{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,23]],"date-time":"2026-06-23T00:43:04Z","timestamp":1782175384851,"version":"3.54.5"},"reference-count":35,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2022,12,30]],"date-time":"2022-12-30T00:00:00Z","timestamp":1672358400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12147169"],"award-info":[{"award-number":["12147169"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12205101"],"award-info":[{"award-number":["12205101"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Materials"],"abstract":"<jats:p>Over the past two decades, effective control of physical fields, such as light fields or acoustics fields, has greatly benefited from transforming media. One of these rapidly growing research areas is transformation thermotics, especially embodied in the thermal conductive and radiative modes. On the other hand, transformation media in thermal convection has seldom been studied due to the complicated governing equations involving both fluid motion and heat transfer terms. The difficulty lies in the robustness of form invariance in the Navier\u2013Stokes equations or their simplified forms under coordinate transformations, which determines whether the transformation operations can be executed on thermal convection to simultaneously regulate the flow and thermal fields. In this work, we show that thermal convection in two-dimensional Hele\u2013Shaw cells keeps form-invariance, while its counterpart in general creeping flows or general laminar flows does not. This conclusion is numerically verified by checking the performances of invisible devices made of transformation media in convective environments. We further exploit multilayered structures constituted of isotropic homogeneous natural materials to realize the anisotropic inhomogeneous properties required for transformation media. Our results clarify the long-term confusion about the validation of the transformation method in thermal convection and provide a rigorous foundation and classical paradigm on inspiring various fascinating metadevices in both thermal and flow fields.<\/jats:p>","DOI":"10.3390\/ma16010376","type":"journal-article","created":{"date-parts":[[2023,1,2]],"date-time":"2023-01-02T03:08:59Z","timestamp":1672628939000},"page":"376","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["On Transformation Form-Invariance in Thermal Convection"],"prefix":"10.3390","volume":"16","author":[{"given":"Gaole","family":"Dai","sequence":"first","affiliation":[{"name":"School of Sciences, Nantong University, Nantong 226019, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3992-7930","authenticated-orcid":false,"given":"Jun","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Physics, East China University of Science and Technology, Shanghai 200237, China"},{"name":"School of Mathematics, East China University of Science and Technology, Shanghai 200237, China"},{"name":"Wenzhou Institute, University of Chinese Academy of Sciences, Wenzhou 325001, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2022,12,30]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1780","DOI":"10.1126\/science.1125907","article-title":"Controlling electromagnetic fields","volume":"312","author":"Pendry","year":"2006","journal-title":"Science"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"1777","DOI":"10.1126\/science.1126493","article-title":"Optical conformal mapping","volume":"312","author":"Leonhardt","year":"2006","journal-title":"Science"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"100819","DOI":"10.1016\/j.mtphys.2022.100819","article-title":"Metamaterials: Optical, acoustic, elastic, heat, mass, electric, magnetic, and hydrodynamic cloaking","volume":"27","author":"Martinez","year":"2022","journal-title":"Mater. 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