{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:27:51Z","timestamp":1760243271583,"version":"build-2065373602"},"reference-count":17,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2014,7,10]],"date-time":"2014-07-10T00:00:00Z","timestamp":1404950400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"funder":[{"name":"BES, DoE Office of Science","award":["DE-SC0004751"],"award-info":[{"award-number":["DE-SC0004751"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>In an earlier paper in Entropy [1] we hypothesized that the entropy generation rate is the driving force for boundary layer transition from laminar to turbulent flow. Subsequently, with our colleagues we have examined the prediction of entropy generation during such transitions [2,3]. We found that reasonable predictions for engineering purposes could be obtained for flows with negligible streamwise pressure gradients by adapting the linear combination model of Emmons [4]. A question then arises\u2014will the Emmons approach be useful for boundary layer transition with significant streamwise pressure gradients as by Nolan and Zaki [5]. In our implementation the intermittency is calculated by comparison to skin friction correlations for laminar and turbulent boundary layers and is then applied with comparable correlations for the energy dissipation coefficient (i.e., non-dimensional integral entropy generation rate). In the case of negligible pressure gradients the Blasius theory provides the necessary laminar correlations.<\/jats:p>","DOI":"10.3390\/e16073808","type":"journal-article","created":{"date-parts":[[2014,7,10]],"date-time":"2014-07-10T11:22:59Z","timestamp":1404991379000},"page":"3808-3812","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Entropy Generation in Steady Laminar Boundary Layers with Pressure Gradients"],"prefix":"10.3390","volume":"16","author":[{"given":"Donald","family":"McEligot","sequence":"first","affiliation":[{"name":"Mechanical Engineering Department, University of Idaho, Idaho Falls, ID 83402, USA"},{"name":"Institut f\u00fcr Kernenergetik und Energiesysteme (IKE), Universit\u00e4t Stuttgart, Pfaffenwaldring 31,  D-70569 Stuttgart, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Edmond","family":"Walsh","sequence":"additional","affiliation":[{"name":"Osney Thermo-fluids Laboratory, Department of Engineering Science, University of Oxford, Osney Mead, Oxford OX2 0ES, UK"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2014,7,10]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"375","DOI":"10.3390\/e6040375","article-title":"On the use of entropy to predict boundary layer stability","volume":"6","author":"Walsh","year":"2004","journal-title":"Entropy"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"512","DOI":"10.1115\/1.2720488","article-title":"Predicting entropy generation rates in transitional boundary layers based on intermittency","volume":"129","author":"Nolan","year":"2007","journal-title":"J. Turbomach"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"061203:1","DOI":"10.1115\/1.4004093","article-title":"Entropy generation in boundary layers transitioning under the influence of free stream turbulence","volume":"133","author":"Walsh","year":"2011","journal-title":"J. Fluids Eng"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"490","DOI":"10.2514\/8.2010","article-title":"The laminar-turbulent transition in a boundary layer","volume":"18","author":"Emmons","year":"1951","journal-title":"J. Aero. Sci"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"306","DOI":"10.1017\/jfm.2013.287","article-title":"Conditional sampling of transitional boundary layers in pressure gradients","volume":"728","author":"Nolan","year":"2013","journal-title":"J. Fluid Mech"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"245","DOI":"10.1017\/S0001925900000184","article-title":"Approximate calculation of the laminar boundary layer","volume":"1","author":"Thwaites","year":"1949","journal-title":"Aero. Q"},{"key":"ref_7","unstructured":"White, F.M. (2006). Viscous Fluid Flow, McGraw-Hill. [3rd ed]."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"865","DOI":"10.1080\/14786443109461870","article-title":"Some approximate solutions of the boundary layer equations","volume":"12","author":"Falkner","year":"1931","journal-title":"Philos. Mag"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"44","DOI":"10.1016\/j.advengsoft.2011.08.005","article-title":"Solution of the Falkner-Skan wedge flow by \u2018HPM-Pade\u2019 method","volume":"43","author":"Bararnia","year":"2012","journal-title":"Adv. Eng. Softw"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"223","DOI":"10.1017\/S0305004100019575","article-title":"On an equation occurring in Falkner and Skan\u2019s approximate treatment of the equations of the boundary layer","volume":"33","author":"Hartree","year":"1937","journal-title":"Proc. Cambridge Philos. Soc"},{"key":"ref_11","unstructured":"Evans, H.L. (1968). Laminar Boundary-Layer Theory, Addison-Wesley."},{"key":"ref_12","unstructured":"Walz, A. (1969). Boundary Layers of Flow and Temperature, MIT Press."},{"key":"ref_13","unstructured":"Schlichting, H. (1968). Boundary Layer Theory, McGraw-Hill. [6th ed]."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"621","DOI":"10.1115\/1.2929299","article-title":"Loss mechanisms in turbomachines","volume":"115","author":"Denton","year":"1993","journal-title":"J. Turbomach"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"211","DOI":"10.1007\/BF00536673","article-title":"Ein Quadraturverfahren zur Berechnung der laminaren und turbulenten Reibungsschicht bei ebener und rotationssymmetrischer Str\u00f6mung","volume":"20","author":"Truckenbrodt","year":"1952","journal-title":"Ing. Arch"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"243","DOI":"10.1007\/BF00548008","article-title":"Anwendung des Energiesatzes von Wieghardt auf einparametrige Geschwindingkeitsprofile in laminaren Grenzschichten","volume":"16","author":"Walz","year":"1948","journal-title":"Ing. Arch"},{"key":"ref_17","unstructured":"Denton, J.D., and Cumpsty, N.A. (IMechE, 1987). Loss mechanisms in turbomachines, IMechE, Paper No. C260\/87."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/16\/7\/3808\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T21:13:30Z","timestamp":1760217210000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/16\/7\/3808"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,7,10]]},"references-count":17,"journal-issue":{"issue":"7","published-online":{"date-parts":[[2014,7]]}},"alternative-id":["e16073808"],"URL":"https:\/\/doi.org\/10.3390\/e16073808","relation":{},"ISSN":["1099-4300"],"issn-type":[{"type":"electronic","value":"1099-4300"}],"subject":[],"published":{"date-parts":[[2014,7,10]]}}}