Improvement of the tilted wick solar still by using a flat plate reflector

142
C For Eq. (1)
cos β = sinφcosθ + cosφsinθcos( ϕ −γ)
C For Eq. (2)
cos β = sinφcosθ −cosφsinθcos( ϕ −γ)
H. Tanaka, Y. Nakatake / Desalination 216 (2007) 139–146
(3)
(4)
Diffuse solar radiation absorbed on the wick,
Q sun,df, can be determined with the assumption that
diffuse radiation comes uniformly from all
directions in the sky dome, and may be expressed
as
Q , = G ( τ ) α × wl
sun df df g df w s
(5)
where G df is the diffuse solar radiation on a
horizontal surface, and (τ g) df is a function of the
angle of the still, θ, and is calculated by integrating
the transmissivity of the glass cover for
diffuse radiation from all directions in the sky
dome. This may be expressed as
−3
−5
2
( τ ) =− 2.03× 10 × θ
g df
− 2.05× 10 × θ + 0.667 θ [ ]
(6)
During the months of April to August, the sun
moves north in the morning and evening, and the
external reflector would obstruct the sunrays and
shade the wick. This causes a decrease in the
direct solar radiation absorbed on the wick, Q sun,dr.
In the calculation, the effect of the shadow is
taken into account, and the solar radiation
absorbed on the wick Q sun,dr and Q sun,re when the
sun moves north may be expressed as:
Q = G τ ( β) α ×
sun, dr dr g w
2
+ lm
2 ⎥
2 tan φ ⎦
(7)
⎡ ⎧ ⎛ cos( ϕ −γ) ⎞ cos( ϕ −γ)
⎫
⎢w⎨ls⎜cosθ −sinθ ⎟−lm
⎬
⎢⎣ ⎩ ⎝ tanφ ⎠ tanφ
⎭
1 cos( ϕ −γ)sin| ϕ −γ
| ⎤
Q = 0
sun, re
3. Heat and mass transfer in the still
(8)
Heat and mass transfer in the still are shown in
Fig. 3. The energy balance for the glass cover and
the evaporating wick may be expressed as
Q + Q + Q + Q = Q
sun, g r, w−g d, w−g e, w−g r, g−a + Q + ( mc )
cg , −a
p g
dT
d t
Q = Q + Q + Q
sun, w r, w−g d, w−g e, w−g g
(9)
dT
(10)
w
+ Qdw , −a
+ Qf+ ( mcp)
d t
where Qsun,g and Qsun,w are the solar radiation
absorbed on the glass cover and the evaporating
wick, and Qr, Qd, Qc and Qe are the heat transfer
rates by radiation, conduction, convection, and
evaporation and condensation. Qf is the increase
in the enthalpy of the saline water fed to the wick.
mcp is heat capacity, T is temperature and t is
time.
The solar radiation absorbed on the glass
cover (Qsun,g) and the evaporating wick (Qsun,w) can be determined as follows:
C For a still with an external reflector:
αg
Qsun, g = ⎡(
Qsun, dr Qsun,
re ) / τ g ( β )
α ⎣
+
w
(11)
+ Qsun,
df /( τ g ) df ⎤
⎦
Q = Q + Q + Q
sun, w sun, dr sun, re sun, df
C For a still without the external reflector:
α
Q Q Q
(12)
( / τ ( β) /( τ ) )
g
sun, g = sun, dr g + sun, df g df
αw
(13)