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Mathematics 2021, 9, 33 15 of 31 The radiative heat transfer coefficient is given by: s s s2 s2 s σ Tp+Tg Tp +Tg hr,p−g= s s 1/εp + 1/εg −1 (13) 3.2. Water Storage Tank In this research study, the feed water of the dehumidifier is being re-used in the brackish water storage, therefore, a mass and energy balance is of key importance. A mass and energy balance applied on the storage tank yields: 15 of 33 (12) (13) Mathematics 2020, 8, x FOR PEER REVIEW Ras 1/3 + + 3.3. Humidifier m3 +m6 +m11 −m1 −m4 = 0 (14) (15) s mh +mhp−g+m h −mh −1m708h =0 3 3 6 6 11 11 1 1 4 4 The radiative heat transfer coefficient is given by: Nu =1+ −1 +1.441− p−g 5830 Rasp−g The humidification section consists of a falling film of water with accompanying airflow. It is assumed that the process is quasi-steady with negligible heat loss. The falling σ Ts +Ts Ts2 +Ts2 (p g)(p g) film is an assumed laminar swith a smooth liquid-gas interface. Figure 3 shows a typical hr,p−g = s s element in the humidifier section wit1h/aεcco+m1p/aεnyin−g1 zones. The mean velocity of a falling (p)(g) film is calculated using the following equation [71]: 3.2. Water Storage Tank h ρwgδw2 uw = 3μ In this research study, the feed water of the dehumidifier is being re-used in the brackish water Mathematics 2020, 8, x FOR PEER REVIEW 16 of 33 storage, therefore, a mass and energy balance is of key importance. A mass and energy balance applied on the storage tank yields: w (16) y2 3.3. Humidif s z y Air Cha nne l m3 +m6 +m11 −m1 −m4 =0 (14) mh+mh+mh−mh−mh=0 (15) ier m idifi Figure 3. Schematic diagrFaimguoref c3o.nStcrh heat transfer coefficient. It can be written as: o w 3μw e With the thickness of the falling film, given by [72]: Eams [74] predicted the water evaporation rate as shown in Equation (20). us ue 33 66 1111 11 44 The hu assumed that the process is quasi-steady with negligible heat loss. The falling film is an assumed laminar with a smooth liquid-gas interface. Figure 3 shows a typical element in the humidifier section with accompanying zones. The mean velocity of a falling film is calculated using the following equation [71]: (16) cation section consists of a falling film of water with accompanying airflow. It is lmvoaltuicmdeiagnralmysiosfocfotnhterohluvmo=liudmifiecatniaolnysiescotifotnh.e humidification section. W =ε*(P−P) M/2πRT (20) jsvn Knudsonconstantofevaporation[75] ε*iswrittenintermsofthecoefficientofevaporation: With the thickness of the falling film, given by [72]: ρ gδ2 hww ε*= 2ε 2−ε whereas the coefficient of evaporation is calculated using [74]: (21) (17) (17) (22) (18) 2πRT T The energy balans ce es quation is [72,73]: ε = h* Considering the evaporation affecting the heat transfer coefficient h * , the concept of wet bulb M ρvλ2 coefficient of heat transfer as proposed by MacLaine-Cross and Banks [76] can be used to correct the ∂Th ∂2Th uh w=α w w ∂z w ∂y2 2 The solution of Equation (18) requires the following boundary condition [73]:PDF Image | Humidification Dehumidification Solar Desalination System
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