A schematic of the problem is shown in Fig. 1. It consist of a rectangular cavity tilted 45° and with parallel slats inside (cross — slope). The front and back boundaries are isothermal walls at and Tft, respectively ( ), and the others are adiabatic walls. The distance

between isothermal walls is L, while the height of the enclosure is H. The parallel slats are formed by multiple layers of thin glass sheets. These are described by the parameters r1, r2, r3, …(see Fig. 1a). The bottom and top air gap thicknesses are denoted by lh and 4, while £ and l give the thickness and height of each glass sheets (for all cases ),

(see Fig. 1b). The distance between glass sheets was considered uniform. The overall

aspect ratio was defined as A = H/L, while the cell aspect ratio was defined as A’ = H’/L. The average Nusselt number and the Rayleigh number are defined as:

where A is the air thermal conductivity; Q is the total rate of heat transfer between the isothermal walls; Ai is the surface area of the isothermal wall; 0 is the gravitational acceleration; and,3, p, cp and p respectively are the thermal expansion coefficient the density the specific heat at constant pressure and the dynamic viscosity, which are assumed con­stant (Prandtl number ). A thermal con­

ductivity ratio value (ДА = A„/A) of 28.6 was cho­sen, where A„ is the glass thermal conductivity.

Computations of three different configurations have been performed. Fig. 2 shows a summary of all cases studied. These are divided in two groups: computational domain whole, where, and

computational domain reduced, where the domain is limited to a cell of multiple glass sheets. In Fig. 2n and к parameters are used in order to properly define the mesh: n is the refinement level, and & is a mathematical parameter which depends on A’.

1.1 Study I: Parallel slats in contact with isother­mal walls.- The grids used were of nx(8+A;n), con­sidering values of к = 1, 1, 2 and 4 (related to A’ values of 0.5, 1, 2 and 4, respectively); n = 5, 10, 20 and 40; and Rayleigh numbers of, 104

and 105 (see Fig. 2-(I b)).

1.2 Study II: Parallel slats in contact only with cold isothermal wall.- For whole computational domains (Fig. 2—(II a)) simulations were performed using grid of nx[(

1) + ] (where rh is the slat number), considering

values of =8, 16, 32 and 64 (in Table 1 — “whole domains” shows theses cases). For reduced computa­tional domains (see Fig. 2—(II b)), the grids used were of nx(8+kn), with values of n = 10, 20, 40 and 80 (in Table 1 — “reduced domains” shows a summary of cases studied).

1.3 Study III: Parallel slats separated from the isother­mal walls.- Three configurations were considered: (i)

Symmetrical: lh = lc, (ii) Asymmetrical close to hot isothermal wall: , and (iii) Asymmetrical close to

cold isothermal wall: lh> lc.

These different configurations have been solved using whole computational domains. As for asymmetrical configurations, both have also been solved using reduced computational domains with periodic boundary conditions.

For whole computational domains, Fig. 2-(III a), the grids used were of Зпх[(гл+1)А;п-|-гл] considering values of n = 3, 6, 12 and 24; while for reduced computational domains, Fig. 2—(III b), grid of 3nx(8 + kn) were performed, with values of n = 5, 10, 20 and 40.

Table 2 shows the summary of asymmetrical cases when slats are close to hot and cold isother­mal walls, while the symmetrical cases studied are summarised in Table 3.