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Mathematics 2021, 9, 33 18 of 31 The specific heat of dry air is given by [81]: ca = 1045.356a + 0.0007083814Ta2 − 2.705209 × 10−7 Ta3 − 0.3161783T The specific heat of water vapour is given by [81]: cv = 1360.5 + 2.31334Ta − 2.46 × 10−10 Ta5 + 5.9 × 10−13 Ta6 Finally, the specific heat of humid air is calculated using [81]: chumid−air = ca + ωcv The dynamic viscosity of dry air in terms of the temperature is given by [81]: μa = 2.287973 × 10−6 + 6.259793 × 10−8 Ta − 3.131956 × 10−11 Ta2 + 8.15038 × 10−15 Ta3 The dynamic viscosity of water vapour is given by [81]: μv = 2.562435 × 10−6 + 1.816683 × 10−8 Ta − 2.579066 × 10−11 Ta2 − 1.067299 × 10−14 Ta3 (29) (30) (31) (32) (33) (34) Finally, for the humid air, the dynamic viscosity is [81]: 1 0.5 ω 0.5 1+1.608ω μa Ma + μhumid−air = 1 M0.5 + 1+1.608ω a 4. Benchmarking of Simulation Results ω+0.622 ω ω+0.622 μv Mv M0.5 v The benchmarking of the current simulation results is accomplished by comparison with the experimental and the simulation results of Dai et al. [75] without considering the waste heat recovery of the feedwater from the condensing coil. A solar desalination study having humidification and dehumidification processes, both mathematically and exper- imentally, was presented. All of the conditions considered by Dai et al. [75] are codified in MATLAB simulation and the desired results are obtained. The initial conditions for this benchmarking are: inlet temperature of the air is 35 ◦C, inlet relative humidity is 40%, MFR of saline water is 1500 kg/h, the NTUs of condensing coil are 4, the MFR of cooling coil is 2500 kg/h, and the incident solar radiation is 700 W/m2. The humidifier is 0.6m long and has a cross-sectional area of 0.56m2. Considering these input parameters in the developed code, the compliance between the current simulation results and the simulation results of Dai et al. [75] are shown in Figure 5 in which the variation in water productivity is shown with changing MFR of working air along with different water film temperature. A maximum discrepancy of 2.33% is observed between both simulation results. The discrepancy is caused by the advanced modelling of solar collector adapted by the authors as compared to the relatively simplified mathematical model of [75]. It is to be stressed here that the feed water recirculation (waste heat recovery) [83] is not included for this comparison to fully replicate the conditions of [75]. The results of the simulation study are also benchmarked by comparison with the experimental results of Dai et al. [75]. A comparison is carried out for two cases. For the case, I, the MFR of air is 615.6 kg/h, and the ambient relative humidity is 54%. For case II: the MFR of air is 661.8 kg/h, and relative humidity is 49%. For both cases: the ambient air temperature is ~22 ◦C, the feedwater temperature is ~19 ◦C, the MFR of saline water is 2310 kg/h and the MFR of feed water in condensing coil is 3780 kg/h. Here it is stressed that the authors of [75] replaced the solar collector by a boiler to obtain quick lab results during experimentation. The authors of the current work carried out analysis by considering the solar collector. Subsequently, an analysis is also carried out by solving the boiler as a heat input. The analysis considering boiler and solar collector along with experimental data of [75] for each of the case I and case II is shown in Figure 6a,b. It can be observed here that the water productivity level for the solar collector is lower than thePDF Image | Humidification Dehumidification Solar Desalination System
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