{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,17]],"date-time":"2026-01-17T22:01:35Z","timestamp":1768687295535,"version":"3.49.0"},"reference-count":36,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2013,11,6]],"date-time":"2013-11-06T00:00:00Z","timestamp":1383696000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>The present study examines embedded open parallel microchannels within a micropatterned permeable surface for reducing entropy generation in MHD fluid flow in microscale systems. A local similarity solution for the transformed governing equations is obtained. The governing partial differential equations along with the boundary conditions are first cast into a dimensionless form and then the reduced ordinary differential equations are solved numerically via the Dormand-Prince pair and shooting method. The dimensionless entropy generation number is formulated by an integral of the local rate of entropy generation along the width of the surface based on an equal number of microchannels and no-slip gaps interspersed between those microchannels. Finally, the entropy generation numbers, as well as the Bejan number, are investigated. It is seen that surface-embedded microchannels can successfully reduce entropy generation in the presence of an applied magnetic field.<\/jats:p>","DOI":"10.3390\/e15114822","type":"journal-article","created":{"date-parts":[[2013,11,6]],"date-time":"2013-11-06T11:41:50Z","timestamp":1383738110000},"page":"4822-4843","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":20,"title":["Reducing Entropy Generation in MHD Fluid Flow over  Open Parallel Microchannels Embedded in a  Micropatterned Permeable Surface"],"prefix":"10.3390","volume":"15","author":[{"given":"Mohammad","family":"Yazdi","sequence":"first","affiliation":[{"name":"Solar Energy Research Institute (SERI), Universiti Kebangsaan Malaysia, 43600 UKM, Bangi, Selangor, Malaysia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shahrir","family":"Abdullah","sequence":"additional","affiliation":[{"name":"Department of Mechanical and Materials Engineering, Faculty of Engineering and Built Environment, Universiti Kebangsaan Malaysia, 43600 UKM, Bangi, Selangor, Malaysia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ishak","family":"Hashim","sequence":"additional","affiliation":[{"name":"School of Mathematical Sciences, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, 43600 UKM, Bangi, Selangor, Malaysia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Kamaruzzaman","family":"Sopian","sequence":"additional","affiliation":[{"name":"Solar Energy Research Institute (SERI), Universiti Kebangsaan Malaysia, 43600 UKM, Bangi, Selangor, Malaysia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2013,11,6]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"917","DOI":"10.1016\/j.snb.2007.10.064","article-title":"MEMS-based micropumps in drug delivery and biomedical applications","volume":"130","author":"Nisar","year":"2008","journal-title":"Sens. Actuators B Chem."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"4149","DOI":"10.1016\/j.energy.2010.06.035","article-title":"Entropy generation minimization of a MHD (magnetohydrodynamic) flow in a microchannel","volume":"35","author":"Cuevas","year":"2010","journal-title":"Energy"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"5590","DOI":"10.1016\/j.ijheatmasstransfer.2008.04.043","article-title":"Microfluidics of nano-drug delivery","volume":"51","author":"Kleinstreuer","year":"2008","journal-title":"Int. J. Heat Mass Trans."},{"key":"ref_4","unstructured":"Avsec, J. (2009, January 7\u201311). Nanofluid and Ferrofluid Slip Flow in Rectangular and Circular Microchannels. Proceedings of 7th Euromech Solid Mechanics Conference, Lisbon, Portugal."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"27","DOI":"10.1007\/128_2011_150","article-title":"Micromixing within microfluidic devices","volume":"304","author":"Capretto","year":"2011","journal-title":"Top. Curr. Chem."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"013407","DOI":"10.1063\/1.3553011","article-title":"Transport of particles and microorganisms in microfluidic channels using rectified ac electro-osmotic flow","volume":"5","author":"Wu","year":"2011","journal-title":"Biomicrofluidics"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"1","DOI":"10.3390\/e14010001","article-title":"Entropy generation analysis of open parallel microchannels embedded within a permeable continuous moving surface: Application to magnetohydrodynamics (MHD)","volume":"14","author":"Yazdi","year":"2012","journal-title":"Entropy"},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Naterer, G.F., and Chomokovski, S. (2007). Entropy-based surface microprofiling for passive near-wall flow control. J. Micromech. Microeng., 17.","DOI":"10.1088\/0960-1317\/17\/10\/028"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"518","DOI":"10.1063\/1.1407604","article-title":"Blasius Boundary Layer Solution with Slip Flow Conditions","volume":"Volume 585","author":"Martin","year":"2001","journal-title":"Proceedings of Rarefied Gas Dynamics: 22nd International Symposium"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"710","DOI":"10.2514\/1.22968","article-title":"Momentum and heat transfer in a laminar boundary layer with slip flow","volume":"20","author":"Martin","year":"2006","journal-title":"J. Thermophys. Heat Trans."},{"key":"ref_11","unstructured":"Vedantam, N.K., and Parthasarathy, R.N. (2006, January 17\u201320). Effects of Slip on the Flow Characteristics of Laminar Flat Plate Boundary-Layer. Proceedings of ASME 2nd Joint U.S.-European Fluids Engineering Summer Meeting Collocated With the 14th International Conference on Nuclear Engineering (FEDSM2006), Miami, FL, USA."},{"key":"ref_12","unstructured":"Yazdi, M.H., Abdullah, S., Hashim, I., Zaharim, A., and Sopian, K. (2008, January 26\u201328). Friction and Heat Transfer in Slip Flow Boundary Layer at Constant Heat Flux Boundary Conditions. Proceedings of the 10th WSEAS International Conference on Mathematical Methods, Computational Techniques and Intelligent Systems, Corfu, Greece."},{"key":"ref_13","unstructured":"Yazdi, M.H., Abdullah, S., Hashim, I., Nopiah, Z.M., Zaharim, A., and Sopian, K. (2010, January 27\u201329). Convective Heat Transfer of Slip Liquid Flow Past Horizontal Surface within the Porous Media at Constant Heat Flux Boundary Conditions. Proceedings of the American Conference on Applied Mathematics: Recent Advances in Applied Mathematics, Cambridge, MA, USA."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"3829","DOI":"10.1016\/j.ijheatmasstransfer.2009.02.013","article-title":"Slip effects on mixed convective flow and heat transfer from a vertical plate","volume":"52","author":"Cao","year":"2009","journal-title":"Int. J. Heat Mass Trans."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"573","DOI":"10.1016\/j.cnsns.2009.04.026","article-title":"Hydrodynamic and thermal slip flow boundary layers over a flat plate with constant heat flux boundary condition","volume":"15","author":"Aziz","year":"2010","journal-title":"Commun. Nonlinear Sci. Numer. Simul."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"3214","DOI":"10.1016\/j.ijheatmasstransfer.2011.04.009","article-title":"Slip MHD liquid flow and heat transfer over non-linear permeable stretching surface with chemical reaction","volume":"54","author":"Yazdi","year":"2011","journal-title":"Int. J. Heat Mass Trans."},{"key":"ref_17","unstructured":"Yazdi, M.H., Abdullah, S., Hashim, I., and Sopian, K. (2010, January 5\u20139). Slip MHD Flow over Permeable Stretching Surface with Chemical Reaction. Proceedings of the 17th Australasian Fluid Mechanics Conference, Auckland, New Zealand."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"963","DOI":"10.1002\/fld.2294","article-title":"MHD flow and heat transfer over permeable stretching sheet with slip conditions","volume":"66","author":"Hayat","year":"2011","journal-title":"Int. J. Numer. Meth. Fl."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"641","DOI":"10.1002\/htj.20367","article-title":"Effects of slip conditions on stretching flow with ohmic dissipation and thermal radiation","volume":"40","author":"Qasim","year":"2011","journal-title":"Heat Trans.\u2014Asian Res."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"886","DOI":"10.1016\/j.ijmecsci.2011.07.012","article-title":"Analytic heat and mass transfer of the mixed hydrodynamic\/thermal slip MHD viscous flow over a stretching sheet","volume":"53","author":"Turkyilmazoglu","year":"2011","journal-title":"Int. J. Mech. Sci."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"024701","DOI":"10.1088\/0256-307X\/28\/2\/024701","article-title":"MHD boundary layer slip flow and heat transfer over a flat plate","volume":"28","author":"Bhattacharyya","year":"2011","journal-title":"Chin. Phys. Lett."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"1127","DOI":"10.1007\/s11012-010-9372-2","article-title":"Locally similar solutions for hydromagnetic and thermal slip flow boundary layers over a flat plate with variable fluid properties and convective surface boundary condition","volume":"46","author":"Rahman","year":"2011","journal-title":"Meccanica"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"2273","DOI":"10.3390\/en4122273","article-title":"Effects of viscous dissipation on the slip MHD flow and heat transfer past a permeable surface with convective boundary conditions","volume":"4","author":"Yazdi","year":"2011","journal-title":"Energies"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"213","DOI":"10.1080\/10893950500195909","article-title":"Surface micro-profiling for reduced energy dissipation and exergy loss in convective heat transfer","volume":"9","author":"Naterer","year":"2005a","journal-title":"Microscale Thermophys. Eng."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"494","DOI":"10.2514\/1.8728","article-title":"Adaptive surface microprofiling for microfluidic energy conversion","volume":"18","author":"Naterer","year":"2004","journal-title":"J. Thermophys. Heat Trans."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"1215","DOI":"10.1002\/er.1108","article-title":"Reducing energy availability losses with open parallel microchannels embedded in a micropatterned surface","volume":"29","author":"Naterer","year":"2005b","journal-title":"Int. J. Energy Res."},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Naterer, G.F., Glockner, P.S., Thiele, D., Chomokovski, S., Venn, G., and Richardson, G. (2005). Surface micro-grooves for near-wall exergy and flow control: Application to aircraft intake de-icing. J. Micromech. Microeng., 15.","DOI":"10.1088\/0960-1317\/15\/3\/010"},{"key":"ref_28","first-page":"462","article-title":"Entropy generation analysis of liquid fluid past embedded open parallel microchannels within the surface","volume":"28","author":"Yazdi","year":"2009b","journal-title":"Eur. J. Sci. Res."},{"key":"ref_29","unstructured":"Yazdi, M.H., Abdullah, S., Hashim, I., and Sopian, K. (2012, January 21\u201323). Second Law Analysis of MHD Flow Over Open Parallel Microchannels Embedded in a Micropatterned Surface. Proceedings of 10th WSEAS International Conference on Heat Transfer, Thermal Engineering and Environment, Istanbul, Turkey."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"L9","DOI":"10.1063\/1.1432696","article-title":"Apparent fluid slip at hydrophobic microchannel walls","volume":"14","author":"Tretheway","year":"2002","journal-title":"Phys. Fluids"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"052105","DOI":"10.1063\/1.3121305","article-title":"The effective slip length and vortex formation in laminar flow over a rough surface","volume":"21","author":"Niavarani","year":"2009","journal-title":"Phys. Fluids"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"359","DOI":"10.1016\/j.energy.2011.11.019","article-title":"Effects of rarefaction, viscous dissipation and rotation mode on the first and second law analyses of rarefied gaseous slip flows confined between a rotating shaft and its concentric housing","volume":"37","author":"Shamshiri","year":"2011","journal-title":"Energy"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"1509","DOI":"10.1063\/1.1669400","article-title":"A generating mechanism for apparent fluid slip in hydrophobic microchannels","volume":"16","author":"Tretheway","year":"2004","journal-title":"Phys. Fluids"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"716","DOI":"10.1016\/j.ijengsci.2007.04.011","article-title":"Erratum to \u201cAn explicit analytic solution for convective heat transfer in an electrically conducting fluid at a stretching surface with uniform free stream\u201d","volume":"2","author":"Xu","year":"2007","journal-title":"Int. J. Eng. Sci."},{"key":"ref_35","unstructured":"Woods, L.C. (1986). The Thermodynamics of Fluid Systems, Oxford University Press."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"133","DOI":"10.1016\/S0096-3003(00)00017-5","article-title":"Local nonsimilarity solutions for mixed convection boundary layer flow of a micropolar fluid on horizontal flat plates with variable surface temperature","volume":"122","author":"Ibrahim","year":"2001","journal-title":"Appl. Math. Comp."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/15\/11\/4822\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T21:50:25Z","timestamp":1760219425000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/15\/11\/4822"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,11,6]]},"references-count":36,"journal-issue":{"issue":"11","published-online":{"date-parts":[[2013,11]]}},"alternative-id":["e15114822"],"URL":"https:\/\/doi.org\/10.3390\/e15114822","relation":{},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2013,11,6]]}}}