{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:53:38Z","timestamp":1760147618186,"version":"build-2065373602"},"reference-count":46,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2023,2,20]],"date-time":"2023-02-20T00:00:00Z","timestamp":1676851200000},"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":["11902291","11872337","U2006221","LGG21E060004","LZY22E060005","LZ22E060002"],"award-info":[{"award-number":["11902291","11872337","U2006221","LGG21E060004","LZY22E060005","LZ22E060002"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"National Natural Science Foundation of China\u2014Joint Foundation of Shandong Province","award":["11902291","11872337","U2006221","LGG21E060004","LZY22E060005","LZ22E060002"],"award-info":[{"award-number":["11902291","11872337","U2006221","LGG21E060004","LZY22E060005","LZ22E060002"]}]},{"DOI":"10.13039\/501100004731","name":"Natural Science Foundation of Zhejiang Province","doi-asserted-by":"publisher","award":["11902291","11872337","U2006221","LGG21E060004","LZY22E060005","LZ22E060002"],"award-info":[{"award-number":["11902291","11872337","U2006221","LGG21E060004","LZY22E060005","LZ22E060002"]}],"id":[{"id":"10.13039\/501100004731","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Natural Science Foundation Key Projects of Zhejiang Province","award":["11902291","11872337","U2006221","LGG21E060004","LZY22E060005","LZ22E060002"],"award-info":[{"award-number":["11902291","11872337","U2006221","LGG21E060004","LZY22E060005","LZ22E060002"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Two-dimensional direct numerical simulations of partitioned thermal convection are performed using the thermal lattice Boltzmann method for the Rayleigh number (Ra) of 109 and the Prandtl number (Pr) of 7.02 (water). The influence of the partition walls on the thermal boundary layer is mainly focused on. Moreover, to better describe the spatially nonuniform thermal boundary layer, the definition of the thermal boundary layer is extended. The numerical simulation results show that the gap length significantly affects the thermal boundary layer and Nusselt number (Nu). The gap length and partition wall thickness have a coupled effect on the thermal boundary layer and the heat flux. Based on the shape of the thermal boundary layer distribution, two different heat transfer models are identified at different gap lengths. This study provides a basis for improving the understanding of the effect of partitions on the thermal boundary layer in thermal convection.<\/jats:p>","DOI":"10.3390\/e25020386","type":"journal-article","created":{"date-parts":[[2023,2,21]],"date-time":"2023-02-21T02:07:44Z","timestamp":1676945264000},"page":"386","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Effect of Gap Length and Partition Thickness on Thermal Boundary Layer in Thermal Convection"],"prefix":"10.3390","volume":"25","author":[{"given":"Zhengyu","family":"Wang","sequence":"first","affiliation":[{"name":"National-Provincial Joint Engineering Laboratory for Fluid Transmission System Technology, School of Mechanical Engineering, Zhejiang Sci-Tech University, Hangzhou 310018, China"}]},{"given":"Huilin","family":"Tong","sequence":"additional","affiliation":[{"name":"National-Provincial Joint Engineering Laboratory for Fluid Transmission System Technology, School of Mechanical Engineering, Zhejiang Sci-Tech University, Hangzhou 310018, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2491-7879","authenticated-orcid":false,"given":"Zhengdao","family":"Wang","sequence":"additional","affiliation":[{"name":"National-Provincial Joint Engineering Laboratory for Fluid Transmission System Technology, School of Mechanical Engineering, Zhejiang Sci-Tech University, Hangzhou 310018, China"}]},{"given":"Hui","family":"Yang","sequence":"additional","affiliation":[{"name":"National-Provincial Joint Engineering Laboratory for Fluid Transmission System Technology, School of Mechanical Engineering, Zhejiang Sci-Tech University, Hangzhou 310018, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5462-1502","authenticated-orcid":false,"given":"Yikun","family":"Wei","sequence":"additional","affiliation":[{"name":"National-Provincial Joint Engineering Laboratory for Fluid Transmission System Technology, School of Mechanical Engineering, Zhejiang Sci-Tech University, Hangzhou 310018, China"}]},{"given":"Yuehong","family":"Qian","sequence":"additional","affiliation":[{"name":"School of Mathematical Science, Soochow University, Suzhou 215006, China"},{"name":"College of Mathematics and Computer Science, Zhejiang Normal University, Jinhua 321004, China"}]}],"member":"1968","published-online":{"date-parts":[[2023,2,20]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"105112","DOI":"10.1063\/5.0024408","article-title":"Correlation of internal flow structure with heat transfer efficiency in turbulent Rayleigh\u2013B\u00e9nard convection","volume":"32","author":"Xu","year":"2020","journal-title":"Phys. Fluids"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"123502","DOI":"10.1103\/PhysRevFluids.5.123502","article-title":"Heat transfer enhancement in Rayleigh-B\u00e9nard convection using a single passive barrier","volume":"5","author":"Liu","year":"2020","journal-title":"Phys. Rev. Fluids"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"A14","DOI":"10.1017\/jfm.2021.58","article-title":"Stabilizing\/destabilizing the large-scale circulation in turbulent Rayleigh-B\u00e9nard convection with sidewall temperature control","volume":"915","author":"Zhang","year":"2021","journal-title":"J. Fluid Mech."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"A60","DOI":"10.1017\/jfm.2021.21","article-title":"Effects of Prandtl number in quasi-two-dimensional Rayleigh-B\u00e9nard convection","volume":"915","author":"Li","year":"2021","journal-title":"J. Fluid Mech."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"65103","DOI":"10.1063\/5.0048775","article-title":"Large-scale structures of turbulent Rayleigh-B\u00e9nard convection in a slim-box","volume":"33","author":"Zhou","year":"2021","journal-title":"Phys. Fluids"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"282","DOI":"10.1006\/jcph.1998.6057","article-title":"A novel thermal model for the lattice Boltzmann method in incompressible limit","volume":"146","author":"He","year":"1998","journal-title":"J. Comput. Phys."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"27","DOI":"10.1017\/S0022112099007545","article-title":"Scaling in thermal convection a unifying theory","volume":"407","author":"Grossmann","year":"2000","journal-title":"J. Fluid Mech."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"016305","DOI":"10.1103\/PhysRevE.66.016305","article-title":"Prandtl and Rayleigh number dependence of the Reynolds number in turbulent thermal convection","volume":"66","author":"Grossmann","year":"2002","journal-title":"Phys. Rev. E"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"503","DOI":"10.1103\/RevModPhys.81.503","article-title":"Heat transfer and large scale dynamics in turbulent Rayleigh-B\u00e9nard convection","volume":"81","author":"Ahlers","year":"2009","journal-title":"Rev. Mod. Phys."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"063030","DOI":"10.1088\/1367-2630\/14\/6\/063030","article-title":"Heat transport by turbulent Rayleigh\u2013B\u00e9nard convection for Pr \u2243 0.8 and 4 \u00d7 1011 \u2272 Ra \u2272 2 \u00d7 1014: Ultimate-state transition for aspect ratio \u0393 = 1.00","volume":"14","author":"He","year":"2012","journal-title":"New J. Phys."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"eaaz8239","DOI":"10.1126\/sciadv.aaz8239","article-title":"Vibration-induced boundary-layer destabilization achieves massive heat-transport enhancement","volume":"6","author":"Wang","year":"2020","journal-title":"Sci. Adv."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"A28","DOI":"10.1017\/jfm.2021.223","article-title":"Melting driven by rotating Rayleigh\u2013B\u00e9nard convection","volume":"916","author":"Ravichandran","year":"2021","journal-title":"J. Fluid Mech."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"5585","DOI":"10.1038\/s41467-021-25838-3","article-title":"Inverse centrifugal effect induced by collective motion of vortices in rotating thermal convection","volume":"12","author":"Ding","year":"2021","journal-title":"Nat. Commun."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"A14","DOI":"10.1017\/jfm.2022.195","article-title":"Experimental evidence for the boundary zonal flow in rotating Rayleigh\u2013B\u00e9nard convection","volume":"939","author":"Wedi","year":"2022","journal-title":"J. Fluid Mech."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"489","DOI":"10.1016\/j.ijheatmasstransfer.2018.05.064","article-title":"Double MRT Lattice Boltzmann simulation of 3-D MHD natural convection in a cubic cavity with sinusoidal temperature distribution utilizing nanofluid","volume":"126","author":"Sajjadi","year":"2018","journal-title":"Int. J. Heat Mass Transf."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"474","DOI":"10.1016\/j.physa.2018.09.164","article-title":"Simulation of three dimensional MHD natural convection using double MRT Lattice Boltzmann method","volume":"515","author":"Sajjadi","year":"2019","journal-title":"Phys. A Stat. Mech. Its Appl."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"A31","DOI":"10.1017\/jfm.2022.181","article-title":"Heat transfer in turbulent Rayleigh\u2013B\u00e9nard convection through two immiscible fluid layers","volume":"938","author":"Liu","year":"2022","journal-title":"J. Fluid Mech."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"R5","DOI":"10.1017\/jfm.2015.610","article-title":"Enhanced heat transport in partitioned thermal convection","volume":"784","author":"Bao","year":"2015","journal-title":"J. Fluid Mech."},{"key":"ref_19","first-page":"57","article-title":"Effect of gap height on multiple enhancement of heat transfer and characteristics of temperature drift","volume":"26","author":"Bao","year":"2017","journal-title":"Comput. Aided Eng."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"7094701","DOI":"10.1088\/1674-1056\/ab343d","article-title":"Strong coupling between height of gaps and thickness of thermal boundary layer in partitioned convection system","volume":"28","author":"Lin","year":"2019","journal-title":"Chin. Phys. B"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"014401","DOI":"10.7498\/aps.69.20191193","article-title":"Characteristics of heat flow as well as process of heat conduction and transport in partitioned thermal convection","volume":"69","author":"Lin","year":"2020","journal-title":"Acta Phys. Sin."},{"key":"ref_22","first-page":"711","article-title":"Remarkable enhancement of heat transfer efficiency in thin partitioned convection system","volume":"35","author":"Xu","year":"2020","journal-title":"Chin. J. Hydrodyn."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"943","DOI":"10.5829\/IJE.2022.35.05B.10","article-title":"Numerical Investigation of Geometric Parameters Effects on Heat Transfer Enhancement in a Manifold Microchannel Heat Sink","volume":"35","author":"Babaei","year":"2022","journal-title":"Int. J. Eng."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"211","DOI":"10.1038\/s41586-020-2666-1","article-title":"Co-designing electronics with microfluidics for more sustainable cooling","volume":"585","author":"Soleimanzadeh","year":"2020","journal-title":"Nature"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"297","DOI":"10.1017\/S0022112010003824","article-title":"Prandtl\u2013Blasius temperature and velocity boundary-layer profiles in turbulent Rayleigh\u2013B\u00e9nard convection","volume":"664","author":"Zhou","year":"2010","journal-title":"J. Fluid Mech."},{"key":"ref_26","first-page":"231","article-title":"Advances and outlook in turbulent Rayleigh\u2013B\u00e9nard convection","volume":"42","author":"Zhou","year":"2012","journal-title":"Adv. Mech."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"325","DOI":"10.1002\/fld.337","article-title":"A coupled lattice BGK model for the Boussinesq equations","volume":"39","author":"Guo","year":"2002","journal-title":"Int. J. Numer."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"577","DOI":"10.1016\/j.ijheatmasstransfer.2017.02.032","article-title":"Accelerated lattice Boltzmann simulation using GPU and OpenACC with data management","volume":"109","author":"Xu","year":"2017","journal-title":"Int. J. Heat Mass Transf."},{"key":"ref_29","doi-asserted-by":"crossref","unstructured":"Xu, A., and Li, B.T. (2022). Multi-GPU thermal lattice Boltzmann simulations using OpenACC and MPI. Int. J. Heat Mass Transf., submitted.","DOI":"10.1016\/j.ijheatmasstransfer.2022.123649"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"105428","DOI":"10.1016\/j.icheatmasstransfer.2021.105428","article-title":"Numerical study of mixed convection of nanofluid inside an inlet\/outlet inclined cavity under the effect of Brownian motion using Lattice Boltzmann Method (LBM)","volume":"126","author":"Zhang","year":"2021","journal-title":"Int. Commun. Heat Mass Transf."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"22","DOI":"10.1016\/j.ijheatmasstransfer.2015.11.042","article-title":"Lattice Boltzmann method simulation of 3-D natural convection with double MRT model","volume":"94","author":"Li","year":"2016","journal-title":"Int. J. Heat Mass Transf."},{"key":"ref_32","doi-asserted-by":"crossref","unstructured":"Wei, Y.K., Shen, P.P., Wang, Z.D., Liang, H., and Qian, Y.H. (2020). Time evolution features of entropy generation rate in turbulent Rayleigh-B\u00e9nard convection with mixed insulating and conducting boundary conditions. Entropy, 22.","DOI":"10.3390\/e22060672"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"479","DOI":"10.1209\/0295-5075\/17\/6\/001","article-title":"Lattice BGK models for Navier-Stokes equation","volume":"17","author":"Qian","year":"1992","journal-title":"Europhys. Lett."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"428","DOI":"10.1016\/j.apm.2020.01.012","article-title":"A bounce back-immersed boundary-lattice Boltzmann model for curved boundary","volume":"81","author":"Wang","year":"2020","journal-title":"Appl. Math Model."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"329","DOI":"10.1146\/annurev.fluid.30.1.329","article-title":"Lattice Boltzmann method for fluid flows","volume":"30","author":"Chen","year":"1998","journal-title":"Annu. Rev. Fluid Mech."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"015103","DOI":"10.1103\/PhysRevE.105.015103","article-title":"Small-scale fluctuation and scaling law of mixing in three-dimensional rotating turbulent Rayleigh-Taylor instability","volume":"105","author":"Wei","year":"2022","journal-title":"Phys. Rev. E"},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"125104","DOI":"10.1063\/1.3662445","article-title":"Horizontal structures of velocity and temperature boundary layers in two-dimensional numerical turbulent Rayleigh-B\u00e9nard convection","volume":"23","author":"Zhou","year":"2011","journal-title":"Phys. Fluids"},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"219","DOI":"10.1006\/jcph.1998.6089","article-title":"Grid refinement for lattice-BGK models","volume":"147","author":"Filippova","year":"1998","journal-title":"J. Comput. Phys."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"2219","DOI":"10.1103\/PhysRevE.62.2219","article-title":"Lattice Boltzmann method on composite grids","volume":"62","author":"Lin","year":"2000","journal-title":"Phys. Rev. E"},{"key":"ref_40","first-page":"181","article-title":"A nonuniform lattice Boltzmann method based on domain decomposition","volume":"18","author":"Guo","year":"2001","journal-title":"Chin. J. Comput. Phys."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"066707","DOI":"10.1103\/PhysRevE.67.066707","article-title":"Theory and applications of an alternative lattice Boltzmann grid refinement algorithm","volume":"67","author":"Dupuis","year":"2003","journal-title":"Phys. Rev. E"},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"1020","DOI":"10.1103\/PhysRevE.48.1020","article-title":"Structure of hard-turbulent convection in two dimensions: Numerical evidence","volume":"48","author":"Werne","year":"1993","journal-title":"Phys. Rev. E"},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"5494","DOI":"10.1103\/PhysRevE.57.5494","article-title":"Spatial structure of the thermal boundary layer in turbulent convection","volume":"57","author":"Lui","year":"1998","journal-title":"Phys. Rev. E"},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"269","DOI":"10.1103\/PhysRevE.50.269","article-title":"Temperature and velocity boundary layers in turbulent convection","volume":"50","author":"Belmonte","year":"1994","journal-title":"Phys. Rev. E"},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"127","DOI":"10.1140\/epjb\/e2003-00081-y","article-title":"Spatial variations of the mean and statistical quantities in the thermal boundary layers of turbulent convection","volume":"32","author":"Wang","year":"2003","journal-title":"Eur. Phys. J. B"},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"204702","DOI":"10.7498\/aps.65.204702","article-title":"Characteristics of flow and thermal boundary layer in turbulent Rayleigh-B\u00e9nard convection","volume":"65","author":"Huang","year":"2016","journal-title":"Acta Phys. Sin."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/25\/2\/386\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T18:37:26Z","timestamp":1760121446000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/25\/2\/386"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,2,20]]},"references-count":46,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2023,2]]}},"alternative-id":["e25020386"],"URL":"https:\/\/doi.org\/10.3390\/e25020386","relation":{},"ISSN":["1099-4300"],"issn-type":[{"type":"electronic","value":"1099-4300"}],"subject":[],"published":{"date-parts":[[2023,2,20]]}}}