Numerical solution of solar energy absorbed in porous medium with a new approach for vapor pressure calculation and consideration of solute crystallization

摘要

The goal of the study is to enhance the productivity of solar stills using an unsaturated porous medium initially saturated by salty water and using concentrating reflector. This paper concentrates only on the mathematical model for the porous medium and its solution using a finite-volume approach. The previous studies dealt with wick medium with high water content and liquid saturation in the wick medium was not determined. A physical model for the initially saturated porous medium was developed. The model takes into consideration the salt concentration in the solution, surface and internal water diffusions to humid air with vapor pressure determined from vapor mass balance. The system of transient one-dimensional differential equations was developed together with the boundaries and initial conditions. A finite-volume method was used for discretisation of the differential equations. A fully-implicit scheme was used for unsteady term discretisation while the convective terms (liquid solution, vapor and dry air) in the energy equation are handled by an upwind scheme method. The nonlinear equations are solved simultaneously by updating the coefficients matrix at one time step until the five variables converge to prescribed tolerance. Matlab was used as a programming tool. Solution of the model is obtained and discussed.