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mathematics Article Mathematical Approach to Improve the Thermoeconomics of a Humidification Dehumidification Solar Desalination System Rasikh Tariq 1,* , Jacinto Torres Jimenez 2, Nadeem Ahmed Sheikh 3 and Sohail Khan 4 Citation: Tariq, R.; Jimenez, J.T.; Ahmed Sheikh, N.; Khan, S. Mathematical Approach to Improve the Thermoeconomics of a Humidification Dehumidification Solar Desalination System. Mathematics 2021, 9, 33. https://dx.doi.org/10.3390/ math9010033 Received: 24 June 2020 Accepted: 15 October 2020 Published: 25 December 2020 1 2 3 4 * Correspondence: rasikhtariq@gmail.com or rasikhtariq@alumnos.uady.mx; Tel.: +52-1-999-174-1935 Abstract: Water desalination presents a need to address the growing water-energy nexus. In this work, a literature survey is carried out, along an application of a mathematical model is presented to enhance the freshwater productivity rate of a solar-assisted humidification-dehumidification (HDH) type of desalination system. The prime novelty of this work is to recover the waste heat by reusing the feedwater at the exit of the condenser in the brackish water storage tank and to carry out the analysis of its effectiveness in terms of the system’s yearly thermoeconomics. The developed mathematical model for each of the components of the plant is solved through an iterative procedure. In a parametric study, the influence of mass flow rates (MFRs) of inlet air, saline water, feedwater, and air temperature on the freshwater productivity is shown with and without the waste heat recovery from the condensing coil. It is reported that the production rate of water is increased to a maximum of 15% by recovering the waste heat. Furthermore, yearly analysis has shown that the production rate of water is increased to a maximum of 16% for June in the location of Taxila, Pakistan. An analysis is also carried out on the economics of the proposed modification, which shows that the cost per litre of the desalinated water is reduced by ~13%. It is concluded that the water productivity of an HDH solar desalination plant can be significantly increased by recovering the waste heat from the condensing coil. Keywords: desalination; humidification-dehumidification; waste heat recovery; mathematical model; yearly analysis; thermo-economics 1. Introduction Water covers almost 71% of the total Earth’s surface [1]. Sea contains 97% of the total water of the Earth [2] and the remaining 3% is stored in the form of rivers, glaciers, underground water storage, and lakes, etc. The freshwater is not evenly distributed in the world, as some geography near the equator has less availability of freshwater. The seawater contains a large number of salts. Therefore, it is not feasible to be used for household, agricultural, or commercial purposes [3]. Considering this aspect, desalination is an important need of the human being. In this regard, Manju et al. [4] provided an extensive review of the need for a desalination system to overcome future freshwater demand for India. Among many desalination processes [5], some can be energy inefficient, costly, and/or can have environmental impacts (CO2 emissions and other dangerous byproducts as referenced by [6]) depending on the design parameters [7]. The use of solar radiation is undergoing intensive research for the desalination pro- cess [5] since solar energy is a low-grade heat source considering the exergetic useful- Facultad de Ingeniería, Universidad Autónoma de Yucatán, Av. Industrias No Contaminantes por Anillo Periférico Norte, Apdo. Postal 150, Cordemex, Mérida 97310, Yucatán, Mexico Ingeniería Eléctrica-Maestría en Tecnologías de la Información, Tecnológico Nacional de México/Instituto Tecnológico Superior de Huauchinango, Av. Tecnológico No. 80, Col. 5 de Octubre, Huauchinango 73173, Puebla, Mexico; jacinto.torres@huauchinango.tecnm.mx Department of Mechanical Engineering, Faculty of Engineering and Technology, International Islamic University, Islamabad 44000, Pakistan; ndahmed@gmail.com Programa de Maestría y Doctorado en Ingeniería, Especialidad en Sistemas Eléctricos de Potencia, Universidad Nacional Autónoma de México, Ciudad de México 04510, Mexico; sohailmomand6@gmail.com Publisher’s Note: MDPI stays neu- tral with regard to jurisdictional claims in published maps and institutional affiliations. Copyright: © 2020 by the authors. Li- censee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/ licenses/by/4.0/). Mathematics 2021, 9, 33. https://dx.doi.org/10.3390/math9010033 https://www.mdpi.com/journal/mathematicsPDF Image | Humidification Dehumidification Solar Desalination System
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