18-20 June, 2003, Budapest, Hungary OSSKI Center (Törley Palace)

with Exhibition and Pre-Session on Thermal Energy in Hungarian
"THERMO-BRIDGE"
between East and West for technology transfer and information exchange

Heat bridges are the connection between the inside of house and outside that provide insulation (In some countries, it is known as cold bridge or thermal bridge). These bridges are formed on the place of especially open outside air's contacting area of inside of house by using different materials.
Balcony, direct lengthening ground can be given as an example. Heat loses is seen on the bridges from one point to another point however, this condition is unimportant and is also safe. Lengthening walls and balconies usually gives problem and should be avoid of them.
Heat bridges do not usually take into consideration for heating needs or cooling needs. However, in some special cases, heat bridges can be more effective for heat loss or heat gain. In these cases ISO 6946/2 norms are based related to heat bridges.
Buildings data for heating should be known or reasonable assumptions should be done appropriate to operating conditions. If given data for energy needs and methods are not accepted then some benefit can be take from VDI 2067 and VDI 3808 specifications, [1].

ISO (International Organization for Standardization) and IEC (International Electro technical Commission) are the associations that work according to Switzerland law. Every country has the possibility of being connection to ISO and IEC establishments and each country also uses their own national standardization institutes. 132 countries are registered to ISO establishment and 55 countries are registered to IEC establishment, [2]. Insufficient developed countries are using direct international standards.
In Turkey, TS 825 "Rules on Thermal Insulation of Buildings" are used for heating energy needs at buildings. TS 825 uses the standards of "EN 832 - Thermal Performance of Buildings, - Calculation of Energy Use for Heating, Residential Buildings" and "ISO 9164 - Thermal Insulation, - Calculation of Space Heating Requirements for Residential Buildings" [3]. Determination of heat loses forming at heat bridges, TS 825 uses the standards of TS 8441 that is based on ISO 6946/2 (Thermal Insulation - Calculation Methods Part 2, thermal bridges of rectangular sections in plane structures), [4]. This standard suggests the simple calculation method for only heat bridges forming combined column / wall.
According to the TS 825 and TS 8441, U_l,  heat bridge linear heat transmissivity value should be calculated for heat bridge elements. For this, b: the length of heat bridge, U_1k : heat transmissivity of heat bridge and  ξ : characteristic factor of heat bridge, then U₁ can be calculated as;

In Germany, evaluation and calculation of heat bridges, and corner factors are used. In England rules, heat bridges and pointing layer is taken into consideration. According to the Turkish and Europe standards, while investigating the thermal performance of heat bridges on the buildings,U₁ value is to be calculated, [5], [6]. Heat loses due to heat bridges makes 15% increment on the U value, [7]. In the practice, concrete floor and floor sidewalls heat losses Q are taken as zero and this is very important fault. For the insulation project that is non-defined floor thickness by not evaluating separately heat losses forming on the floor will cause the wrong calculation.
In the present study, and more appropriate results are aimed to find according to the suggesting calculation method by using the numerical methods. Especially, surface temperature and heat transfer changing on forming different heat bridges are modeled theoretically and simulations of them are also carried out. Thus more appropriate results are given depending on different conditions and seasons.

Heat bridges can be thought as the heat transfer problem with steady state and two-dimensional. There are two important aims to solve heat conduction problem for any system. First aim is to find out temperature distribution in the system. Here, T(x,y) temperature area will be determined for considered heat bridge. Second aim is to determine q_xand q_y. heat flux components and q heat flux vector in the direction
of x and y In the present study, problem is solved numerically by using the finite element method. Following section gives some detail of the finite element method and some information about used software program are given.
Quickfield V 4.2T version can be downloaded from the internet free (www.quickfield.com/free.html). Used program is limited with 200 nodes. With this program, to find the heat distribution in any section below requirement would be need for two-dimensional calculations.
1 - First of all drawing is required. This can be imported from other drawing programs such as Auto-cad.
2 - Thermal conductivity of solid body
3 - Surface boundary conditions (Convection, radiation or heat flux).

Boundary conditions are given at below that were used in quick field software program.
- Thermal conductivity of concrete k=2.1 W/mK
- Thermal conductivity of Brick Wall k=0.4 W/mK
- Thermal conductivity of Insulation Material k= 0.04 W/mK
- Heat Transfer coefficient of inside and outside wall were taken as 7 W/m²  K and 20 W/m²  K respectively.
- No heat generation, two dimensional, steady state and constant thermal conductivity and heat transfer coefficient conditions are assumed for the calculations.

There are many practical engineering problems, which we cannot obtain exact solutions. This inability to obtain an exact solution may be attributed to either the complex nature of governing differential equations or the difficulties that arise from dealing with the boundary and initial conditions. To deal with such problems, numerical approximations are resorted.
The finite element method that is widely used engineering problems in recent years overcomes the difficulty of the variational methods because it provides a systematic procedure for the derivation of the approximation functions. The method is endowed with two basic features, which account for its superiority over other competing methods. First, geometrically complex domain of the problem is represented as a collection of geometrically simple sub-domains, called finite elements. Second, over each finite element the approximation functions are derived using the basic idea that any continuous function can be represented by a linear combination of algebraic polynomials. The finite element method can be interpreted as a piecewise application of the variational methods, in which the approximation functions are algebraic polynomials and the undetermined parameters represent the values of the solution at a finite number of preselected points, called nodes, on the boundary and in the interior of the element
If solution domain is divided element number of N which contains grid number of r, Temperature gradient in an element with shape functions can be written as;

If minimum potential energy method is applied to heat diffusion equation, below equation can be written;

General equation and element equations as matrix can be defined as;

Matrix and vectors in Equation 4 can be written as;

: Element conductance matrix, , : Element conductivity matrix

Figure 1 shows heat bridge that has different wall insulation. Inside and outside ambient temperatures are given as 20^oC, 0^oC respectively, resulting of it inside wall surface temperature values change between 17.7^oC and 13.5^oC . As can be seen from Figure 1c, wall heat flux value could be about 15-20 W/m²  however it is obtained that heat flux value becomes higher about 50-80 W/m2 from the corner forming heat bridge.
Figure 2 shows the same boundary and wall condition as given in Figure 1, but junction of two-wall corner side is made with heat bridge isolation. As can be seen that surface temperature becomes higher and heat transfer to the outside decreases. Especially As seen in Figure 2c, heat flux value becomes less than 30 W/m² , it means that heat flux value becomes closer to the wall heat flux value.
Heat bridge example forming at building corner column is given in Figure 3. Inside and outside temperatures are given as 20^oC, 0^oC respectively. When comparing the heat bridge surface temperature with inside temperature, less inside wall surface temperatures is seen, from this it can be said that higher heat transfer would be occurred. It was obtained that when wall heat flux value is about 20 W/m² however heat flux value on heat bridge surface is obtained as value of about 75-85 W/m² .
Figure 4 shows similar heat bridge example as given in Figure 3. But heat bridge is thought as outside corner for heating condition. Heat bridge surface temperature values are about 9,3^oC with 13,2^oC  but wall surface temperature value is 18.4^oC that is rather different. Heat flux values from heat bridge outside surface is nearly 30 and 65 W/m² however wall heat flux is seem to less then 20 W/m².

Figure 1 Model 1, (a) Construction, (b) Temperature Contours, (c) Heat Flux Vectors

Figure 2 Model 2, (a) Construction, (b) Temperature Contours, (c) Heat Flux Vectors

Figure 3 Model 3, (a) Construction, (b) Temperature Contours, (c) Heat Flux Vectors

Figure 4 Model 4, (a) Construction, (b) Temperature Contours, (c) Heat Flux Vectors

[1] "Enerji Ihtiyaci Bilgisayar Programi Kullanim Kilavuzu" Izocam Tic. ve San. A. S.
Prof. Dr.-Ing. H. WERNER' Telif Hakkina sahiptir. CEN/TC 89 kodlu Avrupa Standardi.
[2] CHZAGOS, HÜTTE, Die Grundlagen der Ingenieurwissenschaften, 31. Auflage. SPRINGER Verlag, BERLIN, 2000.
[3] TSE 825, Binalarda Isi Yalitimi Kurallari, 1989.
[4] TS 8441/Nisan 1990, UDK 699.86.001.24 "Isi Yalitimi Hesaplama Metotlari-Düzlem Yapi Yüzeylerinde Dikdörtgen Kesitli Isi Köprüleri" "Thermal Insulation-Calculation Methods-Parts 2: Thermal Bridges of Rectangular Section in Plane Structures" TSE Ankara,1990.
[5] Schoch, T. "Die neue Energie-Einsparverordnung" Druck-und Verlagshaus Chemielorz GmbH, Ostring 13, 65205 Wiesbaden-Norderstadt, 1. Auflage Februar 2002
[6] EnEV1- Energieeinsparverordnung-vom 16.Nov.2001, Teil Nr 59, "Verordnung über energiesparenden Vaermeschutz und energiesparende Anlagentechnik bei Gebaeuden"
Insb. Abschnitt 2, zu errichtende Gebaeude, § 6 "mindestwaermeschutz, Waermebrücken".
[7] Binalarda Isi Yalitim Yönetmeligi, Bayindirlik ve Iskan Bakanligi, Resmi Gazete, 08.05.200, Nr. 24043.

.

OSSKI Center (Törley Palace)
"Fodor József" National Center of Public Heath
"Frédéric Joliot-Curie" National Research Institute for
Radiobiology and Radiohygiene. (OKK-OSSKI)
www.osski.hu