Prediction of internal temperature swings in direct-gain passive-solar buildings Page: 4 of 7
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If the wall is infinite in thickness, dhc^ ■ Ppck/2i .
If the wall is finite and q2 - 0, dhc - dhc^ 2g , where Z - tanh yX and g - eiw/4
The magnitude and phase of Zg can be expressed in terms of real variables as follows
mag (Zg) «^(cosh 2t - cos 2-r/(cosh 2t + cos 2t) , and
phase (Zg) - arctan (sin 2x/sinh 2t) + */4 , where t - X ^wpc/Pk .
The magnitude of dhc is shown in Fig. 1 for several common building materials. The
phase varies from 90* (for thin materials) to 45* (for thick materials).
If the wall comprises several layers of different materials, the dhc of the com-
posite wall can be determined from y^ using Eqs. (1) and (2) as follows:
y2/a + Zg ,-
y,/a = - where a -\2irkpc/P
1 + Zy2/ag
This equation is used repetitively, working from the outside layer inward, layer by
layer, by setting y2 for each subsequent layer equal to y^ for the previous
layer at the interface. The procedure and derivations are outlined in more detail
by Davies (1973) and Balcomb (1983).
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Fig.
GRPNITC
ICRETE
CONCRETE MfiSONRY
LIMESTONE
BUILDER BRICK
ADOBE
WALL THICKNESS OR HRLF THICKNESS, cm
Ulurnal heat capacities of various materials as a function of thickness.
For Interior partition walls, use 1/2 the total wall thickness to deter-
mine the diurnal heat capacity for each of the two surfaces. These curves
apply to radiation-coupled mass.
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Balcomb, J. D. Prediction of internal temperature swings in direct-gain passive-solar buildings, article, January 1, 1983; New Mexico. (https://digital.library.unt.edu/ark:/67531/metadc1096754/m1/4/: accessed July 16, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.