{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,1]],"date-time":"2026-05-01T14:40:54Z","timestamp":1777646454216,"version":"3.51.4"},"reference-count":28,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2019,4,3]],"date-time":"2019-04-03T00:00:00Z","timestamp":1554249600000},"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 current work will describe the entropy generation in an unsteady magnetohydrodynamic (MHD) flow with a combined influence of mass and heat transfer through a porous medium. It will consider the flow in the XY plane and the plate with isothermal and ramped wall temperature. The wall shear stress is also considered. The influences of different pertinent parameters on velocity, the Bejan number and on the total entropy generation number are reported graphically. Entropy generation in the fluid is controlled and reduced on the boundary by using wall shear stress. It is observed in this paper that by taking suitable values of pertinent parameters, the energy losses in the system can be minimized. These parameters are the Schmitt number, mass diffusion parameter, Prandtl number, Grashof number, magnetic parameter and modified Grashof number. These results will play an important role in the heat flow of uncertainty and must, therefore, be controlled and managed effectively.<\/jats:p>","DOI":"10.3390\/e21040359","type":"journal-article","created":{"date-parts":[[2019,4,4]],"date-time":"2019-04-04T03:13:42Z","timestamp":1554347622000},"page":"359","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":36,"title":["Entropy Generation in MHD Conjugate Flow with Wall Shear Stress over an Infinite Plate: Exact Analysis"],"prefix":"10.3390","volume":"21","author":[{"given":"Arshad","family":"Khan","sequence":"first","affiliation":[{"name":"Institute of Business and Management Sciences, the University of Agriculture, Peshawar 25000, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Faizan","family":"ul Karim","sequence":"additional","affiliation":[{"name":"Department of Mathematics, City University of Science and Information Technology, Peshawar 25000, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2056-9371","authenticated-orcid":false,"given":"Ilyas","family":"Khan","sequence":"additional","affiliation":[{"name":"Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City 72915, Vietnam"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2056-9371","authenticated-orcid":false,"given":"Tawfeeq Abdullah","family":"Alkanhal","sequence":"additional","affiliation":[{"name":"Department of Mechatronics and System Engineering, College of Engineering, Majmaah University, Majmaah 11952, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Farhad","family":"Ali","sequence":"additional","affiliation":[{"name":"Department of Mathematics, City University of Science and Information Technology, Peshawar 25000, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3723-0796","authenticated-orcid":false,"given":"Dolat","family":"Khan","sequence":"additional","affiliation":[{"name":"Department of Mathematics, City University of Science and Information Technology, Peshawar 25000, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5769-4320","authenticated-orcid":false,"given":"Kottakkaran Sooppy","family":"Nisar","sequence":"additional","affiliation":[{"name":"Department of Mathematics, College of Arts and Sciences Wadi Aldawaser, Prince Sattam bin Abdulaziz University, Wadi Aldawaser 11991, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2019,4,3]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"305","DOI":"10.1080\/01495728408961827","article-title":"Mixed convection boundary-layer flow along a vertical surface in a porous medium","volume":"7","author":"Ranganathan","year":"1984","journal-title":"Numer. Heat Transf."},{"key":"ref_2","first-page":"831","article-title":"Effects of radiation and chemical reaction on MHD convective flow over a permeable stretching surface with suction and heat generation","volume":"12","author":"Krishna","year":"2015","journal-title":"Walaliak J. Sci. Technol."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"378","DOI":"10.1016\/j.ijheatmasstransfer.2017.11.007","article-title":"MHD mixed convective stagnation point flow and heat transfer of an incompressible nanofluid over an inclined stretching sheet with chemical reaction and radiation","volume":"118","author":"Gupta","year":"2018","journal-title":"Int. J. Heat Mass Transf."},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Singh, J., Rashidi, M.M., and Kumar, D. (2017). A hybrid computational approach for Jeffery\u2013Hamel flow in non-parallel walls. Neural Comput. Appl., 1\u20137.","DOI":"10.1007\/s00521-017-3198-y"},{"key":"ref_5","first-page":"103","article-title":"A fractional model of convective radial fins with temperature-dependent thermal conductivity","volume":"69","author":"Kumar","year":"2017","journal-title":"Rom. Rep. Phys."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/S0065-2717(08)70172-2","article-title":"Second-law analysis in heat transfer and thermal design","volume":"15","author":"Bejan","year":"1982","journal-title":"Adv. Heat Transf."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"718","DOI":"10.1115\/1.3451063","article-title":"A study of entropy generation in fundamental convective heat transfer","volume":"101","author":"Bejan","year":"1979","journal-title":"J. Heat Transf."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"71","DOI":"10.1016\/j.applthermaleng.2015.09.076","article-title":"Irreversibility analysis of the absorption heat transformer coupled to a single effect evaporation process","volume":"92","author":"Colorado","year":"2016","journal-title":"Appl. Therm. Eng."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"1283","DOI":"10.1016\/j.rinp.2017.12.032","article-title":"Irreversibility analysis in unsteady flow over a vertical plate with arbitrary wall shear stress and ramped wall temperature","volume":"8","author":"Khan","year":"2018","journal-title":"Results Phys."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"182","DOI":"10.1016\/j.icheatmasstransfer.2011.12.003","article-title":"Optimal design of tree-shaped water distribution network using constructal approach: T-shaped and Y-shaped architectures optimization and comparison","volume":"39","author":"Azoumah","year":"2012","journal-title":"Int. Commun. Heat Mass Transf."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"2057","DOI":"10.1016\/j.ijthermalsci.2010.04.024","article-title":"Entropy generation minimization of combined heat and mass transfer devices","volume":"49","author":"Narayan","year":"2010","journal-title":"Int. J. Therm. Sci."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"186","DOI":"10.1016\/j.enconman.2013.03.035","article-title":"Combined constructal and exergy optimization of thermochemical reactors for high temperature heat storage","volume":"71","author":"Neveu","year":"2013","journal-title":"Energy Convers. Manag."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"258","DOI":"10.1016\/0142-727X(87)90062-2","article-title":"The thermodynamic design of heat and mass transfer processes and devices","volume":"8","author":"Bejan","year":"1987","journal-title":"Int. J. Heat Fluid Flow"},{"key":"ref_14","unstructured":"Bejan, A. (1996). Entropy Generation Minimization, CRC Press."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"499","DOI":"10.1007\/s002310050354","article-title":"The effect of variable viscosity on the entropy generation and pumping power in a laminar fluid flow through a duct subjected to constant heat flux","volume":"35","year":"1999","journal-title":"Heat Mass Transf."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"3545","DOI":"10.1088\/0022-3727\/40\/11\/044","article-title":"Constructal entropy generation minimization for heatand mass transfer in a solid-gas reactor based on triangular element","volume":"40","author":"Zhou","year":"2007","journal-title":"J. Phys. D Appl. Phys."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"12","DOI":"10.1016\/j.amc.2018.04.025","article-title":"An efficient numerical algorithm for the fractional Drinfeld\u2013Sokolov\u2013Wilson equation","volume":"335","author":"Singh","year":"2018","journal-title":"Appl. Math. Comput."},{"key":"ref_18","first-page":"1209","article-title":"Analytical techniques for system of time fractional nonlinear differential equations","volume":"54","author":"Choi","year":"2017","journal-title":"J. Korean Math. Soc."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"1251","DOI":"10.2298\/TSCI12041251A","article-title":"A new definition of Bejan number","volume":"16","author":"Awad","year":"2012","journal-title":"Therm. Sci."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"631","DOI":"10.2298\/TSCI130211032A","article-title":"Extending the Bejan number to a general form","volume":"17","author":"Awad","year":"2013","journal-title":"Therm. Sci."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"1245","DOI":"10.2298\/TSCI1304245A","article-title":"Hagen number versus Bejan number","volume":"17","author":"Awad","year":"2013","journal-title":"Therm. Sci."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"S617","DOI":"10.2298\/TSCI131213042A","article-title":"An Alternative Form of the Darcy Equation","volume":"18","author":"Awad","year":"2014","journal-title":"Therm. Sci."},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Awad, M.M. (2015). A review of entropy generation in microchannels. Adv. Mech. Eng., 7.","DOI":"10.1177\/1687814015590297"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.surfrep.2005.08.003","article-title":"Force measurements with the atomic force microscope: Technique, interpretation and applications","volume":"59","author":"Butt","year":"2005","journal-title":"Surf. Sci. Rep."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"1191","DOI":"10.1063\/1.362674","article-title":"Entropy generation minimization: The new thermodynamics of finite size devices and finite-time processes","volume":"79","author":"Bejan","year":"1996","journal-title":"J. Appl. Phys."},{"key":"ref_26","first-page":"187","article-title":"Free convection flow past an impulsively started infinite vertical plate with Newtonian heating in the presence of thermal radiation and mass diffusion","volume":"35","author":"Narahari","year":"2011","journal-title":"Turk. J. Eng. Environ. Sci."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"753","DOI":"10.5560\/zna.2011-0044","article-title":"General solutions for the unsteady flow of second-grade fluids over an inflnite plate that applies arbitrary shear to the fluid","volume":"66","author":"Fetecau","year":"2011","journal-title":"Z. Naturforsch. Sect. A J. Phys. Sci."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"130","DOI":"10.5560\/zna.2012-0083","article-title":"Radiative and porous effects on free con-vection flow near a vertical plate that applies shear stress to the fluid","volume":"68","author":"Fetecau","year":"2013","journal-title":"Z. Naturforsch. Sect. A J. Phys. Sci."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/21\/4\/359\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T12:42:42Z","timestamp":1760186562000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/21\/4\/359"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,4,3]]},"references-count":28,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2019,4]]}},"alternative-id":["e21040359"],"URL":"https:\/\/doi.org\/10.3390\/e21040359","relation":{},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,4,3]]}}}