Experimental and Numerical Analysis of a PCM-Supported ...

x
t u x
u
0 0
, (6.5)
and for a system of equations:
u
u
1
2
x,
t 0 u
x,
t 0 u
1,0
2,0
x
x
(6.6)
In order to implement the PDEs system of the evaporator (as an example) in the
“pdepe” function, the system of equations arranged to fit the terms of equation
(6.1) as shown in table 6.1.
6.2 Solution of the HDH plant lumped model
The primary reason for creating a computer model of a solar desalination system
is to determine how much distillate water the system will supply over a long
period of time, usually over the whole year. Long term system performance is
important in determining the economic viability of its particular design due to the
transient nature of continuously varying weather conditions. As with any
simulation model, the design characteristics of the components and operation
parameters may be varied to help optimizing the system in terms of its
performance and cost.
A complete but simplified system model has been developed to simulate the
proposed solar distiller based on the governing equation systems, which have
been developed in chapter 4 (i.e. equations 4.7 to 4.88). The model was
developed in MATLAB, since it is an integrated package and helpful engineering
tool. With the simulation model, the system performance can virtually be tested in
different environments by altering the meteorological data. The model predicts
the system’s transient behaviour and therefore uses an explicit calculations
scheme for different parameters of interest.
Concerning the boundary conditions, the inlet feed seawater temperature,
ambient conditions and hourly solar irradiation data are given as input
parameters. The water vapor concentration in the air can be determined as a
function of the gas temperature assuming saturation conditions, since the air
circulates in a closed loop cycle. The temporal and spatial evolution of
temperature and concentration fields of fluid and solid phases are then derived
from the solution.
The model comprises three main modules; the evaporator, condenser, and solar
water heater consisting of a solar flat plate collector (FPC) and PCM thermal
storage tank (also referred to as the thermal buffer). Each module was developed
using a ”pdepe” function, tested and refined separately to solve the coupled
partial differential equations governing each component as described in details in
127