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American Society 0/ Heating and Ventilating Engineers Guide, 1926-27;
efficients are always based on the difference between the air temperatures on the inside and the outside of the wall'.
Transmission Coefficients by Computation
If heat transmission coefficients are to be computed, and in many, if not most cases, they should be computed, the following analysis of the transmission of heat through a simple, solid wall is used as the basis for such computations.
The diagram in Fig. 1 exhibits four important temperatures: First the air temperature t inside of the building; second, the temperature t, of the inside surface of the wall; third, the temperature t, of the outside surface of the wall, and fourth, the air temperature to outside of the build ing. Heat reaches or enters the inside surface of the wall by radiation, and convection, since the air and objects A within the building are always
American Society of Heating and Ventilating Engineers Guide, 1926-27
Now Kt may not equal K,, in which case (t,-to) will not equal (t-t,). Usually, in an actual wall exposed to wind on the outside, Ka (Table 5) is greater than K, and (<j-/0) must be less than (t-ti). Moreover, the heat Hc passing through the wall by conduction is equal to H, and H,, and if C is the coefficient of conduction = B.t.u. transmitted per hour per square foot of material per 1 in. thickness per degree difference
between the surface temperatures, then
Hi=Ho=Hc=^ (i, - to) S
(3)
where x = wall thickness in inches.
Fig. 1. Temperature Curve or Gradient from Air Inside to and through Wall To Air Outside, Wall Material Assumed Air-Tight
of
A represents warm surfaces at temperature t of inside outside air. For an actual temperature gradient curve
air; see
B represents Fig. 2.
cold
surfaces
at
temperature
to
warmer than the inside surface of the wall, when the inside air tempera
ture f is greater than the outside air temperature t0. This heat must then
pass through the material of the wall from inside to outside surface by
conduction, and is finally given off from the outside surface by radiation
and convection, provided, of course, that equilibrium has been established
and all four temperatures are constant.
,.
The amount of heat reaching or entering the wall per. hour depends on t and U and a coefficient K, varying with the character of the wall material. K, may be defined as the B.t.u. per hour entering each square foot of wall surface per degree difference between the inside air tempera ture t and the inside surface temperature U, Hence the heat received by inner surface of the wall per hour by both radiation and convection is
H, <= K, (t - t,) S j
(1)
where 5 is the inner wall surface area in square feet and the other terms are as heretofore indicated.
Whatever amount of heat Hi enters the inner wall surface must be given off from the outer wall surface, so that if H2 represents heat emitted from outer surface
77, -- //- -- Kz (I2 -- to) S. 10
(2)
These equations (1), (2) and (3) are fundamental and are used for determining values for Klt K, and C for actual wall materials by test. They cannot be used for computing heat-losses in an actual building, since the surface temperatures t, and G are seldom known, although these surface temperatures can be determined in a test by means of thermo couples. Hence, for actual conditions where the only temperatures known are the inside and outside air temperatures t and to, it is necessary to use a transmission coefficient U = B.t.u. transmitted per hour per square foot of wall surface per degree difference between the inside and Outside air temperatures. Values of U for a limited number of walls are given in Tables 6-12. The heat H transmitted per .hour from air inside to ait
outside is then computed as.follows:
II = U (l - to) S
(4)
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