The air channel is modelled through a stationary one-dimensional volume, with a linearly temperature variation in the vertical direction. Three different working conditions are possible: q”ef = q”g1f; q”ef ^ q”g1f, and adiabatic condition q”ef; q”g1f = 0. Concerning the nature of the flow, three situations are considered: natural, forced (wind or mechanical fan) and mixed convection. In the natural convection situation, two flow regimes exist: the laminar and the turbulent. Besides, a distinction between thin and wide channels is considered. The governing equation, once integrated, can be expressed as:

mcp (Tf — Tf, i) = {q’”f + qgif ]Wy (6)

Where: Tf is the air average temperature at height y (°K); y is the height (m); Tf is the average temperature at the inlet (°K); m is the mass flow rate (Kg/s); Wis the width of the fa? ade (m) and q”ef and q”g1f are the convective heat sources. They are calculated as: qf = q”cond — q"”g and

q"g1f = q"g1 cond + q””g1. Assuming the Newton law of cooling for the heat convection sources, making

some arrangements and integrating along the fa? ade height we can obtain the average wall and outlet temperatures.

The flow-rate is obtained by equating the sum of the pressure differences which drive the flow (wind and buoyancy) with that of those opposing it (hydraulic and friction losses):

A • ( + ) + B h+J — 1 [(fappR”m )• H ++X Kh ] = 0 (i0)

+ H 2SG”

where: H =————- is the dimensionless height; A = —

2R”Dh b P”

is the wind-induced term; S is the stratitification coefficient; Kh are the inlet and outlet hydraulic losses; fapp is the apparent friction factor and Dh is the hydraulic diameter (m). The term fappR” is likewise depending on H+, which means that an iterative process must be set up. The expression of fappR” depends on the boundary conditions, on the flow nature, and on the flow situation: in laminar free convection and symmetric uniform heat fluxes, the correlations of Kaka? [9] were validated through CFD simulations. In the case of adiabatic wall boundary conditions, the correlations of Kaka? [9] are also accepted if G”D < 105. In the case of asymmetric conditions, the new correlation
(see equation 3) is used. In turbulent free convection, the term fappRe is no longer linear dependent on H. For this situation only correlations for forced turbulent fully developed flow exist [6]. In mixed flow convection, a composition of the previous correlations will be used. The pressure difference term (APw) is calculated using a dynamical pressure expression dependent of the pressure coefficients.

Once all the terms are determined, a Newton Raphson method is used to solve Equation 10.