{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,13]],"date-time":"2026-05-13T11:14:25Z","timestamp":1778670865072,"version":"3.51.4"},"reference-count":43,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2017,4,15]],"date-time":"2017-04-15T00:00:00Z","timestamp":1492214400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>The second law performance of double diffusive forced convection in a horizontal porous channel with thick walls was considered. The Soret effect is included in the concentration equation and the first order chemical reaction was chosen for the concentration boundary conditions at the porous-solid walls interfaces. This investigation is focused on two principal types of boundary conditions. The first assumes a constant temperature condition at the outer surfaces of the solid walls, and the second assumes a constant heat flux at the lower wall and convection heat transfer at the upper wall. After obtaining the velocity, temperature and concentration distributions, the local and total entropy generation formulations were used to visualize the second law performance of the two cases. The results indicate that the total entropy generation rate is directly related to the lower wall thickness. Interestingly, it was observed that the total entropy generation rate for the second case reaches a minimum value, if the upper and lower wall thicknesses are chosen correctly. However, this observation was not true for the first case. These analyses can be useful for the design of microreactors and microcombustor systems when the second law analysis is taken into account.<\/jats:p>","DOI":"10.3390\/e19040171","type":"journal-article","created":{"date-parts":[[2017,4,18]],"date-time":"2017-04-18T11:22:04Z","timestamp":1492514524000},"page":"171","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":12,"title":["Entropy Generation of Double Diffusive Forced Convection in Porous Channels with Thick Walls and Soret Effect"],"prefix":"10.3390","volume":"19","author":[{"given":"Mohsen","family":"Torabi","sequence":"first","affiliation":[{"name":"The George W. Woodruff School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, GA 30332, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mehrdad","family":"Torabi","sequence":"additional","affiliation":[{"name":"Young Researchers and Elite Club, Central Tehran Branch, Islamic Azad University, Tehran 19166, Iran"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"G.P.","family":"Peterson","sequence":"additional","affiliation":[{"name":"The George W. Woodruff School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, GA 30332, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2017,4,15]]},"reference":[{"key":"ref_1","first-page":"152","article-title":"An oceanographical curiosity: The perpetual salt fountain","volume":"3","author":"Stommel","year":"1956","journal-title":"Deep Sea Res."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"2801","DOI":"10.1016\/j.ijheatmasstransfer.2011.01.031","article-title":"Heat and mass transfer in unsaturated porous media: Moisture effects in compost piles self-heating","volume":"54","author":"Zambra","year":"2011","journal-title":"Int. J. Heat Mass Transf."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"482","DOI":"10.1016\/j.ijheatmasstransfer.2016.04.054","article-title":"Thermal diffusion and diffusion-thermo effects on mixed convection from an exponentially impermeable stretching surface","volume":"100","author":"Patil","year":"2016","journal-title":"Int. J. Heat Mass Transf."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"1992","DOI":"10.3390\/e13121992","article-title":"Ben Effects of radiation heat transfer on entropy generation at thermosolutal convection in a square cavity subjected to a magnetic field","volume":"13","author":"Hidouri","year":"2011","journal-title":"Entropy"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"869","DOI":"10.1016\/j.icheatmasstransfer.2012.04.010","article-title":"Numerical simulation of three-dimensional double diffusive free convection flow and irreversibility studies in a solar distiller","volume":"39","author":"Ghachem","year":"2012","journal-title":"Int. Commun. Heat Mass Transf."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"84","DOI":"10.1016\/j.desal.2013.06.027","article-title":"Numerical study of conjugate heat and mass transfer in a solar still device","volume":"325","year":"2013","journal-title":"Desalination"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"24","DOI":"10.1016\/j.solener.2009.09.005","article-title":"Experimental study of the salt gradient solar pond stability","volume":"84","author":"Karim","year":"2010","journal-title":"Sol. Energy"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"94","DOI":"10.1016\/j.compfluid.2014.04.007","article-title":"Mesoscopic simulation of double-diffusive mixed convection of Pseudoplastic Fluids in an enclosure with sinusoidal boundary conditions","volume":"97","author":"Kefayati","year":"2014","journal-title":"Comput. Fluids"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"143","DOI":"10.1016\/j.expthermflusci.2012.04.020","article-title":"Experimental investigation of three-dimensional flow in a double-diffusive interface system with lateral heating","volume":"42","author":"Okorafor","year":"2012","journal-title":"Exp. Therm. Fluid Sci."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"23","DOI":"10.1016\/S0894-1777(03)00089-X","article-title":"Double-diffusive convection during solidification of a metal analog system (NH4Cl-H2O) in a differentially heated cavity","volume":"28","author":"Ghenai","year":"2003","journal-title":"Exp. Therm. Fluid Sci."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"119","DOI":"10.1134\/S1810232810030021","article-title":"The influence of cross effects on the characteristics of heat and mass transfer in the conditions of conjugate natural convection","volume":"19","author":"Sheremet","year":"2010","journal-title":"J. Eng. Thermophys."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"1878","DOI":"10.1016\/j.ijthermalsci.2011.05.003","article-title":"A numerical simulation of double-diffusive conjugate natural convection in an enclosure","volume":"50","author":"Kuznetsov","year":"2011","journal-title":"Int. J. Therm. Sci."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"2122","DOI":"10.1016\/j.jtice.2014.05.026","article-title":"Double-diffusive mixed convection of pseudoplastic fluids in a two sided lid-driven cavity using FDLBM","volume":"45","author":"Kefayati","year":"2014","journal-title":"J. Taiwan Inst. Chem. Eng."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"413","DOI":"10.1016\/j.molliq.2014.07.024","article-title":"Mesoscopic simulation of magnetic field effect on double-diffusive mixed convection of shear-thinning fluids in a two sided lid-driven cavity","volume":"198","author":"Kefayati","year":"2014","journal-title":"J. Mol. Liq."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"63","DOI":"10.1016\/j.euromechflu.2015.08.006","article-title":"Instability due to double-diffusive phenomenon in pressure-driven displacement flow of one fluid by another in an axisymmetric pipe","volume":"55","author":"Bhagat","year":"2016","journal-title":"Eur. J. Mech. B Fluids"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"535","DOI":"10.1016\/j.jtice.2012.02.010","article-title":"Double-diffusive natural convection in a rectangular cavity with partially thermally active side walls","volume":"43","author":"Nikbakhti","year":"2012","journal-title":"J. Taiwan Inst. Chem. Eng."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"57","DOI":"10.1016\/j.ijthermalsci.2016.03.012","article-title":"Oscillatory double-diffusive convection in a horizontal cavity with Soret and Dufour effects","volume":"106","author":"Wang","year":"2016","journal-title":"Int. J. Therm. Sci."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"200","DOI":"10.1016\/j.desal.2014.12.034","article-title":"Numerical study of heat and mass transfer in a solar still device: Effect of the glass cover","volume":"359","year":"2015","journal-title":"Desalination"},{"key":"ref_19","unstructured":"Bejan, A. (1995). Entropy Generation Minimization: The Method of Thermodynamic Optimization of Finite-Size Systems and Finite-Time Processes, CRC Press."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"540","DOI":"10.1016\/j.energy.2015.05.009","article-title":"Temperature distribution, local and total entropy generation analyses in MHD porous channels with thick walls","volume":"87","author":"Torabi","year":"2015","journal-title":"Energy"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"917","DOI":"10.1016\/j.ijheatmasstransfer.2016.03.007","article-title":"Entropy generation in thermal systems with solid structures\u2014A concise review","volume":"97","author":"Torabi","year":"2016","journal-title":"Int. J. Heat Mass Transf."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"1","DOI":"10.3390\/e8010001","article-title":"Second law analysis in convective heat and mass transfer","volume":"8","author":"Magherbi","year":"2006","journal-title":"Entropy"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"1721","DOI":"10.1016\/j.energy.2010.12.056","article-title":"Entropy generation of turbulent double-diffusive natural convection in a rectangle cavity","volume":"36","author":"Chen","year":"2011","journal-title":"Energy"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"447","DOI":"10.1016\/j.ijheatmasstransfer.2015.04.023","article-title":"Analysis of entropy generation in double-diffusive natural convection of nanofluid","volume":"87","author":"Chen","year":"2015","journal-title":"Int. J. Heat Mass Transf."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"207","DOI":"10.1016\/j.energy.2013.04.058","article-title":"Entropy generation analysis of heat and mass transfer in mixed electrokinetically and pressure driven flow through a slit microchannel","volume":"56","author":"Matin","year":"2013","journal-title":"Energy"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"605","DOI":"10.1016\/j.aej.2013.09.006","article-title":"Double-diffusive natural convection and entropy generation in an enclosure of aspect ratio 4 with partial vertical heating and salting sources","volume":"52","author":"Oueslati","year":"2013","journal-title":"Alexandria Eng. J."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"267","DOI":"10.1016\/j.ijheatmasstransfer.2015.05.058","article-title":"FDLBM simulation of entropy generation in double diffusive natural convection of power-law fluids in an enclosure with Soret and Dufour effects","volume":"89","author":"Kefayati","year":"2015","journal-title":"Int. J. Heat Mass Transf."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"917","DOI":"10.1016\/j.energy.2016.05.044","article-title":"Simulation of double diffusive MHD (magnetohydrodynamic) natural convection and entropy generation in an open cavity filled with power-law fluids in the presence of Soret and Dufour effects (part II: Entropy generation)","volume":"107","author":"Kefayati","year":"2016","journal-title":"Energy"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"889","DOI":"10.1016\/j.energy.2016.05.049","article-title":"Simulation of double diffusive MHD (magnetohydrodynamic) natural convection and entropy generation in an open cavity filled with power-law fluids in the presence of Soret and Dufour effects (Part I: Study of fluid flow, heat and mass transfer)","volume":"107","author":"Kefayati","year":"2016","journal-title":"Energy"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"223","DOI":"10.1007\/s11242-012-9954-7","article-title":"Entropy generation in double-diffusive convection in a square Porous cavity using Darcy-Brinkman formulation","volume":"93","author":"Mchirgui","year":"2012","journal-title":"Transp. Porous Media"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"105","DOI":"10.1016\/j.compfluid.2014.03.008","article-title":"Second law analysis in double diffusive convection through an inclined porous cavity","volume":"96","author":"Mchirgui","year":"2014","journal-title":"Comput. Fluids"},{"key":"ref_32","first-page":"926","article-title":"Analysis of heatlines and entropy generation during double-diffusive MHD natural convection within a tilted sinusoidal corrugated porous enclosure","volume":"19","author":"Hussain","year":"2016","journal-title":"Eng. Sci. Technol. Int. J."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"582","DOI":"10.1016\/j.ijheatmasstransfer.2015.11.043","article-title":"Simulation of double diffusive natural convection and entropy generation of power-law fluids in an inclined porous cavity with Soret and Dufour effects (Part II: Entropy generation)","volume":"94","author":"Kefayati","year":"2016","journal-title":"Int. J. Heat Mass Transf."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"539","DOI":"10.1016\/j.ijheatmasstransfer.2015.11.044","article-title":"Simulation of double diffusive natural convection and entropy generation of power-law fluids in an inclined porous cavity with Soret and Dufour effects (Part I: Study of fluid flow, heat and mass transfer)","volume":"94","author":"Kefayati","year":"2016","journal-title":"Int. J. Heat Mass Transf."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"684","DOI":"10.1016\/j.applthermaleng.2016.09.148","article-title":"Interface entropy generation in micro porous channels with velocity slip and temperature jump","volume":"111","author":"Torabi","year":"2017","journal-title":"Appl. Therm. Eng."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"585","DOI":"10.1016\/j.ijheatmasstransfer.2016.06.080","article-title":"Effects of velocity slip and temperature jump on the heat transfer and entropy generation in micro porous channels under magnetic field","volume":"102","author":"Torabi","year":"2016","journal-title":"Int. J. Heat Mass Transf."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"1182","DOI":"10.1002\/aic.14319","article-title":"Visualization study of flow condensation in hydrophobic microchannels","volume":"60","author":"Chen","year":"2014","journal-title":"AIChE J."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"134","DOI":"10.1016\/j.icheatmasstransfer.2013.05.001","article-title":"Forced convection heat and mass transfer flow of a nanofluid through a porous channel with a first order chemical reaction on the wall","volume":"46","author":"Matin","year":"2013","journal-title":"Int. Commun. Heat Mass Transf."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"438","DOI":"10.1016\/j.ijheatmasstransfer.2013.10.040","article-title":"Mass transfer rate of a first-order chemical reaction on a wall at high Schmidt numbers","volume":"69","author":"Pallares","year":"2014","journal-title":"Int. J. Heat Mass Transf."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"254","DOI":"10.1016\/j.ijheatmasstransfer.2015.06.062","article-title":"Local mass transfer rates of a first-order chemical reaction on a wall: Application to the prediction of local platelet deposition in a perfusion chamber","volume":"90","author":"Pallares","year":"2015","journal-title":"Int. J. Heat Mass Transf."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"760","DOI":"10.1016\/j.ijheatmasstransfer.2015.05.101","article-title":"First and second thermodynamic laws analyses between and inside two rotating solid cylindrical geometries with magnetohydrodynamic flow","volume":"89","author":"Torabi","year":"2015","journal-title":"Int. J. Heat Mass Transf."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"218","DOI":"10.1016\/j.energy.2014.10.009","article-title":"Temperature distribution, local and total entropy generation analyses in asymmetric cooling composite geometries with multiple nonlinearities: Effect of imperfect thermal contact","volume":"78","author":"Torabi","year":"2014","journal-title":"Energy"},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"1009","DOI":"10.1016\/j.asej.2015.02.014","article-title":"Thermal radiation and heat generation\/absorption effects on viscoelastic double-diffusive convection from an isothermal sphere in porous media","volume":"6","author":"Gaffar","year":"2015","journal-title":"Ain Shams Eng. J."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/19\/4\/171\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T18:32:44Z","timestamp":1760207564000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/19\/4\/171"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,4,15]]},"references-count":43,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2017,4]]}},"alternative-id":["e19040171"],"URL":"https:\/\/doi.org\/10.3390\/e19040171","relation":{},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2017,4,15]]}}}