CC BY
9
Shchipachyova Elena Vladimirovna, doctor, of Engineering, professor, Tashkent Institute of Railway Transport Engineers Sharipova Dilafruz Toufukovna, research associate, external doctorate student, Tashkent Institute of Railway Transport Engineers
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ON THERMAL RESISTANCE OF EXTERNAL ENVELOPE OF BUILDINGS
Abstract: The article describes a new approach to the problem of assessing the heat resistance of building envelopes, based on an improved method for calculating heat conduction in multi-layered external envelopes, which takes solar radiation effect into account.
Keywords: heat conduction, thermal resistance, simulation, heat exchange, external envelope
Due to high temperature and solar radiation in summer, buildings in regions with a hot climate tend to overheat, which negatively affects the well-being and working
capacity of people. In order to achieve a favorable indoor climate, air conditioning and ventilation systems are widely used, consuming a significant amount of electrical energy. Optimization of energy consumption is achievable if we consider climatic environment, the building and its utilities as a unified energy system. A significant role in this system is assigned to rationally design external envelopes of the buildings, but this can only be done after a proper evaluation of their thermal stability.
On the basis of the theory of thermal stability, scientists have developed methods for calculating temperature variations in external envelopes subjected to periodic thermal effects, and approximate formulas have been derived for estimating the damping of temperature variations, thermal inertia, etc. However, the calculation formulas for estimating the thermal stability were obtained on the basis of a linear model of the nonstationary thermal conductivity process. In real conditions, when the composite body is heated by solar radiation and convection simultaneously, the boundary conditions are nonlinear, and for the solution of heat conduction problems in composite bodies, rigorous mathematical methods prove to be of little use. Therefore, in regions with a hot climate, choice of the material of the external envelope that meet the real conditions of optimum thermal resistance must be based on physical models of the heat conduction process in composite bodies, so the approach to solving heat conduction problems allows for analysis of the dynamics of the process. In this respect, the study considers one of the possible variants of constructing such a model.
The physical analogue of the heat exchange process in the external envelope was represented as a composite wall consisting of m layers between which thermal contact resis-
tances Rki is created that determine the temperature difference in the contact zone. In the case of an ideal contact at the joint of the layers, the temperatures of the contacting surfaces will be the same. The coefficients of thermal conductivity \ and thermal diffusivity a. (i=1,2,..., m) of the individual parts of the envelope that were assumed as constant.
In conditions of arid hot climate with a long hot period, the heat flux on the heat-sensing surface is expressed by the nonlinear function of the temperature of the chosen surface. The physical phenomena occurring at the same time are described simultaneously by the Stefan-Boltzmann law
i T
E = £■ cn
T
V 100 y
(1)
where: E [W/m2] - is the heat flux density of the body; ^ = 5.67 [W/(m2-K4)] blackbody coefficient; s= JQX / Jx - emissivity factor, where JQl \W / m2 jj - blackbody intensity, Jx |W / m2 jj - gray body intensity; T[°K] - absolute temperature and Newton-Richmann law
dQ = a•(ts -ta)• dF• dr, (2)
where: heat-exchange coefficient, W/m2K; t - temperature of surface, °C; ta - ambient temperature, °C; dF-heat-conduc-tion area, m2; dz - time, s.
The nonlinearity of the system of equations describing heat conduction arises from the significant influence of solar radiation, i.e. in the summer. The solution of the problem of radiation-convective heat conduction in composite bodies, when the ambient temperature Ta (t ) and the heat flux density of the total solar radiation Ja ( ) are periodic functions of time, is given for the so-called quasistationary state. With a reasonable degree of accuracy, we assume that the inertia of the process is low, i.e. the previous duration of heat exchange is so great that the influence of the initial temperature distribution is no longer manifested.
ON THERMAL RESISTANCE OF EXTERNAL ENVELOPE OF BUILDINGS
The nonstationary temperatures inside a multilayer external envelope are described by the differential heat-conduction equation [1]
dT d2T . t „
-yL = al —2-, i = 1,2,...m, (3)
dx dx
Initial
T = T (x ),T = 0 (4)
and edge conditions on internal surface
-¿1 ^ - am (Tn - Ti ), x = 0, (5)
and also conjugating conditions of joint layers
dT I, -T
dx
R
= 1.
T
dx
X = X:
(6)
and, finally, the boundary conditions on the external surface:
^m = qk + qrad + qrad ,am , X = Rm •
dx
The densities of the heat fluxes in the right-hand side of equation (7) characterizes the amount of heat produced by the surface of the structure due to convection
qk = a ex [_Tc Tm ] ,
as a result of the absorption of solar radiation
qrad = PQ (T) ,
and also due to radiant heat exchange with the "ambience"
qrad am
The most difficult task is to determine the resulting radiation g , between the envelope and the ground, between the
-¿rad, am L o '
envelope and nearby buildings and structures, between the envelope and the "sky".
To reconcile the theoretical and experimental results, we will use for the vertical walls the dependence of qmdam on temperature T[2]:
qradam = Ssf °0 [Tc ) - Tm ] , (8)
Where S^ - is the blackness degree between the surface of envelope and the "ambience".
To reduce the number of parameters and construct the design scheme in the most general form, we represent the system of equations (3) - (7) in generalized dimensionless variables:
6) imperfect contact
ß = ß + 2AFN
Uni F +AF0 Uni ,F„ ^ L
H
ß =ß + 2AFN
Unt +1 ,F0 + AF0 Uni +1 ,F0
Bii ((+
Bi, ( ß
ki \ n ,
da t d2o
—L = A—f
dFn 1dX2
i = 1,2,...m
X = X
(3fl)
(4a) (5a)
(6a)
(7a)
In the scheme:
T *
0 = —- - dimensionless temperature, T - scale of ad-
Tx justment to dimensionless value; X =-- dimensionless
Rm a t
coordinate, Rm- multiple-layer wall thickness; F 0 —
R „,
0, =a (X ) Fo = 0 , -A d0 = Bin, (-Ol ) X = 0,
Lt0 = Bki (0j+1 -o) = 0 1 dx kiV i+1 l) dX
a = Bi 0(F0)-0,] + Ki(F0) + Sk0 (F0)-0m].
Fourier number, T - time; Bi =
in
R
aR
Bi = aexRm
Biot number; Bikj =
4+iRki
K ^m
- dimensionless parameter in-
cluding the value of the thermal resistance R at the contact surface of i and i + 1 layers, characterizing the intensity of heat exchange in the place of contact of the individual layers of the structure;
Ki = PQRm - Stark number; Ai = ^, L =
a A:.,,
m 1 i+1
Analysis of existing solution procedures showed that the most acceptable method for solving system (4a) - (8a) is the differential method [3, 4]. Of the numerous approaches to the implementation of differential schemes, the method of "elementary balances" proposed by A. P. Vanichev [3] was chosen, and the method developed by G. I. Marchuk [4] -"splitting" the composite body into homogeneous elements. As a result, the difference equations approximating the heat conduction problem under consideration (3a) - (7a), depending on the location of the calculated point, have become:
1. Calculated point is inside i layer
OF0 +AFo = O,Fo + AFoN2(6n-1,F0 - 26n,Fo + AO„^ (9)
2. Calculated point is on the border of i and (i + 1) layer (n=n) under:
a) perfect contact
2AFN2 -
°nt F +AF0 °n-t F +'
1 + K
K (0
i v n
(0 c — 0 c
iV ni—1,F0 ni+1>F0
; (10)
ß ,F0 )-NL, (ß ,F0 -ßn.-i,F0 )
"ßn. +1,F0 )-Nq, ( +i,F0 -ßn.+2,F0 )
(11)
3. Calculated point is on the external surface (n = nm)
втЛ+AF« в +2AF0Nja {BiEX
0M-в,.,* +Ki(F o0+sk
-2AF0N (в, F -вп F
0 V nm,F0 nm-l,F0
4. Calculated point is on the internal surface (n = 0)
O0F +AF0 O0,F, +
2AF0N2( O)-2^FNBim(0 -On).
In the above equations:
AFN2 + F0BiexN = At.
). (12)
(13)
(14)
* ~'> K, = ; a V a
n = z
j=1
X. - X. ,
j j-1.
AX.
AX, = —; AX. = AX, P. 1 N ' W a
The solution convergence rate of the differential equations to a given accuracy and the stability of the solution depend on the magnitude of the time increment. In the equation of heat conduction, as a result of the numerical experiments carried out, equality is obtained, according to which an optimal time increment is calculated that ensures high convergence and
Using numerical method At = 0,25. was obtained.
A software complex has been developed with accordance to the above-mentioned difference scheme of problem solving. Taking into account that single-layer and two-layer constructions of external walls were found most widely in civil engineering, the processes of non-stationary heat conduction in structures of this type were subjected to numerical simulation. Single-layer walls made of brick, and five versions of multi-layered envelopes, differing in the material of the bearing layer and the type of insulation, located on the outside of the wall were considered (Table).
stability of solutions:
Table - External wall constructions and their thermal resistances
Variation number Bearing layer Insulation layer R, m2-K /W
material type thickness, m material type thickness, m
I clay brick 0.38 - - 0.71
II reinforced concrete 0.03 expanded polystyrene 0.09 1.991
III reinforced concrete 0.03 autoclaved aerated concrete 0.140 1.591
IV clay brick 0.38 slag wool 0.08 0.844
V clay brick 0.38 fiberglass 0.1 2.417
VI expanded-clay concrete 0.30 Slag wool 0.07 1.276
The numerical calculations and their comparison with full-scale measurements on single-layer and double-layer structures showed high correlation coefficients of 0.989 and 0.969, respectively. This allows us to assume that the developed simulation sufficiently reliably describes the real processes of thermal conductivity in the single-layer and double-layer external envelopes of the buildings.
In addition, the calculated temperatures on the inner surface of the envelope of the buildings, considering the three components of radiation (convective, radiation and "ambience") turned out to be higher than those calculated according to the standard procedure, which means not taking them into account
causes a systematic underestimation of temperatures during the day. Comparative estimates of the temperature field of the external envelope, calculated by the developed and standard methods, showed that the greatest discrepancy in the damping values of the calculated amplitude of temperature fluctuations is observed in the VI type of external envelope and is 32%.
Therefore, a new approach to assessing the heat resistance of external envelopes of the buildings, based on the method for calculating heat transfer in multilayer external envelopes, taking into account the effect of solar radiation, will allow optimizing the design of envelopes, including the choice of insulation material.
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