Daily Estimate of Pure Water in a Desalination Unit by Solar Membrane Distillation

Abstract

Cp: Specific heat (kJ/kg.K) Cs: Mole fraction of NaCl Ds; Diffusion coefficient of the NaCl, (m 2 /s) Dv/a: Diffusion coefficient of the vapour in the vapour/air mixture, (m 2 /s) Jv: Local permeate flux at the hot side of membrane, in vapour phase (kg/m 2 .s) k: Thermal conductivity (W/m.K) K: Permeability of the membrane (s/m) H: Membrane length (m) Mv: Molar mass (kg/mol) Pm: Average pressure partial of the air (Pa) PT: Total pressure (air + vapor) (Pa) r: Sze (m) rp: Membrane pore size (m) R: Universal gas constant (J/mol.K) r 1 : Interior radius of the membrane (m) r 2 : Exterior radius of membrane (m) T: Inlet temperature of hot solution (°C) Tm: Average temperature of the membrane (°C) Ve: Velocity at the inlet of the hot channel (m/s) Vr: Radial velocity (m/s) Vz: Axial velocity (m/s) Greek: ρ: Density (kg/m 3) ε: Porosity of membrane; τ: Tortuosity Abstract A membrane distillation process using solar energy has been studied. This system has been modelled to provide approximations of the flow of distillate, the thermal effectiveness and the quantities of heat exchanged by conduction and evaporation during the production process of water. Then, simulations have been carried out using MATLAB to highlight the transfers of mass and energy in a dynamic regime under the effect of variable solar radiation and to illustrate the temporal evolution of the parameters related to the operation of the membrane. So, to estimate the production of water, a polynomial approximation was used. δm: Thickness or width=R 2 ln(R 2 /R 1) δg: Thickness or air (m) δf: Thickness of film of condensation (m) μ: Dynamic viscosity (kg/m.s)