The model of unsteady energy transfer through, outside and inside building elements has been developed [1]. In order to reduce the number of variables to a level that allows different design options of a room to be compared in a meaningful way it has been useful to make some simplifications. A fixed room size (16 m2) and room temperature requirement (constant in time and space, equal to 200C) have been assumed. The model of unsteady energy transfer outside, through and inside the wall has included heat conduction and heat capacity of wall elements, heat convection with indoor and outdoor room surrounding, and radiation exchange between indoor and outdoor room surrounding and the wall. Solar radiation absorption and reflection on wall surfaces, and the effects of orientation and inclination on them have been considered.

The energy balance of a room includes energy transferred through opaque and transparent elements, including direct transfer of solar energy through windows, energy needed for ventilation, and energy supplied by the internal heat sources. It has been assumed that energy supplied by the heating/cooling system (HVAC) is treated as internal heat source. According to assumption made, the indoor temperature is constant in time and space. It means that HVAC system operates all the time providing required (by the constant indoor temperature) heating or cooling energy. The mathematical model developed has been used for numerical simulation using Matlab as the programming language. It allows many cases of different location of rooms to be evaluated. Selected results of simulation studies of attic rooms are presented in Fig. 5-8. Figures 5-8 present distribution of heating/cooling demands for the whole averaged year (averaged curves for every month) with the south and north inclined envelope with small and big windows, respectively.

For the south orientation the maximum hourly cooling demand is at noon in July and August and for a room with the small window it is about 1,3 MJ and with the big window it is about 5,5 MJ. There is no cooling demand from November till January for the room with the small window. Apart from these months during a day time there is need for cooling. Duration of cooling mode depends on the month of the year and depends on solar irradiance and ambient temperature. For the room with the big south window all year round during day time there is need for cooling (different number of hours of operation of the cooling system for different months). In winter there is heating demand with maximum early in the morning (about sunrise) in January and it accounts to 0,8 MJ/h for the room with the small window and to 1,8 MJ/h for the room with the big window.

For the north orientation the maximum hourly cooling demand is at noon in July and June and for a room with the small window it is about 0,7 MJ/h and with the big window it is about 2,8 MJ/h. There is no cooling demand from October till March for the room with the small window. In the rest of the year during a day time there is need for cooling, the duration of cooling mode depends on the month of the year (because of the level of solar irradiance and ambient temperature). For the room with the big south window there is no need for cooling from October till February, during the rest 8 months the cooling mode exists with different operation time. In winter there is heating demand with maximum early in the morning (about sunrise) in January and it accounts to more than 0,8 MJ/h for the room with the small window and to 1,8 MJ/h for the room with the big window.

It is evident that night heating demands are resulted from the ambient temperature fluctuation. Heat losses are mainly through windows. Opaque walls have the designed thermal capacity. Heat stored during day time influences indoor climate in the night. During day time the influence of solar radiation and energy transferred through windows is evident. Solar radiation causes need for cooling in summer and reduces heating demand in the rest of the year. Solar gains could be so high that there is no need

for heating for a few or several hours per day. It is remarkable that shapes of curves of solar radiation through windows (Fig. 1-4) are similar to curves of energy demands (Fig. 5-8) during the day time.

Fig. 5. Distribution of daily heating/cooling energy demands for all months, south room with small window

x 106 Heat balance of the room, with X = 0.52, Beta= 45, Gamma = 0 Xt = 2Yt = 2

2. Conclusions

Figures 5-8 show daily distribution of energy required per hour to meet the heating/cooling demands of the rooms under consideration. Table 1 presents the sums of seasonal heating/cooling demands in the form of seasonal energy indexes (energy required to meet heating/cooling demands for the whole heating or cooling season with regard to 1 m2 of the room floor area). The space heating energy consumption indexes are below limits given by national standards (72,5 kWh/(m3a)). No regulations exist for space cooling indexes, however, it is evident that they are very high and limits for space cooling should be introduced as soon as possible.

Other results of simulation studies show that cooling season for south, east and west oriented attic rooms (floor area 16 m2, external wall area 12 m2, 3 layers, Uwall= 0,3 W/m2K, window — 4 m2, Uwin=1,6 W/m2K) lasts 8, 6 and 6 months and the cooling demands are about 5500, 3800, 3300 MJ per season respectively. The heating season for the same rooms lasts 4, 6 and 6 months and the heating demands are about 2000, 2700, 3000 MJ per season respectively. In all cases cooling demand is higher than heating demand, for the south room even nearly three times, which is surprising for high latitude country (Warsaw 520 N).

It appears that overheating in summer due to high solar irradiation and energy transmitted and absorbed in glazing can be a real problem for rooms in attics. To assure stable indoor thermal comfort of rooms in attics (mainly to avoid overheating, according to the assumptions made in the model), i. e. to keep a constant temperature in the rooms under consideration, it is necessary to use shading, e. g. external blinds. If no shading is applied then air-conditioning systems, which are usually electrically driven and consume a lot of primary energy, must be used. Of course there is one simple conclusion: not use the attic spaces for living spaces.

References

[1] D. Chwieduk, (2006). Modelowanie i analiza pozyskiwania oraz konwersji termicznej energii promieniowania slonecznego w budynku. IFTR Reports, 11/2006, Warszawa.

[2] D. Chwieduk, Some Aspects of Modeling the Impact of Solar Energy on the Energy Balance of a Room, Solar Energy (in print).

[3] D. Chwieduk, B. Bogdanska, Some recommendations for inclinations and orientations of building elements under solar radiation in Polish conditions, Renewable Energy Journal, 29 (2004) 1569 — 1581.

[4] S. Sherbiny, G. Raithby, K. G. Hollands. Heat transfer by natural convection across vertical and inclined air layers, Journal of Heat Transfer 104 (1982) 96-102

[5] D. T. Reindl, J. A. Duffie, W. A. Beckman, Evaluation of Hourly Tilted Surface Radiation Models, Solar Energy, 45 (1999) 9 — 14