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Mathematics 2021, 9, 33 26 of 31 where m is the mass flow rate (kg/s) of water in the section, H is the enthalpy (kJ/kg) and ηm is the mechanical efficiency of pump which is considered 0.96 [86]. The blower Wblower is calculated by considering the pressure drop and it is given by [87]: Wblower = Q × ∆P × C (39) η0 × η1 The details of the parameters used in Equation (39) is given as follows: 1. The pressure drop is calculated by considering the hydraulic calculation formulas, and it is given by: ff L ρu2 ∆P = Re·d · 2 (40) e where f f is the friction factor, Re is the non-dimensional Reynolds number, L is the effective length of the channel, de is the hydraulic diameter, ρ is the density of air, and u is the averaged velocity of the channel calculated using the ratio of volume flow rate per unit cross-sectional area. These parameters are calculated for humidifier and dehumidifier section differently and finally, the aggregation of both pressure differences gives the total pressure difference. The friction factor ( f f ) is given by the empirical formula: f f = 961 − 1.3553AR + 1.9467AR2 − 1.7012AR3 + 0.9564AR4 − 0.2537AR5 (41) The aspect ratio is a comparison between the shorter and the longer side of the cross-section of the air channel given by: AR = Shorter dimension of the cross − section of air channel (42) Longer dimension of the cross − section of air channel 2. η0 is the internal efficiency of the fan which is considered 0.75 [88]. 3. η1 is the mechanical efficiency of the fan which is considered 0.9 [89]. 4. C is the motor capacity coefficient which is 1.1 [90]. For an industrial rate of the cost of electricity at 12 PKR/kWh, the annual running cost is 8,176,000 PKR. The salvage value is calculated using the sinking fund factor, given by: SRF = i (43) (1+i)n −1 Finally, the total annual cost is calculated using the balance of life cycle costs, given by: Total Annual cost = First Annual Cost + Annual Maintenance Cost + Annual Running Cost − Annual Salvage Value (44) With this methodology, the production cost of desalinated water is 17.16 PKR/litre (0.15 USD/litre) without waste heat recovery and it is 14.85 PKR/litre (0.13 USD/litre) with waste heat recovery. Therefore, the production cost of the water is decreased by ~13% by recovering the waste heat from the condensing coil. 7. Conclusions In this research paper, a simulation is carried out for the humidification-dehumidification (HDH) type of desalination system in which the emphasis is given to the performance of the plant by recovering the heat from the condensing coil by reusing the feed water in the brackish water storage tank. The feedwater is recirculated because it has relatively high enthalpy as it absorbs energy in the dehumidification process of air. The mathemat- ical model of the system is simulated, and the results are validated by comparing them with the previously published experimental and numerical results without waste heatPDF Image | Humidification Dehumidification Solar Desalination System
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