For the purpose of the presented studies, calculations of solar radiation incident on surfaces with different azimuth and inclination angles have been performed using the averaged representative hourly solar radiation data for Warsaw [3] for the anisotropic sky model, Hay — Davies — Klucher — Reindl [5]. To describe and solve problems of the dynamics of processes in the building envelope and surrounding, a mathematical model of energy transfer phenomena in opaque and transparent elements has been developed [1], [2]. Focus has been put on the influence of solar energy and because of that, special attention has been paid to energy transfer through the windows.

Window consists of three main components: centre glass area, edges of glass, frame. All these 3 components influence on each other from the point of view of the heat transfer [4]. The model of unsteady energy transfer outside and inside the window, as well as within the cavity formed by the glass sheets has been developed [1]. It includes heat conduction and heat capacity of opaque (frame) and transparent (centre glass area, edge of glass) elements. It also includes heat convection (free) with indoor and (forced) outdoor surrounding and inside window cavity; and radiation (thermal — long wave) exchange between the ground, the sky, i. e. the outdoor environment, and windows; and radiation exchange between windows and the room cavity, i. e. indoor environment; and radiation exchange between glass panes of the window.

Solar radiation incident on surfaces with different orientation and inclination is considered in details. Window constitutes three dimensional object. Solar irradiance on glazing and front surfaces of the frame is the same at given time but it differs for frame surfaces perpendicular to glazing (that have not only different orientation but inclination, too). The developed model takes into account all these phenomena and solar absorption at frame surfaces. Solar absorption, transmission and reflection of all transparent surfaces (bodies) are analysed, and the effects of orientation and inclination on them are considered.

The developed model enables to calculate energy transferred through the window into/out of the room at any time. These energy transfer takes into account not only heat transfer because of temperature difference between indoor and outdoor environment, and specific conditions at boundary surfaces (including absorption of solar energy), but also solar energy transferred directly into the room under consideration. The results of calculations of energy transferred through the some selected examples of windows throughout the averaged year are presented in Fig. 1-4. Figures 1-2 show the case of inclined (450) small (1 x 1 m2) and big (2 x 2 m2) south windows respectively and Figures 3-4 show the case of inclined (450) small (1 x 1 m2) and big (2 x 2 m2) north windows respectively. The opposite orientation (south and north) and different size of windows have been selected to show the influence of orientation and size of a window, and in consequence the influence of solar energy, on energy transferred through the window. For the south orientation the maximum hourly solar radiation that enters the room through a window is at noon in May and for the small window it is about 1,15 MJ for 1 m2 (of the window) and for the big window it is about 5,1 MJ for 4 m2 (of the window). The minimum is in December and for the small window at noon it is about 0,25 MJ for 1 m2 (of the window) and for the big window it is about 1,1 MJ for 4 m2 (of the window). For the north orientation the maximum hourly solar radiation that enters the room through a window is at noon in June and for the small window it is about 0,57 MJ for 1 m2 (of the window) and for the big window is about 2,6 MJ for 4 m2 (of the window). The minimum hourly solar radiation that enters the room through a window at noon is in December and for the small window is about 0,11 MJ for 1 m2 (of the window) and for the big window is about 0,5 MJ for 4 m2 (of the window). Generally hourly solar radiation entering the south room is about two times bigger than for the north room. It can be seen that the increase of size of the window cause the increase of energy flow through a window but not exactly proportional.

x io5 Solar heat through window, with Beta = 45, Gamma = 0 Xt = 1Yt = 1

Jan —— Feb Mar Apr May Jun Jul — Aug — Sep Oct — Nov — Dec

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Apr May Jun

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— Dec