## Characteristics of a thermal storage wall

A thermal storage wall is essentially a high-capacitance solar collector directly coupled to the room. Absorbed solar radiation reaches the room either by conduction through the wall to the inside wall surface from which it is convected and radiated into the room or by the hot air flowing though the air gap. The wall loses energy to the environment by conduction, convection, and radiation through the glazing covers.

A thermal storage wall is shown diagrammatically in Figure 6.4. Depending on the control strategy used, air in the gap can be exchanged with either the room air or the environment, or the flow through the gap can be stopped. The flow of air can be driven by a fan or be thermosiphonic, i.e., driven by higher air temperatures in the gap than in the room. Analytical studies of the thermosi-phonic effect of air are confined to the case of laminar flow and neglect pressure losses in the inlet and outlet vents. Trombe et al. (1977) reported measurements of thermosiphon mass flow rates, which indicate that most of the pressure losses are due to expansion, contraction, and change of direction of flow, all associated with the inlet and outlet vents. For hot summer climates, a vent is provided at the upper part of the glazing (not shown in Figure 6.4) to release the hot air produced in the gap between the glass and the thermal wall by drawing air from the inside of the room.

In the Trombe wall model used in TRNSYS (see Chapter 11, Section 11.5.1), the thermosiphon air flow rate is determined by applying Bernoulli's equation to the entire air flow system. For simplicity, it is assumed that the density and temperature of the air in the gap vary linearly with height. Solution of Bernoulli's equation for the mean air velocity in the gap yields (Klein et al., 2005):

where

C2 g total gap cross-sectional area (m2). total vent area (m2). vent pressure loss coefficient. gap pressure loss coefficient. acceleration due to gravity (m/s2). mean air temperature in the gap (K).

The term Ts is either Ta or TR, depending on whether air is exchanged with the environment (Ta) or the room (TR). The term Ci(AgIAv)2 + C2 represents the pressure losses of the system. The ratio (AgIAv)2 accounts for the difference between the air velocity in the vents and the air velocity in the gap.

The thermal resistance (R) to energy flow between the gap and the room when mass flow rate (m) is finite is given by

2hcA

2hcA

2h A

where

gap air heat transfer coefficient (W/m2-K).

The value of hc, the heat transfer coefficient between the gap air and the wall and glazing, depends on whether air flows through the gap (Klein et al., 2005). For a no-flow rate (Randal et al., 1979),

where ka = air thermal conductivity (WIm-°C). L = length (m). Gr = Grashof number. Pr = Prandtl number.

For a flow condition and Reynolds number, Re > 2000 (Kays, 1966), k hc (0.0158 Re08) c L

For a flow condition and Re < 2000 (Mercer et al., 1967), where h = ka-

hc L

RePr g

According to Figure 6.4, h is the distance between lower and upper openings (m) and w is the wall width (m).