Abstract
At the present study, a one-dimensional model for the flat sheet direct contact membrane distillation (DCMD) for desalination purposes is proposed. Flows and membrane properties have been estimated by appropriate temperature-dependent correlations. Results show that the numerical model is in a very good agreement with experimental data at various feed temperatures, flow rates and concentrations. A constructal design is investigated for DCMD to assess how constructal law can improve the DCMD performance. With the same thermal efficiency of 93.5%, constructal design improves the water mass flux by 37.5% in comparison with the conventional DCMD design. Also, an evolutionary-based optimization algorithm is employed to increase the efficiency of the constructal and conventional design. The Pareto frontier of the constructal and conventional design is compared with each other and the correlations between design variables are investigated. Overall, the present study demonstrates how constructal law can increase the performance of energy systems with a simple modification.
Highlights
At the present study, a one-dimensional model for the flat sheet direct contact membrane distillation (DCMD) for desalination purposes is proposed
The equilibrium point is closer to the constructal Pareto frontier so as a result, the constructal design can strike a better balance between the thermal efficiency and water mass flux
Speed-constrained Multi-objective particle swarm optimization (SMPSO) optimization algorithm is implemented to assess whether the constructal design can improve the performance of the DCMD
Summary
Where R is the gas constant, Mw is the water molecular weight and T is the membrane temperature. Where the water vapor pressure at each side of the membrane can be written: Pw.p.m(T) = Psat.w(T). The water vapor pressure at the feed channel can be expressed as: Pw.f .m(T) = γw(1 − X)Psat.w(T). Where mf is the water mass flow rate, hf .b is the bulk enthalpy of liquid water and hv.f .m represents the vapor enthalpy at the membrane surface which flows through the membrane into the permeate channel. It is assumed that no mass is added or removed inside the membrane and all vapor flows from the feed channel into the permeate channel without any condensation in the membrane pores. Where Tf .b , Tp.b , Tf .m , Tp.m are the bulk and membrane surface temperature of the feed and permeate channel, respectively. Geometrical parameters Length, L Width, w Channel depth, hch Membrane thickness, δm Porosity, ǫ Pore size, rp Operational parameters Feed inlet temperature,Tin.f Permeate inlet temperature, Tin.p Feed inlet volumetric flow rate, qin.f Permeate inlet volumetric flow rate,qin.f Feed Inlet salinity, sin
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