{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,17]],"date-time":"2026-03-17T14:50:20Z","timestamp":1773759020549,"version":"3.50.1"},"reference-count":37,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2016,2,2]],"date-time":"2016-02-02T00:00:00Z","timestamp":1454371200000},"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>Results are presented for an innovative computational procedure that predicts time-dependent instabilities and deterministic ordered structures in three-dimensional steady-state laminar boundary-layer flows. The flow configuration considered is a corner flow with sidewall surface mass injection into a horizontal boundary-layer flow. The equations for the velocity fluctuations are cast into a spectral Lorenz-type format and incorporated into the overall computational procedure for the three-dimensional flow. The non-linear time-dependent solutions of the spectral equations predict deterministic spectral ordered structures within spiral structures. Spectral analysis of these fluctuating solutions yields the resulting entropy generation rates resulting from the dissipation of the ordered structures. The results for the entropy generation rates indicate the prediction of a strong burst of ordered structures within the range of injection velocities studied. This new computational method is applicable to only selected thermal design processes.<\/jats:p>","DOI":"10.3390\/e18020047","type":"journal-article","created":{"date-parts":[[2016,2,3]],"date-time":"2016-02-03T01:48:18Z","timestamp":1454464098000},"page":"47","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Entropy Generation through Deterministic Spiral Structures in Corner Flows with Sidewall Surface Mass Injection"],"prefix":"10.3390","volume":"18","author":[{"given":"LaVar","family":"Isaacson","sequence":"first","affiliation":[{"name":"Mechanical Engineering, University of Utah, 2067 Browning Avenue, Salt Lake City, UT 84108, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2016,2,2]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"5304","DOI":"10.3390\/e17085304","article-title":"Entropy Generation through Deterministic Spiral Structures in a Corner Boundary-Layer Flow","volume":"17","author":"Isaacson","year":"2015","journal-title":"Entropy"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"53","DOI":"10.3390\/e15010053","article-title":"Ordered Regions within a Nonlinear Time Series Solution of a Lorenz Form of the Townsend Equations for a Boundary-Layer Flow","volume":"15","author":"Isaacson","year":"2013","journal-title":"Entropy"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"4134","DOI":"10.3390\/e15104134","article-title":"Spectral Entropy, Empirical Entropy and Empirical Exergy for Deterministic Boundary-Layer Structures","volume":"15","author":"Isaacson","year":"2013","journal-title":"Entropy"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"1555","DOI":"10.3390\/e13091555","article-title":"Spectral Entropy in a Boundary Layer Flow","volume":"13","author":"Isaacson","year":"2011","journal-title":"Entropy"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"6006","DOI":"10.3390\/e16116006","article-title":"Entropy Generation through a Deterministic Boundary-Layer Structure in Warm Dense Plasma","volume":"16","author":"Isaacson","year":"2014","journal-title":"Entropy"},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Attard, P. 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