{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,28]],"date-time":"2025-10-28T18:24:58Z","timestamp":1761675898668,"version":"build-2065373602"},"reference-count":11,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2011,10,21]],"date-time":"2011-10-21T00:00:00Z","timestamp":1319155200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Micromachines"],"abstract":"<jats:p>This paper introduces a simple theoretical model for the response time of thermal flow sensors. Response time is defined here as the time needed by the sensor output signal to reach 63.2% of amplitude due to a change of fluid flow. This model uses the finite-difference method to solve the heat transfer equations, taking into consideration the transient conduction and convection between the sensor membrane and the surrounding fluid. Program results agree with experimental measurements and explain the response time dependence on the velocity and the sensor geometry. Values of the response time vary from about 5 ms in the case of stagnant flow to 1.5 ms for a flow velocity of 44 m\/s.<\/jats:p>","DOI":"10.3390\/mi2040385","type":"journal-article","created":{"date-parts":[[2011,10,21]],"date-time":"2011-10-21T11:37:59Z","timestamp":1319197079000},"page":"385-393","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":22,"title":["Modeling of the Response Time of Thermal Flow Sensors"],"prefix":"10.3390","volume":"2","author":[{"given":"Safir","family":"Issa","sequence":"first","affiliation":[{"name":"IMSAS (Institute for Microsensors, Actuators and Systems), Microsystems Center Bremen (MCB), University of Bremen, Otto-Hahn-Allee, Bld. NW1, D-28359 Bremen, Germany"},{"name":"IGS (International Graduate School for Dynamics in Logistics), University of Bremen, c\/o BIBA Hochschulring 20, D-28359 Bremen, Germany"}]},{"given":"Hannes","family":"Sturm","sequence":"additional","affiliation":[{"name":"IMSAS (Institute for Microsensors, Actuators and Systems), Microsystems Center Bremen (MCB), University of Bremen, Otto-Hahn-Allee, Bld. NW1, D-28359 Bremen, Germany"}]},{"given":"Walter","family":"Lang","sequence":"additional","affiliation":[{"name":"IMSAS (Institute for Microsensors, Actuators and Systems), Microsystems Center Bremen (MCB), University of Bremen, Otto-Hahn-Allee, Bld. NW1, D-28359 Bremen, Germany"},{"name":"IGS (International Graduate School for Dynamics in Logistics), University of Bremen, c\/o BIBA Hochschulring 20, D-28359 Bremen, Germany"}]}],"member":"1968","published-online":{"date-parts":[[2011,10,21]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"373","DOI":"10.1016\/j.sna.2010.03.019","article-title":"Thermal flow sensors for MEMS spirometric devices","volume":"162","author":"Hedrich","year":"2010","journal-title":"Sens. Actuat. A: Phys."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"262","DOI":"10.1016\/j.sna.2006.02.009","article-title":"A high temperature thermopile fabrication process for thermal flow sensors","volume":"130-131","author":"Buchner","year":"2006","journal-title":"Sens. Actuat. A: Phys."},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Sosna, C., Walter, T., and Lang, W. (2011). Response time of thermal flow sensors with air as fluid. Sens. Actuat. A: Phys.","DOI":"10.1016\/j.sna.2011.02.023"},{"key":"ref_4","unstructured":"Buchner, R. (2009). Hochtemperaturprozess zur Fertigung miniaturisierter thermischer Str\u00f6mungssensoren und ihre Applikation in Fl\u00fcssigkeiten, Verlag Dr. Hut."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"7","DOI":"10.1016\/S0924-4247(98)00248-9","article-title":"Thermal flow sensor for liquids and gases based on combinations of two principles","volume":"73","author":"Ashauer","year":"1999","journal-title":"Sens. Actuat. A: Phys."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"109","DOI":"10.1016\/S0263-2241(02)00058-1","article-title":"Development of miniaturized semiconductor flow sensors","volume":"33","author":"Kohl","year":"2003","journal-title":"Measurement"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"186","DOI":"10.1088\/0960-1317\/9\/2\/320","article-title":"Bi-directional fast flow sensor with a large dynamic range","volume":"9","author":"Jansen","year":"1999","journal-title":"J. Micromech. Microeng."},{"key":"ref_8","unstructured":"Pitts, D., and Sissom, L. (1998). Schaum's Outlines of Theory and Problems of Heat Transfer, McGraw-Hill. [2nd ed.]."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"958","DOI":"10.1109\/16.52430","article-title":"Heat transport from a chip","volume":"37","author":"Lang","year":"1990","journal-title":"IEEE Trans. Electron Devices"},{"key":"ref_10","unstructured":"Incropera, F.P., and DeWitt, D.P. (2002). Fundamentals of Heat and Mass Transfer, John Wiley & Sons. [5th ed.]."},{"key":"ref_11","unstructured":"Gianchandani, Y., Tabata, O., and Zappe, H. (2007). Comprehensive Microsystems, Elsevier Science and Technology."}],"container-title":["Micromachines"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2072-666X\/2\/4\/385\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T21:57:45Z","timestamp":1760219865000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2072-666X\/2\/4\/385"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2011,10,21]]},"references-count":11,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2011,12]]}},"alternative-id":["mi2040385"],"URL":"https:\/\/doi.org\/10.3390\/mi2040385","relation":{},"ISSN":["2072-666X"],"issn-type":[{"type":"electronic","value":"2072-666X"}],"subject":[],"published":{"date-parts":[[2011,10,21]]}}}