On rate type fluid flow induced by rectified sine pulses

Kehong Zheng; Fuzhang Wang; Muhammad Kamran; Rewayat Khan; Ali Sikandar Khan; Sadique Rehman; Aamir Farooq; Kehong Zheng; Fuzhang Wang; Muhammad Kamran; Rewayat Khan; Ali Sikandar Khan; Sadique Rehman; Aamir Farooq

doi:10.3934/math.2022094

AIMS Mathematics

2022, Volume 7, Issue 2: 1615-1627. doi: 10.3934/math.2022094

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On rate type fluid flow induced by rectified sine pulses

1.
College of Water Conservancy and Ecological Engineering, Nanchang Institute of Technology, Nanchang 330099, China
2.
Nanchang Institute of Technology, Nanchang 330044, China
3.
College of Computer Science and Technology, Huaibei Normal University, Huaibei 235000, China
4.
School of Mathematical and Statistics, Xuzhou University of Technology, Xuzhou 221018, China
5.
Department of Mathematics, COMSATS University Islamabad, Wah Campus 47040, Pakistan
6.
Department of Mathematics, Abbottabad University of Science and Technology, Havelian 22500, Pakistan
7.
Department of Pure and Applied Mathematics, University of Haripur, Haripur, KPK, Haripur, Pakistan

Received: 07 April 2021 Accepted: 21 October 2021 Published: 29 October 2021
MSC : 35C15, 35Q61, 76A05, 76S99, 76W99

This investigation aims to present the unsteady motion of second grade fluid in an oscillating duct induced by rectified sine pulses. Some of the most dominant means for solving problems in engineering, mathematics and physics are transform methods. The objective is to modify the domain of the present problem to a new domain which is easier for evaluation. Such modifications can be done by different ways, one such way is by using transforms. In present work Fourier sine transform and Laplace transform techniques are used. The solution thus obtained is in form of steady state, with combination of transient solution which fulfills all required initial and boundary conditions. The influence of various parameters of interest for both developing and retarding flows on the flow characteristics will also be sketched and discussed. Also, the problem is reduced to the flow model where side walls are absent by bringing the aspect ratio parameter (ratio of length to width) to zero.
Citation: Kehong Zheng, Fuzhang Wang, Muhammad Kamran, Rewayat Khan, Ali Sikandar Khan, Sadique Rehman, Aamir Farooq. On rate type fluid flow induced by rectified sine pulses[J]. AIMS Mathematics, 2022, 7(2): 1615-1627. doi: 10.3934/math.2022094

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Abstract

This investigation aims to present the unsteady motion of second grade fluid in an oscillating duct induced by rectified sine pulses. Some of the most dominant means for solving problems in engineering, mathematics and physics are transform methods. The objective is to modify the domain of the present problem to a new domain which is easier for evaluation. Such modifications can be done by different ways, one such way is by using transforms. In present work Fourier sine transform and Laplace transform techniques are used. The solution thus obtained is in form of steady state, with combination of transient solution which fulfills all required initial and boundary conditions. The influence of various parameters of interest for both developing and retarding flows on the flow characteristics will also be sketched and discussed. Also, the problem is reduced to the flow model where side walls are absent by bringing the aspect ratio parameter (ratio of length to width) to zero.

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