Unsteady Casson fluid flow over a vertical surface with fractional bioconvection

Muhammad Imran Asjad; Muhammad Haris Butt; Muhammad Armaghan Sadiq; Muhammad Danish Ikram; Fahd Jarad; Muhammad Imran Asjad; Muhammad Haris Butt; Muhammad Armaghan Sadiq; Muhammad Danish Ikram; Fahd Jarad

doi:10.3934/math.2022451

AIMS Mathematics

2022, Volume 7, Issue 5: 8112-8126. doi: 10.3934/math.2022451

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Unsteady Casson fluid flow over a vertical surface with fractional bioconvection

1.
Department of Mathematics, University of Management and Technology, Lahore 54770, Pakistan
2.
Department of Mathematics, Cankaya University, Etimesgut, Ankara, Turkey
3.
Department of Mathematics, King Abdul Aziz University, Jeddah, Saudi Arabia
4.
Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, Taiwan

Received: 07 October 2021 Revised: 13 January 2022 Accepted: 27 January 2022 Published: 24 February 2022
MSC : 35A22, 76A05

This paper deals with unsteady flow of fractional Casson fluid in the existence of bioconvection. The governing equations are modeled with fractional derivative which is transformed into dimensionless form by using dimensionless variables. The analytical solution is attained by applying Laplace transform technique. Some graphs are made for involved parameters. As a result, it is found that temperature, bioconvection are maximum away from the plate for large time and vice versa and showing dual behavior in their boundary layers respectively. Further recent literature is recovered from the present results and obtained good agreement.
- Casson fluid,
- bioconvection,
- fracional modeling,
- heat transfer,
- vertical plate
Citation: Muhammad Imran Asjad, Muhammad Haris Butt, Muhammad Armaghan Sadiq, Muhammad Danish Ikram, Fahd Jarad. Unsteady Casson fluid flow over a vertical surface with fractional bioconvection[J]. AIMS Mathematics, 2022, 7(5): 8112-8126. doi: 10.3934/math.2022451

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Abstract

This paper deals with unsteady flow of fractional Casson fluid in the existence of bioconvection. The governing equations are modeled with fractional derivative which is transformed into dimensionless form by using dimensionless variables. The analytical solution is attained by applying Laplace transform technique. Some graphs are made for involved parameters. As a result, it is found that temperature, bioconvection are maximum away from the plate for large time and vice versa and showing dual behavior in their boundary layers respectively. Further recent literature is recovered from the present results and obtained good agreement.

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