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Journal of Applied Mathematics
Volume 2016 (2016), Article ID 1487616, 18 pages
http://dx.doi.org/10.1155/2016/1487616
Research Article

Chaotic Convection in a Viscoelastic Fluid Saturated Porous Medium with a Heat Source

Department of Mathematics, Institute of Science, Banaras Hindu University, Varanasi 221005, India

Received 12 October 2015; Revised 5 January 2016; Accepted 28 January 2016

Academic Editor: Nasser-Eddine Tatar

Copyright © 2016 B. S. Bhadauria. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Chaotic convection in a viscoelastic fluid saturated porous layer, heated from below, is studied by using Oldroyd’s type constituting relation and in the presence of an internal heat source. A modified Darcy law is used in the momentum equation, and a heat source term has been considered in energy equation. An autonomous system of fourth-order differential equations has been deduced by using a truncated Fourier series. Effect of internal heat generation on chaotic convection has been investigated. The asymptotic behavior can be stationary, periodic, or chaotic, depending upon the flow parameters. Construction of four-scroll, or “two-butterfly,” and chaotic attractor has been examined.