Humidification Dehumidification Solar Desalination System

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Humidification Dehumidification Solar Desalination System ( humidification-dehumidification-solar-desalination-system )

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Mathematics 2021, 9, 33 14 of 31 s 􏲂 s s􏰰 1 1 􏰱􏲃−1 F′=WULss sss+ss (3) (4) (5) UL[D +(M −D )F ] Fs = tanh[ζs(Ms − Ds)/2] πDihc,w ζs(Ms − Ds/2) 􏳤 Us ζs = L k sp t sp The temperature of the absorber plate is calculated through an iterative method by the solution of Equations (1)–(5) coupled with: Ts =Ts+Qsu/Asc(1−Fs) (6) p 2 FRsULs R The total absorbed solar radiation (S) is evaluated by considering the beam and dif- fused components of incident solar radiation along with the incorporation of optical losses (i.e., transmittance-absorptance product). Ss = Ibs(τα)sb + Ids(τα)sd (7) The transmittance-absorptance product is calculated separately for beam and diffused radiation. s τ bs , d α sp (τα)b,d= 􏱃 s􏱄 s (8) 1− 1−αp R Fresnel’s expressions [61] are derived for the reflection of unpolarized radiation passing from medium 1 to medium 2 with different refractive indexes given the angle of incidence and refraction for the parallel and perpendicular components of the beam and diffused radiation. This procedure gives two Fresnel’s expressions of the beam and dif- fused radiation with averaged parallel and the perpendicular component of each one, and finally, it is used to calculate the transmissivity of solar radiation from the glass cover to the absorber plate. Along with that, the incident angle for direct radiation is the angle of incidence, given by: cosθbs = sinδs sinφs +cosδs cosφs cosωs (9) Afterwards, Snell’s law [61] is utilized to obtain the refractive angles from the glazing. By taking into account the top heat loss coefficient only, the overall heat loss coefficient Utsop is computed as follows. 􏳞1 1􏳟−1 Utsop= hs +hs +hs +hs (10) c,g−a r,g−a c,p−g r,p−g The bottom and side heat loss coefficients are considered negligible. Practically, it can be made possible through the usage of insulation materials which can be glass mineral roll [65], rice husk and sunflower stalks [66], petiole piece, fibres and gypsum [67], and mineral wool [68]. The convective heat transfer coefficient is calculated using [61,69]: hsa = 5.7 + 3.8vsa (11) The method proposed in [70] is used to compute the Nusselt number between the absorber plate and the glass cover. 􏰤Rasp−g􏰥1/3 + 􏳞 1708 􏳟+ Nusp−g=1+ 5830 −1 +1.44 1−Ras (12) p−g

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