Peristaltic transport of viscoelastic bio-fluids with fractional derivative models

Authors

  • Emilia Bazhlekova Institute of Mathematics and Informatics - Bulgarian Academy of Sciences
  • Ivan Bazhlekov Institute of Mathematics and Informatics - Bulgarian Academy of Sciences

DOI:

https://doi.org/10.11145/j.biomath.2016.05.161

Abstract

Peristaltic flow of viscoelastic fluid through a uniform channel is considered under the assumptions of long wavelength and low Reynolds number. The fractional Oldroyd-B constitutive viscoelastic law is employed. Based on models for peristaltic viscoelastic flows given in a series of papers by Tripathi et al. (e.g. Appl Math Comput. 215 (2010) 3645–3654; Math Biosci. 233 (2011) 90–97) we present a detailed analytical and numerical study of the evolution in time of the pressure gradient across one wavelength. An analytical expression for the pressure gradient is obtained in terms of Mittag-Leffler functions and its behavior is analyzed. For numerical computation the fractional Adams method is used. The influence of the different material parameters is discussed, as well as constraints on the parameters under which the model is physically meaningful.

Downloads

Published

2016-06-02

Issue

Vol. 5 No. 1 (2016)

Section

Original Articles

License

The journal Biomath is an open access journal. All published articles are immeditely available online and the respective DOI link activated. All articles can be access for free and no reader registration of any sort is required. No fees are charged to authors for article submission or processing. Online publications are funded through volunteer work, donations and grants.

Authors who publish with this journal agree to the following terms:

  • Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License 4.0 that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
  • Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
  • Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).