1.1 Forced convection cooling

1.1.1 System description

The cross-sectional view of immersion system of forced convection cooling is shown in Fig.1. The fluid enters the vessel with the temperature T and leaves at the temperature To. Heat from solar cells is transferred to the liquids through convection and conduction. The system is tilted at an angle equal to the local latitude (39.13°).

1.1.2 Thermal model

The thermal network of forced convection cooling system is shown in Fig.2.

The heat balance equations are now presented as followed:

For transparent cover,

G + h (T — T) + hf(Tf — T) + h (T — T) = 0 (1)

g ag a g fg f g eg c g

Where Gg is the total solar energy absorbed by transparent cover

(2) (3) (4) (5) (6)

Gg = Gd ~Pg )«g

The heat transfer coefficient from the top cover to the surroundings is calculated using the relation by Duffie[11],

hag = hw + hgs

hw = 2.8 + 3.0v

h

gs

— t4) Tg — Ta

The relationship between sky temperature and local air temperature is

Ts = 273.15 + 0.0552(Ta -273.15)15

h

eg

s(T2 + t2) H є +1/єс -1

Assuming linear heat rise, Tf = (T + To )/2

(7) (8)

The radiation heat transfer coefficient between solar cells and top cover can be written as

For liquid,

AgGf + Agh, (Tg — Tf) + 2Achcf (T-Tf) = qu + T — Ta)

where

Gf = Gaf (1 — Pg )(1 -«g)

qu = mc(T0 — Ti)

For solar cells,

G + 2hc(Tf -T) + h (T — T) = E

c fc f c gc g c

where Gc is the total solar energy absorbed by solar cells,

Gc = G^c(1 — Pg)(1 — ag)(1 — pf )(1 — af)

The conversion efficiency of the PV ^ is a function of its temperature calculated by the relation [12]:

E = Gcqc = 0.125Gc [1 — 0.004(Tc — 293)]

The convection heat transfer coefficient hgf and hfc are calculated using the relation given by Bejan [13]. Relevant parameters of system have been given in Table 1. The silicone oil properties are obtained from [14].

Table 1 values of parameters used in simulations parameter value parameter value £g 0.9 ac 0.9 Ec 0.9 Ag 0.15m2 af 0.1 Ac 0.08m2 ag 0.06 Pg 0.04 2.1.3 Results

The model is used to simulate solar cell temperature (Tc), transparent cover temperature (Tg) and outlet fluid temperature (To) with different operational parameters.

(9) (10) (11) (12) (13) Tc and is (14)

Fig.4. shows three various components temperatures as a function of irradiance at fixed mass flow rate and fixed inlet liquid temperature. The temperature of solar cells is increased from 301 to 374K when irradiance is increased from 1000 to 9000 W/m2K. In fact, to maintain low temperature of solar cells at high irradiance, system parameters need change correspondingly. Fig.5. represents the variation of three components temperature as a function of inlet fluid temperature. It is obvious that solar cells temperature increases with the increase of inlet temperature. In practical operation, it is important to understand the result of various inlet fluid temperatures because it is difficult to maintain fixed inlet temperature. The effect of mass flow rate on system temperatures is shown in Fig.6. Because the fluid is in laminar flow and irradiance is not too high, the temperatures of three components vary little with the increase of mass flow rate.

1.2 Free convection cooling

1.2.1 System description

The configuration of free convection cooling is similar to forced convection cooling system. There is no need for additional pump for fluid flow because free convection is caused by fluid motion due to density differences. It can decrease system cost. The vessel is filled with silicone oil and the inlet valve and the outlet valve are closed.

1.2.2 Thermal model

Heat from solar cells is transferred to the vessel walls by silicone oil through convection and conduction. Mathematical model of free convection resembles model of force convection. Equation (9) is replaced by equation (15) and equation (8) and (11) are cancelled.

For liquid,

(15)

AgGf + Aghfg (Tg — Tf) + 2Achf (Tc-Tf) = hfy (Tf — Ta)

fa f

^g fg g

2.2.2 Results

Fig.7 and Fig.8 illustrate the temperature variation of three components as a function of ambient temperature and irradiance. The solar cells temperature in free convection cooling

system is higher than in force convection at the same irradiance. The temperature of solar cells increases with the increase of ambient temperature.

To decrease the temperature of fluid and solar cells, natural convection system should be high heat flux between the vessel walls and surroundings. That means t o increase heat transfer area and heat transfer coefficient between them. Vessel walls should be high thermal conductivity and thin thickness. Adding fins on vessel walls can extend available heat transfer surface area.