1.3. Theoretical model

A schematic description of the ICS is presented in figure 4. The model consists of a multilayer system containing a transparent glass cover, an air layer, an absorbent surface, an exchanger, a composite storage material, a polymer envelope and a thermal insulation.

x

Transparent Glass Cover (Tg) Air Layer

Absorber surface (Ta)

Heat transfert fluid (Tf)

Composite material (TJ

L

nsulation

Polymer Enveloppe (Tp)

Exterior (Tamb)

Z

Fig.4: Schematic representation of the ICS

We consider here a uniform temperature of both the glass cover and the absorber. Only the composite material and the polymer envelope are discretized along the x direction.

Cp,^=g[ — [.+p,)]+t~t—■.(Ta ‘ — T, ■)+e,* (r* ‘ — Tg ■)+…

m

(eq.4)

Temperatures of the absorber surface and the transparent cover are determined using equation 4 and 7. For the transparent cover (Tg):

г г

a g

10.3

… + 1.05Ta — T, .(Ta — T,) + hamb/,(Tamb — T,)

These expressions take into account successively the absorption of solar energy by the cover, thermal radiative heat transfert between the absorber and the cover6 and also between the cover and the sky. The temperature Tsky is calculated through the empirical formula[7]:

(eq.5)

Ty = 0.0552X15,

sky amb

Convective transfer coefficients between the glass and the absorber are calculated using equation 6[8].

ha/, = 1.05.|Т — Tg f 3 (eq.6)

Convective transfer with the environment are supposed to be constant and approximate to hc-amb=17 W. m"2.K_1 which is the value for a wind speed parallel to the solar collector of 3m. s_1.

(eq.7)

C dTa G( ) maCPa~dT = G(T, aa ) +

a

1 + -1 — 1

^4 — Г,4) + 1.05Ta — Tg .(Ta — Tg ) + hQ /, .(TQ — Tc )

г

г

a

g

For the absorber (Ta)

Absorber temperature is function of the solar absorbance, radiative heat transfert between the absorber and the cover, convective exchange between absorber and glass cover. The thermal resistance of contact between the absorber and the composite is taken into account in a global transfer coefficient

ha/c.

Considering a global heat transfer coefficient between the polymer and the composite, the system of differential equation is given by:

For the composite:

(eq8)

(eq.9)

pccpc дт — + V(-kc VTC) = 0 dt

For the polymer

P Рсрр~^ + V(-Ap VTp) = 0

— к

c

h /, (T — TP)

(eq-10)

These equations are linked through the heat exchange at the interface between the composite and the polymer:

— к

( дТ Л

(eq11)

= hp / c (Tp — Tamt, )

The heat exchange at the exterior boundary of the polymer is calculated via equation 11.

Where hp/c is a global transfer coefficient regarding both transfer with the insulated material and the convection at the top back of the ICS.

In the model, the effective heat capacity Cpc of the PCM takes into account its latent heat (solidification/fusion) through the integration of an effective function (Cp=f(T)) defined by a preliminary calorimetric analysis of the material.

These are solved with the simulation package Comsol® which is based on the finite-element method. The geometry of the solar collector leads to a simple one-dimensional system during the charge. During discharge, the flowing fluid imposes to consider a two-dimension system.