{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,21]],"date-time":"2026-04-21T22:49:09Z","timestamp":1776811749738,"version":"3.51.2"},"reference-count":26,"publisher":"European Society of Computational Methods in Sciences and Engineering","issue":"5","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["JCM"],"published-print":{"date-parts":[[2023,10,6]]},"abstract":"<jats:p>Thermoelectricity technology, as a kind of cost-effective and pollution-free power generation solution, is often used for waste heat recovery and utilization. In this paper, the temperature distribution of a Two-stage Thermoelectric Generator (TTEG) under constant temperature conditions has been studied using a one-dimensional heat conduction model. Moreover, by combining the obtained temperature distribution with the three-dimensional size of TTEG, a calculation formula of resistance and voltage was developed based on the calculus method. When the sum of cross-sectional areas of all the PN-type thermoelectric arms respectively in high- and low-temperature layers is constant, the optimal ratio between cross-sectional areas of a single PN-thermoelectric arm respectively in high- and low-temperature layers can be calculated using the proposed formula in this study to achieve the maximum output power. Results also showed the relationship between the heights of PN-type thermoelectric arms and the temperature distributions in high- and low-temperature layers. Using PbTe as the medium temperature thermoelectric material and Bi2Te3 as the low temperature thermoelectric material, a case study was conducted on the PN-type thermoelectrics with the same total height and the same total cross-sectional area. The theoretical calculation results showed that the bigger of maximum output power between the two-stage thermoelectric generator and that of the Segmented Thermoelectric Generator (STEG) is related to the hot and cold end temperature.<\/jats:p>","DOI":"10.3233\/jcm-226876","type":"journal-article","created":{"date-parts":[[2023,6,20]],"date-time":"2023-06-20T11:28:11Z","timestamp":1687260491000},"page":"2463-2483","source":"Crossref","is-referenced-by-count":0,"title":["Optimization and comparison of two-stage thermoelectric generators considering the influence of temperature variation on materials for waste heat utilization"],"prefix":"10.66113","volume":"23","author":[{"given":"Wensheng","family":"Cao","sequence":"first","affiliation":[{"name":"College of Marine Equipment and Mechanical Engineering, Jimei University, Xiamen, Fujian, China"},{"name":"Fujian Province Key Lab of Energy Cleaning Utilization and Development, Jimei University, Xiamen, Fujian, China"},{"name":"Cleaning Combustion and Energy Utilization Research Center of Fujian Province, Jimei University, Xiamen, Fujian, China"},{"name":"Marine Platform Support System Fujian University Engineering Research Center, Jimei University, Xiamen, Fujian, China"},{"name":"Fujian Province University Key Laboratory of Ocean Renewable Energy Equipment, Jimei University, Xiamen, Fujian, China"}]},{"given":"Jie","family":"Lei","sequence":"additional","affiliation":[{"name":"College of Marine Equipment and Mechanical Engineering, Jimei University, Xiamen, Fujian, China"}]},{"given":"Jianzhuang","family":"Xu","sequence":"additional","affiliation":[{"name":"College of Marine Equipment and Mechanical Engineering, Jimei University, Xiamen, Fujian, China"}]},{"given":"Baolin","family":"Wang","sequence":"additional","affiliation":[{"name":"College of Marine Equipment and Mechanical Engineering, Jimei University, Xiamen, Fujian, China"}]},{"given":"Meiying","family":"Huang","sequence":"additional","affiliation":[{"name":"College of Marine Equipment and Mechanical Engineering, Jimei University, Xiamen, Fujian, China"}]},{"given":"Ruifang","family":"Zhang","sequence":"additional","affiliation":[{"name":"College of Marine Engineering, Jimei University, Xiamen, Fujian, China"}]},{"given":"Christoph","family":"Bluth","sequence":"additional","affiliation":[{"name":"University of Bradford, West Yorkshire, Bradford, UK"}]}],"member":"55691","reference":[{"key":"10.3233\/JCM-226876_ref1","doi-asserted-by":"crossref","first-page":"540","DOI":"10.1016\/j.apenergy.2017.01.002","article-title":"Geometry optimization of two-stage thermoelectric generators using simplified conjugate-gradient method","volume":"190","author":"Liu","year":"2017","journal-title":"Applied Energy."},{"key":"10.3233\/JCM-226876_ref2","doi-asserted-by":"crossref","unstructured":"Liu C, Deng YD, Wang XY, Wang X, Liu YP. 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