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 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.

Answer

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 m ‘2 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 rrf2.

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	0.90	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	0.10	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	0.70	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)

Solar thermal radiation Shading coefficients

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 Air Conditioning Engineering