{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,30]],"date-time":"2025-10-30T07:13:00Z","timestamp":1761808380295,"version":"build-2065373602"},"reference-count":47,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2020,6,17]],"date-time":"2020-06-17T00:00:00Z","timestamp":1592352000000},"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":["11872337"],"award-info":[{"award-number":["11872337"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Time evolution features of kinetic and thermal entropy generation rates in turbulent Rayleigh-B\u00e9nard (RB) convection with mixed insulating and conducting boundary conditions at Ra = 109 are numerically investigated using the lattice Boltzmann method. The state of flow gradually develops from laminar flow to full turbulent thermal convection motion, and further evolves from full turbulent thermal convection to dissipation flow in the process of turbulent energy transfer. It was seen that the viscous, thermal, and total entropy generation rates gradually increase in wide range of t\/\u03c4 &lt; 32 with temporal evolution. However, the viscous, thermal, and total entropy generation rates evidently decrease at time t\/\u03c4 = 64 compared to that of early time. The probability density function distributions, spatial-temporal features of the viscous, thermal, and total entropy generation rates in the closed system provide significant physical insight into the process of the energy injection, the kinetic energy, the kinetic energy transfer, the thermal energy transfer, the viscous dissipated flow and thermal dissipation.<\/jats:p>","DOI":"10.3390\/e22060672","type":"journal-article","created":{"date-parts":[[2020,6,17]],"date-time":"2020-06-17T13:11:32Z","timestamp":1592399492000},"page":"672","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":9,"title":["Time Evolution Features of Entropy Generation Rate in Turbulent Rayleigh-B\u00e9nard Convection with Mixed Insulating and Conducting Boundary Conditions"],"prefix":"10.3390","volume":"22","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5462-1502","authenticated-orcid":false,"given":"Yikun","family":"Wei","sequence":"first","affiliation":[{"name":"Joint Engineering Lab of Fluid Transmission System Technology, Faculty of Mechanical Engineering and Automation, Zhejiang Sci-Tech University, Hangzhou 310018, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Pingping","family":"Shen","sequence":"additional","affiliation":[{"name":"Joint Engineering Lab of Fluid Transmission System Technology, Faculty of Mechanical Engineering and Automation, Zhejiang Sci-Tech University, Hangzhou 310018, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zhengdao","family":"Wang","sequence":"additional","affiliation":[{"name":"Joint Engineering Lab of Fluid Transmission System Technology, Faculty of Mechanical Engineering and Automation, Zhejiang Sci-Tech University, Hangzhou 310018, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hong","family":"Liang","sequence":"additional","affiliation":[{"name":"Department of Physics, Hangzhou Dianzi University, Hangzhou 310018, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yuehong","family":"Qian","sequence":"additional","affiliation":[{"name":"School of Mathematical Science, Soochow University, Suzhou 215006, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2020,6,17]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"479","DOI":"10.1115\/1.2911298","article-title":"Natural convection with radiation in a cavity with open top end","volume":"114","author":"Lage","year":"1992","journal-title":"J. Heat Transf."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"236","DOI":"10.1016\/j.ijheatmasstransfer.2013.12.019","article-title":"Transition to an unsteady flow induced by a fin on the sidewall of a differentially heated air-filled square cavity and heat transfer","volume":"71","author":"Xu","year":"2014","journal-title":"Int. J. Heat Mass Transf."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"216","DOI":"10.1016\/S0140-7007(98)00055-3","article-title":"Experiments on stratified chilled-water tanks","volume":"22","author":"Nelson","year":"1999","journal-title":"Int. J. Refrig."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"3551","DOI":"10.1016\/S0017-9310(03)00147-9","article-title":"Experimental benchmark data for turbulent natural convection in an air filled square cavity","volume":"19","author":"Ampofo","year":"2003","journal-title":"Int. J. Heat. Mass Transf."},{"key":"ref_5","first-page":"1450","article-title":"Experimental uncertainty of measured entropy production with pulsed laser PIV and planar laser induced fluorescence","volume":"48","author":"Adeyinka","year":"2005","journal-title":"Appl. Ther. Eng."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"335","DOI":"10.1146\/annurev.fluid.010908.165152","article-title":"Small-scale properties of turbulent Rayleigh\u2013B\u00e9nard convection","volume":"42","author":"Lohse","year":"2010","journal-title":"Annu. Rev. Fluid Mech."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"3803","DOI":"10.1016\/j.ijheatmasstransfer.2008.01.005","article-title":"On the double-layer structure of the thermal boundary layer in a differentially heated cavity","volume":"51","author":"Xu","year":"2008","journal-title":"Int. J. Heat Mass Transf."},{"key":"ref_8","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_9","doi-asserted-by":"crossref","first-page":"144504","DOI":"10.1103\/PhysRevLett.97.144504","article-title":"Cascades of velocity and temperature fluctuations in buoyancy-driven thermal turbulence","volume":"97","author":"Sun","year":"2006","journal-title":"Phys. Rev. Lett."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"152","DOI":"10.1017\/S0022112010000820","article-title":"Aspect ratio dependence of heat transfer and large-scale flow in turbulent convection","volume":"655","author":"Emran","year":"2010","journal-title":"J. Fluid Mech."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"281","DOI":"10.1017\/jfm.2012.392","article-title":"Thermal and viscous boundary layers in turbulent Rayleigh-Benard convection","volume":"711","author":"Scheel","year":"2012","journal-title":"J. Fluid Mech."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"075006","DOI":"10.1088\/1367-2630\/12\/7\/075006","article-title":"Physical and geometrical properties of thermal plumes in turbulent Rayleigh-B\u00e9nard convection","volume":"12","author":"Zhou","year":"2012","journal-title":"New J. Phys."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"5","DOI":"10.1017\/jfm.2012.207","article-title":"Boundary layer structure in turbulent Rayleigh-Benard convection","volume":"706","author":"Shi","year":"2012","journal-title":"J. Fluid Mech."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"075022","DOI":"10.1088\/1367-2630\/12\/7\/075022","article-title":"Boundary layer structure in turbulent thermal convection and its consequences for the required numerical resolution","volume":"12","author":"Shishkina","year":"2010","journal-title":"New J. Phys."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"383","DOI":"10.1017\/S002211200800013X","article-title":"Analysis of sheet like thermal plumes in turbulent Rayleigh-B\u00e9nard convection","volume":"599","author":"Shishkina","year":"2012","journal-title":"J. Fluid Mech."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"390","DOI":"10.1016\/j.ijheatmasstransfer.2013.10.009","article-title":"A numerical study on natural convection and entropy generation in a porous enclosure with heat sources","volume":"69","author":"Lami","year":"2014","journal-title":"Int. J. Heat Mass Transf."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"339","DOI":"10.1016\/j.ijthermalsci.2007.02.008","article-title":"On the importance of thermal boundary conditions in heat transfer and entropy generation for natural convection inside a porous enclosure","volume":"47","author":"Zahmatkesh","year":"2008","journal-title":"Int. J. Therm. Sci."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"3221","DOI":"10.1016\/j.ijheatmasstransfer.2006.01.032","article-title":"Entropy generation in natural convection in a symmetrically and uniformly heated vertical channel","volume":"49","author":"Andreozzi","year":"2006","journal-title":"Int. J. Heat Mass Transf."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"502","DOI":"10.1016\/j.icheatmasstransfer.2007.01.003","article-title":"Entropy generation for natural convection in \u0393-shaped enclosures","volume":"34","author":"Dagtekin","year":"2007","journal-title":"Int. Commun. Heat Mass Transf."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"89","DOI":"10.1017\/S0022112008003947","article-title":"Analysis of the thermal plumes in turbulent Rayleigh-B\u00e9nard convection based on well-resolved numerical simulations","volume":"618","author":"Kaczorowski","year":"2011","journal-title":"J. Fluid Mech."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"1255","DOI":"10.1016\/j.ijheatmasstransfer.2018.02.045","article-title":"Thermal and velocity slip effects on Casson nanofluid flow over an inclined permeable stretching cylinder via collocation method","volume":"122","author":"Usman","year":"2018","journal-title":"Int. J. Heat Mass Transf."},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Wang, Z.D., and Qian, Y.H. (2018). Numerical study on entropy generation in thermal convection with differentially discrete heat boundary conditions. Entropy, 20.","DOI":"10.3390\/e20050351"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"1167","DOI":"10.1016\/j.rser.2014.11.104","article-title":"Entropy generation analysis as a design tool\u2014A review","volume":"43","author":"Sciacovelli","year":"2015","journal-title":"Renew. Sustain. Energy Rev."},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Wei, Y.K., Wang, Z.D., and Qian, Y.H. (2017). A numerical study on entropy generation in two-dimensional Rayleigh-B\u00e9nard convection at different Prandtl number. Entropy, 19.","DOI":"10.3390\/e19090443"},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Jin, Y. (2017). Second-law analysis: A powerful tool for analyzing Computational Fluid Dynamics results. Entropy, 19.","DOI":"10.3390\/e19120679"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"622","DOI":"10.1016\/j.applthermaleng.2015.12.072","article-title":"Transient local entropy generation analysis for the design improvement of a thermocline thermal energy storage","volume":"101","author":"Pizzolato","year":"2016","journal-title":"Appl. Therm. Eng."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"1417","DOI":"10.1016\/j.applthermaleng.2008.07.012","article-title":"Entropy generation and natural convection in rectangular cavities","volume":"29","author":"Rejane","year":"2009","journal-title":"Appl. Therm. Eng."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"514","DOI":"10.1016\/j.ijheatmasstransfer.2013.06.010","article-title":"A review on entropy generation in nanofluid flow","volume":"65","author":"Mahian","year":"2013","journal-title":"Int. J. Heat Mass Transf."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"543","DOI":"10.1166\/jon.2016.1248","article-title":"Entropy generation with nonlinear thermal radiation in MHD boundary layer flow over a permeable shrinking\/stretching sheet: Numerical solution","volume":"5","author":"Bhatti","year":"2016","journal-title":"J. Nanofluids"},{"key":"ref_30","doi-asserted-by":"crossref","unstructured":"Abbas, M.A., Bai, Y., Rashidi, M.M., and Bhatti, M.M. (2016). Analysis of Entropy Generation in the Flow of Peristaltic Nanofluids in Channels with Compliant Walls. Entropy, 18.","DOI":"10.3390\/e18030090"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"1007","DOI":"10.1177\/0957650919840964","article-title":"Effects of Vortex Structure on Performance Characteristics of a Multiblade Fan with Inclined tongue","volume":"233","author":"Lun","year":"2019","journal-title":"Proc. Inst. Mech. Eng. Part A J. Power Energy"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"114055","DOI":"10.1016\/j.applthermaleng.2019.114055","article-title":"Thermal conductivity and sorption performance of nano-silver powder\/FAPO-34 composite fin","volume":"160","author":"Zheng","year":"2019","journal-title":"Appl. Therm. Eng."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"442","DOI":"10.1016\/j.powtec.2020.01.022","article-title":"Fluidization characteristics of particles in a groove induced by horizontal air flow","volume":"363","author":"Lin","year":"2020","journal-title":"Powder Technol."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"1480","DOI":"10.1177\/0020294019877482","article-title":"Experimental investigations on the performance and noise characteristics of a forward-curved fan with the stepped tongue","volume":"52","author":"Yang","year":"2019","journal-title":"Meas. Control"},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"11","DOI":"10.1016\/j.icheatmasstransfer.2017.10.015","article-title":"Partitioning effect on natural convection in a circular enclosure with an asymmetrically placed inclined plate","volume":"90","author":"Zhang","year":"2018","journal-title":"Int. Commun. Heat Mass Transf."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/s42241-018-0001-1","article-title":"Spectral\/hp element methods: Recent developments, applications, and perspectives","volume":"30","author":"Xu","year":"2018","journal-title":"J. Hydrodyn."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"334","DOI":"10.1016\/j.jcp.2013.08.054","article-title":"Lattice Boltzmann Phase Field Modeling Thermocapillary Flows in a Confined Microchannel","volume":"256","author":"Liu","year":"2014","journal-title":"J. Comput. Phys."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"2780","DOI":"10.1103\/PhysRevE.55.2780","article-title":"Simulation of Rayleigh-B\u00e9nard convection using a lattice Boltzmann method","volume":"55","author":"Shan","year":"1997","journal-title":"Phys. Rev. E"},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"487","DOI":"10.1016\/j.apm.2019.03.009","article-title":"Lattice boltzmann modeling of wall-bounded ternary fluid flows","volume":"73","author":"Liang","year":"2019","journal-title":"Appl. Math. Model."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"30","DOI":"10.1016\/j.compfluid.2015.09.004","article-title":"Simulation of natural convection heat transfer in an enclosure at different Rayleigh number using lattice Boltzmann method","volume":"124","author":"Wei","year":"2016","journal-title":"Comput. Fluids"},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"97","DOI":"10.1016\/j.compfluid.2017.07.003","article-title":"A novel two-dimensional coupled lattice Boltzmann model for incompressible flow in application of turbulence Rayleigh-Taylor instability","volume":"156","author":"Wei","year":"2017","journal-title":"Comput. Fluids"},{"key":"ref_42","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_43","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_44","doi-asserted-by":"crossref","first-page":"38","DOI":"10.1002\/fld.4771","article-title":"Simplified lattice Boltzmann method for non-Newtonian power-law fluid flows","volume":"92","author":"Chen","year":"2020","journal-title":"Int. J. Numer. Methods Fluids"},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"120","DOI":"10.1140\/epjp\/s13360-020-00206-0","article-title":"A new analytical solution of longitudinal fin with variable heat generation and thermal conductivity using DRA","volume":"135","author":"Mohamed","year":"2020","journal-title":"Eur. Phys. J. Plus"},{"key":"ref_46","unstructured":"Nawel, B., Mohamed, K., Ismai, T., and Mohamed, R.E. (2019). On numerical and analytical solutions for mixed convection Falkner-Skan flow of nanofluids with variable thermal conductivity. Waves Random Complex Media, 1\u201319."},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"97","DOI":"10.1515\/jnet-2019-0073","article-title":"Effects of NP Shapes on Non-Newtonian Bio-Nanofluid Flow in Suction\/Blowing Process with Convective Condition: Sisko Model","volume":"45","author":"Mohamed","year":"2020","journal-title":"J. Non-Equilib. Thermodyn."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/22\/6\/672\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T09:39:46Z","timestamp":1760175586000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/22\/6\/672"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,6,17]]},"references-count":47,"journal-issue":{"issue":"6","published-online":{"date-parts":[[2020,6]]}},"alternative-id":["e22060672"],"URL":"https:\/\/doi.org\/10.3390\/e22060672","relation":{},"ISSN":["1099-4300"],"issn-type":[{"type":"electronic","value":"1099-4300"}],"subject":[],"published":{"date-parts":[[2020,6,17]]}}}