# The heat absorbed by glass

The amount of the solar energy absorbed by the glass during the passage of the direct rays of the sun through it depends on the absorption characteristics of the particular type of glass.

Ordinary glass does not have a very large coefficient of absorption, but certain specially made glasses absorb a good deal of heat. The heat absorbed causes an increase in the temperature of the glass, and heat then flows by conduction through the glass to both its surfaces. At the indoor and outdoor surfaces the heat is convected and radiated away at a rate dependent on the value of the inside and outside surface film coefficients of heat transfer, hsi and hso.

If values are assumed for the temperature in the room, tr, and for the temperature outside, t0, a heat balance equation can be drawn up and a value calculated for the mean temperature of the glass. It is assumed in doing this that, because the glass is so thin, the surface temperatures are virtually the same as the mean.

Referring to Figure 7.12, taking the mean glass temperature as ts and the absorptivity of the glass as a or a’ the heat balance is

Oc/g + oc /s = (tg — to^hsQ + (tg — t^)h\$ whence

_ 0^8 + W 4 hsotQ + hs[tr s" (hso+hsi)

EXAMPLE 7.9

Given that the solar altitude is 43°30′, the solar azimuth is 66° west of south, the window faces south-west, the outside temperature is 28°C, the room temperature is 22°C, hso is 22.7 W m-2 and hsi is 7.9 W m-2, calculate the mean temperature of a single sheet of glass in July, for the following cases: (a) 6 mm clear float glass; (b) 6 mm heat-absorbing bronze glass.

 Fig. 7.12 Heat absorbed by glass in sunlight.

The window faces 45° west of south hence the wall-solar azimuth is 66° — 45° = 21°. Refer to Table 7.1 and determine that the direct solar radiation on a plane normal to the rays of the sun is 830 W m-2 for a solar altitude of 43°30′. Then, for direct radiation, by equation (7.6):

/v = 830 cos 43°30′ cos 21° = 830 x 0.7254 x 0.9336 = 564 W nT2

Further reference, to Table 7.7, shows that, for a solar altitude of 43°30′ the intensity of radiation scattered from the sky is 54 W nT2 and the intensity of radiation scattered from the ground is 66 W nT2, for a vertical surface in July. Hence the additional, scattered radiation, normally incident on the vertical window, is (54 + 66) = 120 W irf2.

Reference to Table 7.6 shows that the absorption coefficients for 6 mm clear float and

6 Mm heat-absorbing bronze are 0.15 and 0.49, respectively. It is reasonable to assume that the coefficients refer to both direct and scattered solar radiation so we can now calculate the glass temperatures by equation (7.12):

(a) For 6 mm clear float glass

Fg = [0.15 x 564 + 0.15 x 120 + 22.7 x 28 + 7.9 x 22]/(22.7 + 7.9) = 29.8°C

(b) For 6 mm heat-absorbing bronze glass

Fg = [0.49 x 564 + 0.49 x 120 + 22.7 x 28 + 7.9 x 22]/(22.7 + 7.9) = 37.4°C If no solar radiation is absorbed it can be verified by equation (7.12) that the glass temperature

Table 7.6 Transmission performance data for windows and shades. (Based on data from Pilkington (1991))

 Solar thermal radiation Shading coefficients Light Trans. % Absn. % Trans. % Total Trans. % Radn. conv. total
 Single unshaded glass Ordinary 4 mm glass 87 8 84 87 0.96 0.04 1.00 4 mm clear float 89 11 82 86 0.94 0.04 0.98 6 mm clear float 87 15 78 83 0.9 0.05 0.95 6 mm heat-absorbing bronze 50 49 46 62 0.53 0.19 0.72 6 mm heat-absorbing green 72 49 46 62 0.53 0.19 0.72 6 mm heat-reflecting bronze 10 73 6 24 0.07 0.20 0.27 6 mm heat-reflecting blue 20 64 15 33 0.17 0.21 0.38 Single glass + internal Venetian blinds Ordinary 4 mm glass 44 11 47 0.12 0.41 0.53 6 mm clear float — 52 9 47 0.1 0.44 0.54 6 mm heat-absorbing bronze — 80 5 42 0.06 0.42 0.48 6 mm heat-reflecting bronze — 78 1 22 0.01 0.24 0.25 Double unshaded glass Ordinary glass 4 mm inner 4 mm outer 76 16 71 76 0.77 0.08 0.85 Clear float 6 mm inner 6 mm outer 76 28 61 72 0.7 0.12 0.82 Double heat-reflecting glass 6 mm clear inner, 6 mm bronze outer 9 74 5 16 0.06 0.12 0.18 6 mm clear inner, 6 mm blue outer 18 67 12 24 0.14 0.13 0.27 Double glass + internal Venetian blinds Ordinary glass 4 mm inner 4 mm outer 48 0.12 0.35 0.55 Clear float 6 mm inner 6 mm outer 62 7 47 0.08 0.46 0.54 Double heat-reflecting glass + internal Venetian blinds 6 mm clear float inner 6 mm bronze outer — 78 1 15 0.01 0.16 0.17 6 mm clear float inner 6 mm blue outer — 76 2 20 0.02 0.21 0.23 Double glass + Venetian blinds between the panes Ordinary glass 4 mm inner 4 mm outer — 50 5 25 0.08 0.17 0.29
 ( Contd)

166 Heat gains from solar and other sources Table 7.6 (Contd)

Light total

Trans. absn. trans. trans. radn. conv. total

TOC o "1-5" h z % % % %

Clear float 4 mm inner

4 mm outer — 54 7 25 0.08 0.21 0.29

Double heat-reflecting glass + Venetian blinds between the panes 6 mm clear float inner

6 mm bronze outer — 78 1 13 0.01 0.14 0.15

6 mm clear float inner

6 mm blue outer — 76 2 16 0.02 0.16 0.18

 Solar altitude Month Surface Radiation 5° 10° 15° 20° 25° O O 35° O O Tf O O ON O O O O R-~ 00 O O 1 Horizontal Sky 14 32 41 47 51 54 56 57 59 61 62 62 Jan Vertical Sky 7 16 21 24 26 27 28 29 30 30 31 31 Vertical Ground 3 13 22 32 42 52 61 69 84 96 106 109 Horizontal Sky 14 32 42 48 52 55 57 58 60 62 62 63 Feb Vertical Sky 7 16 21 24 26 27 28 29 30 31 31 32 Vertical Ground 3 12 22 32 42 51 60 68 83 95 104 110 Horizontal Sky 14 38 46 53 58 62 64 66 69 70 72 72 Mar Vertical Sky 7 19 23 27 29 31 32 33 34 35 36 36 Vertical Ground 3 13 21 31 40 50 58 66 81 93 102 107 Horizontal Sky 14 39 55 65 72 77 80 83 87 90 91 92 Apr Vertical Sky 7 20 27 32 36 38 40 42 44 45 45 46 Vertical Ground 3 11 20 30 39 47 56 64 77 89 97 102 Horizontal Sky 14 43 61 75 84 91 95 98 104 107 109 110 May Vertical Sky 7 21 31 38 42 46 47 49 52 53 54 55 Vertical Ground 2 10 19 29 38 46 55 62 75 87 95 100 Horizontal Sky 14 45 66 80 90 97 102 106 112 115 118 119 June Vertical Sky 7 22 33 40 45 48 51 53 56 57 59 59 Vertical Ground 2 10 19 29 37 46 54 62 75 86 94 99 Horizontal Sky 14 45 66 81 90 98 103 107 113 116 118 120 July Vertical Sky 7 22 33 40 45 49 52 53 56 58 59 60 Vertical Ground 2 10 19 28 37 46 54 61 75 86 94 99 Horizontal Sky 14 42 62 75 84 90 95 99 104 107 109 110 Aug Vertical Sky 7 21 31 38 42 45 48 50 52 53 55 55 Vertical Ground 2 10 19 29 38 46 54 62 76 86 95 100 Horizontal Sky 14 38 53 63 70 74 78 80 84 86 88 89 Sep Vertical Sky 7 19 27 32 35 37 39 40 42 43 44 44 Vertical Ground 3 11 20 30 39 48 56 64 78 90 98 104 Horizontal Sky 14 35 47 55 60 63 66 68 71 72 74 75 Oct Vertical Sky 7 17 24 27 30 32 33 34 35 36 37 38 Vertical Ground 3 12 21 31 40 50 58 67 81 93 102 107 Horizontal Sky 14 33 43 50 54 57 59 61 64 65 65 66 Nov Vertical Sky 7 16 22 25 27 29 30 31 32 32 33 33 Vertical Ground 3 12 22 32 42 51 60 69 84 96 104 110 Horizontal Sky 14 31 41 46 50 53 55 57 58 60 60 61 Dec Vertical Sky 7 16 20 23 25 26 27 28 29 30 30 30 Vertical Ground 4 13 23 33 42 52 61 69 85 97 106 112

We see that, for 4 mm clear float, the presence of solar radiation on the glass increases the heat transfer to the room by (61.6 — 35.6) = 26.0 W m-2. If heat-absorbing glass is used the figure goes up to 86.1 W m-2. It is evident that the heat absorbed by clear glass makes only a small contribution but, if heat-absorbing glass is used it can become significant.

Glass temperatures can rise to very high values (well over 60°C) when the incident solar radiation is high, the absorptivity is large and the heat transfer coefficients for the surfaces are small—as would be the case for glazing with a sheltered outside exposure and stratified temperature conditions on the inside. High glazing temperatures cause stresses that can be a risk if not considered. Reference to the manufacturers should be made in such cases as Pilkington (1980) shows.

Posted in Engineering Fifth Edition