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.

The heat absorbed by 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

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


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