The ASW is schematized with two slabs, A outer and B inner, delimiting a duct into which air flows (see Fig. 2).

L is the duct length (in the air flow direction), h is the width, d the thickness, AF=hL the area, D=2dh/(d+h)s2d the equivalent hydraulic diameter. Later on the following quantities will be used:

■ G (Wm-2) mean solar radiation intensity,

■ a the absorptivity to solar radiation of the outer face of the slab A,

■ k (Wm-1K-1) air thermal conductivity,

■ Te sol-air temperature,

■ Ti indoor air temperature,

■ T1 temperature of the wall A inner face,

■ T2 temperature of the wall B inner face,

■ Ra and RB thermal resistances, respectively, of the slabs A and B,

■ Rtnv thermal resistance between the indoor air and the outdoor one in the case of non- ventilated duct;

■ Rt thermal resistance between the indoor air and the outdoor one in the case of ventilated duct;

■ Re thermal resistance between the ventilated duct and the outdoor environment;

■ Rcd closed air duct thermal resistance;

■ re and ri thermal resistances, respectively, of the wall’s outer and inner surface.

All the thermal resistances are given per surface unit (m2KW-1). We have: Te=T0+areG with T0 outdoor air temperature in the shade and Rtnv=RA+RB+re+ri+Rcd. The following dimensionless parameters are also used: z=Re/Rt and x=Rtnv/Rt.

State conditions are here considered to be steady and heat transfer schematized as one­dimensional. The case of ASW in which the duct thickness is small and the air flow inside is laminar is studied. Under laminar flow conditions the inlet phenomena, both dynamic and thermal, can be disregarded, if [12]:

Gz < 20 (1)

where Gz is the Graetz number, defined by:

Gz = — ■ Re — Pr L

with Pr Prandtl number and Re Reynols number (referring to the hydraulic diameter D) concerning the air flowing into the duct. Under these conditions, when the duct slabs are at

the same temperature Tp (uniform), the Nusselt number (Nu) is constant (independent from Pr and Re) and it results to be [12-13]:

Nu = — = 7.54 kp

with p thermal resistance between the inner faces of the duct slabs and the air flowing into the duct itself. From the previous relation it follows that either of the two slabs shows, compared to the fluid, a thermal resistance given by:

p =

and the heat flux q (Wm-2) absorbed by the fluid results: q = 2 (Tp

temperature of the fluid mixing [12].

The more general problem concerning the heat transfer within a duct, inside which the fluid flow is laminar, with the two slabs delimiting the duct at different temperatures is discussed in [13]. In [10] a simple and intuitive procedure which makes allowance also for the radiative heat transfers (characterizable by a radiative resistance Г) is reported in order to calculate the flux q2 coming into the room through the ventilation duct; the following relation is obtained:

The mean heat flux Q0 coming into the room when the ventilated duct is closed is:

Q0 = (Te — Ti )/Rtnv

The study of an ASW energy performance can be carried out using a percentage saving S, defined by [4, 8]:

S = (Q0 — Q)/Q0

The meaning of S is strongly intuitive, particularly when it assumes values from 0 to 1; negative values of S clearly show that ventilation is not convenient.

If the air temperature at the duct inlet is assumed to coincide with the air temperature in the shade T0, the air temperature inside the duct can be written as follows [8]:

f

T(x) = Tm +(T0 — Tm )exp — Xx

( ) m v 0 m} p[ yL[H + z(1 — z)]

where: Tm=zT+(1-z)Te and Y=cRtnv, with c specific heat capacity rate. The quantity H is the radiative correction factor defined in [8]. The radiative factor H is due to the fact that the introduction of the surface thermal resistance heat transfer coefficients (instead of the convective ones) is not sufficient for quantifying entirely the radiative heat transfer inside the duct.