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Mathematics 2021, 9, 33 13 of 31 Afterwards, the salty water is pumped to the humidification section from state 4 to 5 where it comes in direct contact with the ambient air entering at state 7. Depending on the climatic conditions, ambient air blown through the humidification chamber at state 7 where it absorbs moisture from the falling film of water. The saturated moist air leaves the humidification section at state 8, whereas the remaining salty water is re-circulated to the brackish water storage. The corresponding psychometric description of this process is presented in Figure 2a1 in which the air leaves at the saturation conditions [49]. The moist air at state 8 enters the dehumidification section where feed/cooling water is circulated at a relatively high flow rate to facilitate dehumidification. As a result, fresh condensed water is collected in a tank at state 12, and the air leaves the system to the environment. The corresponding dehumidification process is described on a psychometric chart as in Figure 2a2 [49]. The feed water at exit 11 of the dehumidification section has relatively high enthalpy because it receives heat from the humid air. In this work, the heat from this feed water is recovered by supplying it back to the brackish water storage tank. There can be many practical ways to collect the condensed water from the dehumidifi- cation section. For instance, in other configurations of thermal desalination, Patel et al. [52] and Nayi et al. [53] have shown that an outlet pipe supported with a trough placed inside assembly of a solar still can be used and finally the condensed water can be collected in a beaker outside. In a theoretical and experimental study of seawater desalination based on humidification-dehumidification technique, Mohamed et al. [54] have demonstrated that the freshwater can be collected at the bottom of the condensation coil for a vertical section. In another work, Rajaseenivasan et al. [55] presented an experimentally verified HDH system with a dual-purpose collector and employed a horizontal flow shell-and-tube heat exchanger with the condensed water collected at the bottom from the end of the dehumidifier. Another configuration is demonstrated by Xu et al. [56] in which a novel enhanced HDH method with weakly compressed air and internal heat recovery based on traditional mechanical vapour compression is developed in which the moist air is used as a working fluid instead of a vapour. In this experimentally developed configuration [57], the freshwater is extracted from the evaporator-condenser assembly having airflow in the horizontal direction. 3. Mathematical Model The thermal performance of the solar-assisted desalination plant is evaluated by developing a mathematical [58] expression of the components involved such as solar collector, brackish water storage, humidifier [59], and dehumidifier. 3.1. Flat Plate Solar Collector Ioan Sarbu and Calin Sebarchievici [60] have reported that the flat-plate collectors are the heart of any solar energy collection system designed for operation in the low- temperature range (less than 60 ◦C) [60] or the medium temperature range (less than 100 ◦C) [60]. It is used to absorbed solar energy, convert it into heat, and then to transfer that heat to a stream of liquid (as in this case). They use both direct and diffuse solar radiations [60], do not require tracking of the sun [60], and require little maintenance [60]. They are mechanically simpler than concentrating collectors [60]. The major applications of these units are in solar water heating, building heating, air conditioning, and industrial process heating [60]. For quasi-steady-state conditions [61] at a given solar time, along with other standard assumptions [62–64], the following energy balance equation can be written Qs =AsSs−UsTs−T =AsFs[Ss−Us(Ts−T )]=ms c (Ts−Ts) (1) uc Lpamb cR L2amb w,1p,w32 where: s msw,1cp,w AscULs F′s FR= AsUs 1−exp ms c (2) c L w,1 p,wPDF Image | Humidification Dehumidification Solar Desalination System
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