Third-order partial differential equations arising in the impulsive motion of a flat plate |
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| Authors: | Robert A Van Gorder K Vajravelu |
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| Institution: | 1. School of Mathematics and Statistics, Gansu Key Laboratory of Applied Mathematics and Complex Systems, Lanzhou University, Lanzhou 730000, China;2. School of Mathematical Sciences, University of Jinan, Jinan, Shandong 250022, China;1. Department of Mathematics, Aligarh Muslim University, Aligarh 202 002, Uttar Pradesh, India;2. Department of Mathematics and Statistics, University of Victoria, Victoria, British Columbia V8W 3R4, Canada;1. LUNAM Université, Université d?Angers, Laboratoire de Photonique d?Angers, EA 4464, 2 Boulevard Lavoisier, 49000 Angers, France;2. Horia Hulubei National Institute for Physics and Nuclear Engineering, 30 Reactorului, Magurele-Bucharest 077125, Romania;3. Academy of Romanian Scientists, 54 Splaiul Independentei, 050094 Bucharest, Romania;4. Department of Physical Electronics, School of Electrical Engineering, Faculty of Engineering, Tel Aviv University, Tel Aviv 69978, Israel |
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| Abstract: | We obtain numerical solutions to a class of third-order partial differential equations arising in the impulsive motion of a flat plate for various boundary data. In particular, we study the case of constant acceleration of the plate, the case of oscillation of the plate, and a case in which velocity is increasing yet acceleration is decreasing. We compare the numerical solutions with the known exact solutions in order to establish the validity of the method. Several figures illustrating both solution forms and the relative strength of the second and third-order terms are presented. The results obtained in this study reveal many interesting behaviors that warrant further study on the non-Newtonian fluid flow phenomena. |
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