{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,14]],"date-time":"2026-05-14T10:07:00Z","timestamp":1778753220773,"version":"3.51.4"},"reference-count":55,"publisher":"Springer Science and Business Media LLC","issue":"4","license":[{"start":{"date-parts":[[2022,4,27]],"date-time":"2022-04-27T00:00:00Z","timestamp":1651017600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2022,4,27]],"date-time":"2022-04-27T00:00:00Z","timestamp":1651017600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Engineering with Computers"],"published-print":{"date-parts":[[2023,8]]},"DOI":"10.1007\/s00366-022-01646-1","type":"journal-article","created":{"date-parts":[[2022,4,27]],"date-time":"2022-04-27T19:03:18Z","timestamp":1651086198000},"page":"2717-2733","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["A numerical approach for optimization of the working fluid of a standing-wave thermo-acoustic refrigerator"],"prefix":"10.1007","volume":"39","author":[{"given":"R.","family":"Rahpeima","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1567-1136","authenticated-orcid":false,"given":"R.","family":"Ebrahimi","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2022,4,27]]},"reference":[{"key":"1646_CR1","doi-asserted-by":"crossref","first-page":"135","DOI":"10.1016\/S0065-2156(08)70233-3","volume":"20","author":"N Rott","year":"1980","unstructured":"Rott N (1980) Thermoacoustics. Adv Appl Mech 20:135\u2013175","journal-title":"Adv Appl Mech"},{"issue":"4","key":"1646_CR2","doi-asserted-by":"crossref","first-page":"1145","DOI":"10.1121\/1.396617","volume":"84","author":"GW Swift","year":"1988","unstructured":"Swift GW (1988) Thermoacoustic engines. J Acoust Soc Am 84(4):1145\u20131180","journal-title":"J Acoust Soc Am"},{"issue":"1","key":"1646_CR3","doi-asserted-by":"crossref","first-page":"43","DOI":"10.1007\/BF01596277","volume":"26","author":"N Rott","year":"1975","unstructured":"Rott N (1975) Thermally driven acoustic oscillations, part III: Second-order heat flux. Zeitschrift f\u00fcr angewandte Mathematik und Physik ZAMP 26(1):43\u201349","journal-title":"Zeitschrift f\u00fcr angewandte Mathematik und Physik ZAMP"},{"key":"1646_CR4","doi-asserted-by":"crossref","first-page":"828","DOI":"10.1016\/j.energy.2015.09.005","volume":"93","author":"T Jin","year":"2015","unstructured":"Jin T et al (2015) Thermoacoustic prime movers and refrigerators: thermally powered engines without moving components. Energy 93:828\u2013853","journal-title":"Energy"},{"issue":"1","key":"1646_CR5","doi-asserted-by":"crossref","first-page":"153","DOI":"10.1121\/1.389624","volume":"74","author":"J Wheatley","year":"1983","unstructured":"Wheatley J et al (1983) An intrinsically irreversible thermoacoustic heat engine. J Acoust Soc Am 74(1):153\u2013170","journal-title":"J Acoust Soc Am"},{"issue":"4","key":"1646_CR6","doi-asserted-by":"crossref","first-page":"595","DOI":"10.2514\/3.466","volume":"7","author":"SL Garrett","year":"1993","unstructured":"Garrett SL, Adeff JA, Hofler TJ (1993) Thermoacoustic refrigerator for space applications. J Thermophys Heat Transfer 7(4):595\u2013599","journal-title":"J Thermophys Heat Transfer"},{"key":"1646_CR7","doi-asserted-by":"crossref","unstructured":"Ballister SC, McKelvey DJ (1995) Shipboard electronics thermoacoustic cooler. Naval Postgraduate School Monterey CA.","DOI":"10.1121\/1.414330"},{"issue":"6","key":"1646_CR8","doi-asserted-by":"crossref","first-page":"L37","DOI":"10.1121\/1.429324","volume":"107","author":"JA Adeff","year":"2000","unstructured":"Adeff JA, Hofler TJ (2000) Design and construction of a solar-powdered, thermoacoustically driven, thermoacoustic refrigerator. J Acoust Soc Am 107(6):L37\u2013L42","journal-title":"J Acoust Soc Am"},{"issue":"21","key":"1646_CR9","doi-asserted-by":"crossref","first-page":"4730","DOI":"10.1016\/j.ijheatmasstransfer.2011.06.003","volume":"54","author":"A Berson","year":"2011","unstructured":"Berson A et al (2011) Nonlinear temperature field near the stack ends of a standing-wave thermoacoustic refrigerator. Int J Heat Mass Transf 54(21):4730\u20134735","journal-title":"Int J Heat Mass Transf"},{"key":"1646_CR10","doi-asserted-by":"crossref","first-page":"52","DOI":"10.1016\/j.ijrefrig.2017.01.013","volume":"75","author":"SG Yahya","year":"2017","unstructured":"Yahya SG, Mao X, Jaworski AJ (2017) Experimental investigation of thermal performance of random stack materials for use in standing wave thermoacoustic refrigerators. Int J Refrig 75:52\u201363","journal-title":"Int J Refrig"},{"key":"1646_CR11","doi-asserted-by":"crossref","first-page":"635","DOI":"10.1007\/978-981-13-6148-7_61","volume-title":"Smart technologies for energy, environment and sustainable development","author":"AS Raut","year":"2019","unstructured":"Raut AS, Wankhede US, Ramteke S (2019) Experimental study on the performance of standing wave thermoacoustic refrigeration system. Smart technologies for energy, environment and sustainable development. Springer, pp 635\u2013641"},{"issue":"8","key":"1646_CR12","doi-asserted-by":"crossref","first-page":"639","DOI":"10.1080\/15435075.2019.1602533","volume":"16","author":"MA Alamir","year":"2019","unstructured":"Alamir MA (2019) Experimental study of the stack geometric parameters effect on the resonance frequency of a standing wave thermoacoustic refrigerator. Int J Green Energy 16(8):639\u2013651","journal-title":"Int J Green Energy"},{"issue":"1","key":"1646_CR13","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1016\/S0140-7007(96)00064-3","volume":"20","author":"M Wetzel","year":"1997","unstructured":"Wetzel M, Herman C (1997) Design optimization of thermoacoustic refrigerators. Int J Refrig 20(1):3\u201321","journal-title":"Int J Refrig"},{"key":"1646_CR14","doi-asserted-by":"crossref","unstructured":"Herman C, Lavin C, Tr\u00e1vn\u00ed\u010dek ZK (2008) Performance of thermoacoustic refrigerators: cooling load and coefficient of performance. In: ASME 2008 Heat Transfer Summer Conference collocated with the Fluids Engineering, Energy Sustainability, and 3rd Energy Nanotechnology Conferences. American Society of Mechanical Engineers","DOI":"10.1115\/HT2008-56436"},{"issue":"7","key":"1646_CR15","doi-asserted-by":"crossref","first-page":"1338","DOI":"10.2514\/1.4342","volume":"42","author":"D Marx","year":"2004","unstructured":"Marx D, Blanc-Benon P (2004) Numerical simulation of stack-heat exchangers coupling in a thermoacoustic refrigerator. AIAA J 42(7):1338","journal-title":"AIAA J"},{"issue":"5","key":"1646_CR16","doi-asserted-by":"crossref","first-page":"2993","DOI":"10.1121\/1.2063087","volume":"118","author":"D Marx","year":"2005","unstructured":"Marx D, Blanc-Benon P (2005) Computation of the temperature distortion in the stack of a standing-wave thermoacoustic refrigerator. J Acoust Soc Am 118(5):2993\u20132999","journal-title":"J Acoust Soc Am"},{"key":"1646_CR17","doi-asserted-by":"crossref","first-page":"243","DOI":"10.1016\/j.enconman.2016.06.041","volume":"123","author":"T Jin","year":"2016","unstructured":"Jin T et al (2016) Acoustic field characteristics and performance analysis of a looped travelling-wave thermoacoustic refrigerator. Energy Convers Manage 123:243\u2013251","journal-title":"Energy Convers Manage"},{"issue":"8","key":"1646_CR18","doi-asserted-by":"crossref","first-page":"301","DOI":"10.3390\/e18080301","volume":"18","author":"M Gholamrezaei","year":"2016","unstructured":"Gholamrezaei M, Ghorbanian K (2016) Thermal analysis of shell-and-tube thermoacoustic heat exchangers. Entropy 18(8):301","journal-title":"Entropy"},{"key":"1646_CR19","doi-asserted-by":"crossref","first-page":"139","DOI":"10.1016\/j.cryogenics.2018.09.012","volume":"98","author":"S Mergen","year":"2019","unstructured":"Mergen S, Y\u0131ld\u0131r\u0131m E, Turkoglu H (2019) Numerical study on effects of computational domain length on flow field in standing wave thermoacoustic couple. Cryogenics 98:139\u2013147","journal-title":"Cryogenics"},{"key":"1646_CR20","doi-asserted-by":"crossref","first-page":"1203","DOI":"10.1016\/j.applthermaleng.2018.12.093","volume":"149","author":"R Rahpeima","year":"2019","unstructured":"Rahpeima R, Ebrahimi R (2019) Numerical investigation of the effect of stack geometrical parameters and thermo-physical properties on performance of a standing wave thermoacoustic refrigerator. Appl Therm Eng 149:1203\u20131214","journal-title":"Appl Therm Eng"},{"issue":"13","key":"1646_CR21","doi-asserted-by":"crossref","first-page":"1441","DOI":"10.1080\/01430750.2018.1517673","volume":"41","author":"MA Alamir","year":"2020","unstructured":"Alamir MA, Elamer AA (2020) A compromise between the temperature difference and performance in a standing wave thermoacoustic refrigerator. Int J Ambient Energy 41(13):1441\u20131453","journal-title":"Int J Ambient Energy"},{"issue":"6","key":"1646_CR22","doi-asserted-by":"crossref","first-page":"168781402093084","DOI":"10.1177\/1687814020930843","volume":"12","author":"O Miled","year":"2020","unstructured":"Miled O, Dhahri H, Mhimid A (2020) Numerical investigation of porous stack for a solar-powered thermoacoustic refrigerator. Adv Mech Eng 12(6):1\u201314","journal-title":"Adv Mech Eng"},{"key":"1646_CR23","doi-asserted-by":"crossref","first-page":"151","DOI":"10.1016\/j.enganabound.2020.06.005","volume":"119","author":"M Abbaszadeh","year":"2020","unstructured":"Abbaszadeh M, Dehghan M (2020) Simulation flows with multiple phases and components via the radial basis functions-finite difference (RBF-FD) procedure: Shan-Chen model. Eng Anal Boundary Elem 119:151\u2013161","journal-title":"Eng Anal Boundary Elem"},{"key":"1646_CR24","doi-asserted-by":"crossref","first-page":"248","DOI":"10.1016\/j.apnum.2020.02.012","volume":"153","author":"V Mohammadi","year":"2020","unstructured":"Mohammadi V, Dehghan M (2020) A meshless technique based on generalized moving least squares combined with the second-order semi-implicit backward differential formula for numerically solving time-dependent phase field models on the spheres. Appl Numer Math 153:248\u2013275","journal-title":"Appl Numer Math"},{"key":"1646_CR25","doi-asserted-by":"crossref","first-page":"188","DOI":"10.1016\/j.enganabound.2020.04.006","volume":"118","author":"M Abbaszadeh","year":"2020","unstructured":"Abbaszadeh M, Dehghan M (2020) Direct meshless local Petrov-Galerkin method to investigate anisotropic potential and plane elastostatic equations of anisotropic functionally graded materials problems. Eng Anal Boundary Elem 118:188\u2013201","journal-title":"Eng Anal Boundary Elem"},{"key":"1646_CR26","unstructured":"Tasnim SH (2011) Porous Media Thermoacoustic Stacks: Measurements and Models. Dissertation, University of Waterloo.\u00a0http:\/\/hdl.handle.net\/10012\/6296"},{"issue":"6","key":"1646_CR27","doi-asserted-by":"crossref","first-page":"3671","DOI":"10.1121\/1.409938","volume":"95","author":"WC Ward","year":"1994","unstructured":"Ward WC, Swift GW (1994) Design environment for low-amplitude thermoacoustic engines. J Acoust Soc Am 95(6):3671\u20133672","journal-title":"J Acoust Soc Am"},{"issue":"6","key":"1646_CR28","doi-asserted-by":"crossref","first-page":"3484","DOI":"10.1121\/1.420395","volume":"102","author":"M Watanabe","year":"1997","unstructured":"Watanabe M, Prosperetti A, Yuan H (1997) A simplified model for linear and nonlinear processes in thermoacoustic prime movers. Part I. Model and linear theory. J Acoust Soc Am 102(6):3484\u20133496","journal-title":"J Acoust Soc Am"},{"issue":"6","key":"1646_CR29","doi-asserted-by":"crossref","first-page":"3497","DOI":"10.1121\/1.420396","volume":"102","author":"H Yuan","year":"1997","unstructured":"Yuan H, Karpov S, Prosperetti A (1997) A simplified model for linear and nonlinear processes in thermoacoustic prime movers. Part II. Nonlinear oscillations. J Acoust Soc Am 102(6):3497\u20133506","journal-title":"J Acoust Soc Am"},{"key":"1646_CR30","unstructured":"Salih A (2011) Conservation equations of fluid dynamics. Department of Aerospace Engineering Indian Institute of Space Science and Technology, Thiruvananthapuram"},{"key":"1646_CR31","first-page":"130","volume":"3","author":"J Dalton","year":"1802","unstructured":"Dalton J (1802) On the expansion of elastic fluids by heat. J Nat Philos Chemis Arts 3:130\u2013134","journal-title":"J Nat Philos Chemis Arts"},{"key":"1646_CR32","volume-title":"Chemistry: the molecular nature of matter and change with advanced topics","author":"M Silberberg","year":"2018","unstructured":"Silberberg M (2018) Chemistry: the molecular nature of matter and change with advanced topics. McGraw-Hill, New York"},{"key":"1646_CR33","unstructured":"Davidson TA (1993) A simple and accurate method for calculating viscosity of gaseous mixtures. US Department of the Interior, Bureau of Mines"},{"issue":"1313","key":"1646_CR34","doi-asserted-by":"crossref","first-page":"161","DOI":"10.1098\/rspa.1961.0154","volume":"263","author":"P Gray","year":"1961","unstructured":"Gray P, Wright P (1961) The thermal conductivity of mixtures of nitrogen, ammonia and hydrogen. Proc R Soc Lond Series A 263(1313):161\u2013188","journal-title":"Proc R Soc Lond Series A"},{"issue":"22","key":"1646_CR35","first-page":"737","volume":"5","author":"A Wassiljewa","year":"1904","unstructured":"Wassiljewa A (1904) Heat conduction in gas mixtures. Physikalische Zeitschrift 5(22):737\u2013742","journal-title":"Physikalische Zeitschrift"},{"issue":"5","key":"1646_CR36","doi-asserted-by":"crossref","first-page":"361","DOI":"10.1063\/1.1724352","volume":"1","author":"E Mason","year":"1958","unstructured":"Mason E, Saxena S (1958) Approximate formula for the thermal conductivity of gas mixtures. Phys fluids 1(5):361\u2013369","journal-title":"Phys fluids"},{"issue":"223","key":"1646_CR37","doi-asserted-by":"crossref","first-page":"507","DOI":"10.1080\/14786449308620508","volume":"36","author":"W Sutherland","year":"1893","unstructured":"Sutherland W (1893) LII. The viscosity of gases and molecular force. Lond Edinburgh Dublin Philos Mag J Sci 36(223):507\u2013531","journal-title":"Lond Edinburgh Dublin Philos Mag J Sci"},{"issue":"12","key":"1646_CR38","doi-asserted-by":"crossref","first-page":"1231","DOI":"10.1119\/1.1485720","volume":"70","author":"DA Russell","year":"2002","unstructured":"Russell DA, Weibull P (2002) Tabletop thermoacoustic refrigerator for demonstrations. Am J Phys 70(12):1231\u20131233","journal-title":"Am J Phys"},{"key":"1646_CR39","doi-asserted-by":"crossref","unstructured":"Pedagopu VM, Pattapu K (2013) A novel approach to design and fabrication of thermo-acoustic refrigerator using high amplitude sound waves.\u00a0IOSR J Mech Civ Eng\u00a08: 15\u201324","DOI":"10.9790\/1684-0861524"},{"issue":"5","key":"1646_CR40","doi-asserted-by":"crossref","first-page":"2677","DOI":"10.1121\/1.426884","volume":"105","author":"JR Belcher","year":"1999","unstructured":"Belcher JR et al (1999) Working gases in thermoacoustic engines. J Acoust Soc Am 105(5):2677\u20132684","journal-title":"J Acoust Soc Am"},{"issue":"1","key":"1646_CR41","doi-asserted-by":"crossref","first-page":"134","DOI":"10.1121\/1.1489451","volume":"112","author":"M Tijani","year":"2002","unstructured":"Tijani M, Zeegers J, De Waele A (2002) Prandtl number and thermoacoustic refrigerators. J Acoust Soc Am 112(1):134\u2013143","journal-title":"J Acoust Soc Am"},{"key":"1646_CR42","unstructured":"Engineering ToolBox (2003) Solids, Liquids and Gases - Thermal Conductivities. [online] Available at: https:\/\/www.engineeringtoolbox.com\/thermal-conductivity-d_429.html"},{"key":"1646_CR43","unstructured":"Hilsenrath J (1955) Tables of thermal properties of gases: comprising tables of thermodynamic and transport properties of air, argon, carbon dioxide, carbon monoxide, hydrogen, nitrogen, oxygen, and steam. 564. US Govt. Print. Off."},{"key":"1646_CR44","unstructured":"Yaws CL (1995) Handbook of transport property data: viscosity, thermal conductivity, and diffusion coefficients of liquids and gases.: Inst of Chemical Engineers."},{"key":"1646_CR45","unstructured":"Reid RC, JM Prausnitz and BE Poling (1987) The properties of gases and liquids, 4th edition, McGraw-Hill"},{"issue":"5","key":"1646_CR46","doi-asserted-by":"crossref","first-page":"109","DOI":"10.1246\/bcsj.19.109","volume":"19","author":"K Hirota","year":"1944","unstructured":"Hirota K (1944) The quantum mechanical treatment of viscosity by use of the rigid elastic sphere model. II. The Sutherland constant. Bull Chem Soc Jpn 19(5):109\u2013113","journal-title":"Bull Chem Soc Jpn"},{"key":"1646_CR47","doi-asserted-by":"crossref","DOI":"10.1007\/978-981-287-212-8","volume-title":"Air pollution and greenhouse gases: from basic concepts to engineering applications for air emission control","author":"Z Tan","year":"2014","unstructured":"Tan Z (2014) Air pollution and greenhouse gases: from basic concepts to engineering applications for air emission control. Springer, New York"},{"issue":"2","key":"1646_CR48","doi-asserted-by":"crossref","first-page":"170","DOI":"10.1080\/02786829408959706","volume":"21","author":"S Dua","year":"1994","unstructured":"Dua S et al (1994) Gravitational transport of particles in pure gases and gas mixtures. Aerosol Sci Technol 21(2):170\u2013178","journal-title":"Aerosol Sci Technol"},{"key":"1646_CR49","unstructured":"Kim J (2014) Architectural Acoustics. Sejin Co"},{"key":"1646_CR50","volume-title":"Mylar polyester film physical-thermal properties","author":"DT Films","year":"2003","unstructured":"Films DT (2003) Mylar polyester film physical-thermal properties. DuPont Teijin Films, Hopewell"},{"key":"1646_CR51","unstructured":"Shah V (1998) Handbook of plastics testing technology, 2nd edn, John Wiley & Sons.\u00a0https:\/\/www.osti.gov\/biblio\/6174437"},{"key":"1646_CR52","doi-asserted-by":"publisher","unstructured":"Valencia\u00a0 JJ & Quested PN (2013) Thermophysical properties, ASM Handbook, vol 15. Casting ASM Handbook Committee, pp 468\u2013481. https:\/\/doi.org\/10.1361\/asmhba0005240","DOI":"10.1361\/asmhba0005240"},{"key":"1646_CR53","volume-title":"Fox and McDonald\u2019s introduction to fluid mechanics","author":"RW Fox","year":"2020","unstructured":"Fox RW, McDonald AT, Mitchell JW (2020) Fox and McDonald\u2019s introduction to fluid mechanics. John Wiley & Sons, Hoboken"},{"key":"1646_CR54","unstructured":"Convective heat transfer coefficients table chart. Available from: https:\/\/www.engineersedge.com\/heat_transfer\/convective_heat_transfer_coefficients__13378.htm. Accessed 2000"},{"issue":"2","key":"1646_CR55","doi-asserted-by":"crossref","first-page":"831","DOI":"10.1121\/1.1430687","volume":"111","author":"H Ishikawa","year":"2002","unstructured":"Ishikawa H, Mee DJ (2002) Numerical investigations of flow and energy fields near a thermoacoustic couple. J Acoust Soc Am 111(2):831\u2013839","journal-title":"J Acoust Soc Am"}],"container-title":["Engineering with Computers"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00366-022-01646-1.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s00366-022-01646-1\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00366-022-01646-1.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,7,17]],"date-time":"2023-07-17T22:06:09Z","timestamp":1689631569000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s00366-022-01646-1"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,4,27]]},"references-count":55,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2023,8]]}},"alternative-id":["1646"],"URL":"https:\/\/doi.org\/10.1007\/s00366-022-01646-1","relation":{},"ISSN":["0177-0667","1435-5663"],"issn-type":[{"value":"0177-0667","type":"print"},{"value":"1435-5663","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,4,27]]},"assertion":[{"value":"2 March 2021","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"18 March 2022","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"27 April 2022","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}]}}