Isı köprüleri
Thermal bridges
Yazar: OZAN NAKIOĞLU
Danışman: PROF. DR. ALPİN KEMAL DAĞSÖZ
İstanbul Teknik Üniversitesi / Fen Bilimleri Enstitüsü / Makine Mühendisliği Ana Bilim Dalı / Enerji Bilim Dalı
Derece: Yüksek Lisans, 1997
Konu: Makine Mühendisliği = Mechanical Engineering
Dizin: Isı köprüsü = Thermal bridge

Özet:
Isı, köprüleri üzerine yapılan çalışmaların sayısı az olduğundan, bu çalışmada, öncelikle ısı köprüsü ile ilgili kavram ve terimlerin oturtulması amacıyla, hesaplarda ve anlatımda kullanılan kavram ve terimlerin tanımlarına yer verilmiştir. Isı köprülerinin oluşum nedenlerine göre ve şekillerine göre sınıflandırılması yapılmıştır. Bu çalışmada özellikle ısı köprülerin hesaplanmasına ait yöntemler üzerinde durulmuştur. Hesap yönteminde öncelikle ısı köprüsünün geometrik bir modeli oluşturulur. Geometrik modelin oluşturulmasında ölçülerde ve malzemelerin ısı iletim katsayılarında bazı ihmaller ve düzeltmeler yapılır. Hesap sonucunda, ısı köprüsünün ifadesinde ve hesabında kullanılacak ısı köprüsünün ısıl iletim değeri (L) ve sıcaklık etki faktörleri (g) bulunur. Belli bir konstruksiyon için bulunan bu karakteristik değerler ile o konstruksiyonun farklı dış sıcaklıklardaki ısı kaybı ve en düşük yüzey sıcaklığı hesabının yapılması olanaklıdır. Isı köprüsünde öncelikle ısı köprüsü söz konusu olan bölgeden olan ısı kaybı ve bu bölgede ortaya çıkan minimum iç yüzey sıcaklıklığı önem kazanır. Bu bölümde ayrıca konstruksiyondaki sıcaklık dağılımı hesabının yapılabilmesi için sayısal yöntem önerilmiştir. Isı köprüsü etkisinin ortaya çıktığı her farklı konstruksiyon için farklı bir sıcaklık dağılımı söz konusudur. Bu nedenden ötürü her tip ısı köprüsü için farklı bir L ve g değeri bulunacaktır. Bu değerlerin bulunması için de her konstruksiyon için belli sınır şartlarında sıcaklık dağılımı hesabının yapılması gerekecektir. Bu işlemin de tek boyutlu ısı iletimi hesabına göre daha fazla zaman gerektirdiği açıktır. Bu sebepten dolayı ısı köprüsünün sık karşılaşıldığı belli konstruksiyonların kapsandığı ısı köprüleri katalogları oluşturulması gerekecektir. Böylece ısı kaybı hesaplanan bir yapının ısı köprüsü ortaya çıkan bölgeleri için her seferinde yeniden ısıl iletim değerleri ve sıcaklık etki faktörleri bulunmasıne gerek olmayacaktır. Son bölümde, ısı köprüsü ortaya çıkan yapı konstruksiyonların görülen özel etkiler üzerinde durulmuştur. Bu etkilerin özellikle yapının ilk planlanması aşamasında göz önüne alınması gereklidir. Böylece yapıda ısı köprüsü etkilerinin görülebileceği bölgeler önceden tahmin edilip gereken konstruktif önlemler alınabilir.

Abstract:
Novadays, the exact calculation of the heat losses in buildings became more important. Because the need for energy is increasing and energy expenses are getting always higher. In order to calculate the heat losses precisely, heat loss from the thermal bridges should also be taken into consideration. Generally, thermal bridges have two important physical effects. If a thermal bridge occurs in a construction the heat flux will be effected. Secondly, the surface temperatures will decrease at the places where thermal bridges appear. A thermal bridge is the part of the outer skin of a construction where the heat flux vector is not perpendicular to the surfaces of that construction part because of 3 reasons: a) Thermal conductivity of the materials of the construction can be different. b) The change of the thickness of a part of the construction. c) The difference between the sizes of the areas of the inner and outer surfaces of the construction. Thermal bridges can be classified according to the reason why they appear and according to the shape of them. Accoring to the reason of the appearance: a) Geometry of the construction: Examples of this type is the wall corners, or edges. b) Material of the construction: They occur because of the high thermal conductivity of a material in a construction. Concrete coloumns or fixing elements can be mentioned as an example of this type. c) Fluid flow: Fluid with a low temperature which flows through the construction can cause that changes in the temperature distribution of the solid construction around this area. Cold water pipes in the walls in a building is an example of this type. XId) Locally different air temperatures: The surface temperature or air temperature can be high or low around a certain place. The surfaces behind the heaters will be a thermal bridge, because the temperatures behind the wall heaters are higher than the surface temperatures at the rest of the surface. According to the shape of the thermal bridge there are two types: Linear or point shaped. The procedure of the calculation of the thermal bridges begins with the help of a model of the construction. The thermal bridge part of the construction will be separated with planes from the other parts of the building. In order to simplify the model and its properties, the dimensional deviations of the model can be corrected. For nonhomogeneous materials, equivalent thermal conductivity coefficients can be considered. The number of the conductivity coefficients of a thermal bridge depends on the number of the rooms which surrounds the thermal bridge. There is no difficulty for the calculations of one dimensional case. But if a thermal bridge occurs, there will always be 2 or 3 dimensional heat flux at the construction. Because of the multidimensional heat flux the surface temperatures will depend on the location. The location of the minimum surface temperature is important, because the risk for condensation is high at this location. But the place of the minimum will not change if the air temperatures changes. Let us consider a construction which has more than one boundary to the different rooms with different air temperatures. If the air temperatures are given, we can calculate the temperature distribution of the construction. With the help of the assumptions, there is no heat generation in the construction, the construction is in steady state, the physical properties in the construction does depend on temperature, the following linear and homogen differential equation can be found. div (k. grad 8) = 0 (1) Equation (2) gives the third type of boundary condition with the known room temperatures 8i (i=l,2,..m) and heat transfer coefficient hj. (k-grad6)-n+hi-e = hi.0i (2) If there is no heat transfer at the boundary equation (3) can be used. XII(k-grad9)n = 0 (3) Equation (1) has special solutions which will be called as "base solutions" -gj(x,y,z), j=l,2,..m- and be found with boundary conditions. All solutions can be obtained with base solutions. A base solution can be defined with the assumption that a boundary air temperature is 1 and the other boundary temperatures are 0. We can write the base solution for boundary conditions as follows: -> (k-grad gj)-n+hi ?gi = h^ (4) Where Sij is Krönecker symbol and has the value 0 Only if i=j, 8jj has the value of 1. If we express the temperature distribution as the linear combination of base solutions we obtain: e(x,y,z) = £6j-gi(x,y,z) (5) j=0 The base solutions gj(x,y,z) have no dimension. Equation (5) shows that the temperature at a known place in the construction is the sum of the surrounding air temperatures with g factors. If we assume that all of the air temperatures are equal, we find the equation (6); because in this case the whole temperatures in the construction will have the same value. £gj(x,y,Z) = l (6) The g values can be found if we know the temperature distribution in the construction. The second important definition for a construction in which thermal bridge appears is Ly thermal conduction coefficient of the bridge. After finding the temperature distribution at the inner surface, the total heat flux which goes through this area of construction can be found with equation (7). Qtop=J(Öi-e*)hi.dA (7) After finding the total heat flux with equation (8) L;j values can be found. XlllFor almost every construction minimum surface temperature appears at the surface which belongs to thermal bridge part of the building. In this region there is a risk for condensation. If the condition in the equation (9) is satisfied, there will not be condensation risk for that construction part. 6*..> ft mm "^ °yoğ 8yoğ depends on the humidity ratio in the room. (9) Numerical methods allow us to find the temperature distribution. The governing differential equation can be casted in discretization equation for two dimensions as given below. Control Volume Figure 1 Control volume for two-dimensional situation. aP -ep = aE -9E +aw -0W +aN -9N +as -9S +b ke-Ay (5x)6 ' (10) (Ha) aw _ kw-Ay (lib) aw - kn-Ax N (6y)n ' (lie) as - ksAx (5y)s ' (lid) aP=aE+aw+aN+as-qs-Ax-Ay, (He) b = qc-Ax-Ay (llf) These equations can also be used for the materials with different xivthermal conductivities, k values are interface conductivities between two grid points. To solve the discretization equations, first the grid point cluster should be formed and these equations should be written for every grid point. The equations are to be solved with line by line or alternating direction implicit method which are explained in numerical analyses books [8,9]. Because of the reason that for every dissimilar construction occurs different temperature distribution, different L and g values should be found in every construction. In order to find L and g, the temperatures in the construction should be calculated with numerical methods. This situation do not allow for every user to find L and g easily. For this reason, thermal bridge example catalogs should be published. Even in a construction part that seems to be without a thermal problem a thermal bridge effect can appear. There are also special thermal bridge effects. These effects should be taken into consideration before beginning to plan a building. The negative effects of the thermal bridges can be expressed in three points. a) Increase in the heat losses, b) Decrease of the living comfort in the building, because of low surface temperatures, c) Condensation risk at the inner surfaces because of low surface temperatures. For these reasons the following negative conditions occur in the building. a) Undesired bad appearance of room walls because of the dust gathering on condensated surfaces. c) Sponge formation due to the moisture and its spoiling the hygen conditions. d) Decrease in strenght in contruction parts. e) Decomposition of construction parts due to the corrosion and freezing. f) Decaying of materials such as wall paint, polish, plaster etc. g) Increasing heat loss and decrease in the benefit with applied insulation material due to increase in thermal conductivity coefficients of the materials because of changes depending on temperature. xv