an insulator with a stationary layer of air, with a thickness of 15-45 mm - with an almost stationary layer, and, finally, air layers with a thickness of over 45-50 mm should be considered layers with convection currents arising in them and therefore subject to calculation for general basis.