A building with a thermal storage wall is shown in Figure 6.5a, where Lm is the monthly energy loss from the building, Qaux is the auxiliary energy required to cover the load, QD is the excess absorbed energy above what is required to cover the load that cannot be stored and must be dumped, and TR is the mean room temperature, which is also equal to the low set point temperature setting of the room thermostat. The analysis of thermal storage walls is presented by Monsen et al.

Ambient G|azing temperature

Storage wall hi

Room

FiGURE 6.5 (a) schematic of a thermal storage wall. (b) Equivalent electric circuit for the heat flow through the wall.

(1982) as part of the unutilizability method developed to design this type of systems, presented in Chapter 11, Section 11.4.2.

The monthly energy loss from the building, Lm, is defined as:

Lm = f [(UA)(Tr - Ta) - g]+dt = f [(UA)(T - Ta)]+dt (6.44)

month month where

(UA) = product of overall heat transfer coefficient and area of the building structure (W/°C). g = rate of internal heat generation (W). Ta = mean outdoor ambient temperature (°C). Tb = mean indoor balance temperature (°C), = TR - g/(UA).

The variable of integration in Eq. (6.44) is time t, and the plus sign indicates that only positive values are considered. If (UA) and g are constant, Lm can be found from

where (DD)b = monthly degree days evaluated at Tb.

The monthly energy loss from the building through the thermal storage wall, Lw, assuming that the glazing has zero transmissivity for solar radiation, can be found from:

where

Aw = thermal storage wall area (m2).

Uw = overall heat transfer coefficient of the thermal storage wall, including glazing (W/m2-°C). _

(DD)r = monthly degree days evaluated at TR.

From Figure 6.5b, the overall heat transfer coefficient of the thermal storage wall, including glazing, is given from

k = thermal conductivity of thermal storage wall (W/m-°C). h = inside wall surface film coefficient, = 8.33 W/m2-°C, from Table A5.5, Appendix 5.

U0 = average overall heat transfer coefficient from the outer wall surface through the glazing to the ambient (W/m2-°C).

Usually, night insulation is used to reduce the night heat losses. In this case, the average overall heat transfer coefficient Uo is estimated as the time average of the daytime and nighttime values from

U0 = overall coefficient with no night insulation (W/m2-°C). Rins = thermal resistance of insulation (m2-°C /W). F = fraction of time in which the night insulation is used.

A typical value of U0 for single glazing is 3.7 W/m2-°C and for double glazing is 2.5 W/m2-°C.

The monthly energy balance of the thermal storage wall gives

where

Ht = monthly average daily radiation per unit area incident on the wall (J/m2). (Ta) = monthly average transmittance of glazing and absorptance of wall product. Tw = monthly average outer wall surface temperature; see Figure 6.5a (°C). Tr = monthly average room temperature (°C). Ta = monthly average ambient temperature (°C). At = number of seconds in a day.

Uk = overall heat transfer coefficient from outer wall surface to indoor space (W/m2-°C).

The overall heat transfer coefficient from the outer wall surface to the indoor space can be obtained from

Equation (6.49) can be solved for monthly average outer wall surface temperature:

Finally, the net monthly heat gain from the thermal storage wall to the building is obtained from

where N = number of days in a month.

Methods for calculating the dump energy, QD, and auxiliary energy, Qaux, are presented in Chapter 11, Section 11.4.2.

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