Effects of temperature - Concrete Structures: Stresses and Deformations - page 356

Only a portion of this solar radiation reaches the earth's surface, because
of the atmosphere which acts like a lter. The amount of radiation which

reaches the surface of the earth depends upon the length of the path of the
sun's rays through the atmosphere, hence on the latitude and altitude. It also
depends upon the air pollution. The angle of incidence of the sun's rays on
the surface also a

fi

ects the amount of solar radiation. 6
The maximum solar radiation in summer on a horizontal surface in Europe
and North America (around latitude 50) is in the order of 800-900 W/m 2
(250-300 Btu/(h ft 2 )).
The amount of heat transfer by convection is given by Newton's law of
cooling:

ff

q c = h c ( T − T a ) (10.5)

where T and T a are temperatures of the surface and of the surrounding air,
respectively; h c is the convection heat transfer coe cient (W/(m 2 ° C) or Btu/(h

ft 2 F) ). The value h c depends mainly upon wind speed and to a small degree

on the orientation and con

°

guration of the surface and type of material. 7
The amount of re-radiation from the surface to the air is given by the
Stefan-Boltzmann law which may be written in the form:

fi

q r = h r ( T − T a ) (10.6)

where h r is the radiation heat transfer coe cient given by

h r = C s α e [( T + T *) 2 + ( T a + T *) 2 ]( T + T a + 2 T *) (10.7)

where C s = Stefan-Boltzmann constant = 5.67 × 10 −8 (W/(m 2 K 4 ) or (0.171 ×

10 −8 Btu/(h ft 2 ° R 4 ) ); T * = constant = 273 used to convert temperature from

degrees Celsius ( ° C) to degrees Kelvin (K) (or = 460 to convert degrees Fahr-

enheit ( cient of emissiv-

ity of the surface, and takes a value between 0 and 1. The latter value is for an
ideal radiator, the black body .
Equation (10.7) indicates that h r can be calculated only when the tempera-
ture T of the surface is known. However, because h r is only slightly a

° F) to degrees Rankin ( ° R); α e is a dimensionless coe

ected
by T , in a time-incremental solution of Equations (10.1) and (10.2), an
approximate value of h r can be employed, based on earlier values of T .
The convection and re-radiation coe

ff

cients h c and h r may be combined in

one overall heat transfer coe cient for the surface

h = h c + h r (10.8)

and the heat ow by convection and re-radiation, q cr , can be expressed by one

equation combining Equations (10.5) and (10.6):

fl