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

Previous Article Next Article

Research article Special Issues

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

Related Papers:

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.

References

[1]	M. Ahmad, M. I. Asjad, A. Akgül, D. Baleanu, Analytical solutions for free convection flow of casson nanofluid over an infinite vertical plate, AIMS Math., 6 (2021), 2344–2358. doi: 10.3934/math.2021142. doi: 10.3934/math.2021142
[2]	M. N. Alam, M. A. Akbar, K. Khan, Some new exact traveling wave solutions to the (2+1)-dimensional breaking soliton equation, World Appl. Sci. J., 25 (2013), 500–523. doi: 10.5829/idosi.wasj.2013.25.03.1193. doi: 10.5829/idosi.wasj.2013.25.03.1193
[3]	Y. M. Chu, N. A. Shah, H. Ahmad, J. D. Chung, S. Khaled, A comparative study of semi-analytical methods for solving fractional-order cauchy-reaction diffusion equation, Fractals, 29 (2021), 2150143. doi: 10.1142/S0218348X21501437. doi: 10.1142/S0218348X21501437
[4]	J. E. Dunn, R. L. Fosdick, Thermodynamics, stability, and boundedness of fluids of complexity 2 and fluids of second grade, Arch. Rational Mech. Anal., 56 (1974), 191–252. doi: 10.1007/BF00280970. doi: 10.1007/BF00280970
[5]	M. E. Erdoǧan, C. E. İmrak, Effects of the side walls on the unsteady flow of a second-grade fluid in a duct of uniform cross-section, Int. J. Non-Linear Mech., 39 (2004), 1379–1384. doi: 10.1016/j.ijnonlinmec.2003.12.004. doi: 10.1016/j.ijnonlinmec.2003.12.004
[6]	M. Erdoǧan, C. İmrak, The effects of the side walls on the flow of a second grade fluid in ducts with suction and injection, Int. J. Non-Linear Mech., 42 (2007), 765–772. doi: 10.1016/j.ijnonlinmec.2007.03.001. doi: 10.1016/j.ijnonlinmec.2007.03.001
[7]	A. Farooq, M. Kamran, Y. Bashir, H. Ahmad, A. Shahzad, Y. M. Chu, On the flow of mhd generalized maxwell fluid via porous rectangular duct, Open Phys., 18 (2020), 989–1002. doi: 10.1515/phys-2020-0209. doi: 10.1515/phys-2020-0209
[8]	C. Fetecau, C. Fetecau, Starting solutions for some unsteady unidirectional flows of a second grade fluid, Int. J. Eng. Sci., 43 (2005), 781–789, doi: 10.1016/j.ijengsci.2004.12.009. doi: 10.1016/j.ijengsci.2004.12.009
[9]	C. Fetecau, M. Nazar, C. Fetecau, Unsteady flow of an Oldroyd-B fluid generated by a constantly accelerating plate between two side walls perpendicular to the plate, Int. J. Non-Linear Mech., 44 (2009), 1039–1047, doi: 10.1016/j.ijnonlinmec.2009.08.008. doi: 10.1016/j.ijnonlinmec.2009.08.008
[10]	A. Ghosh, S. Pintu, On hydromagnetic channel flow of an Oldroyd-B fluid induced by tooth pulses, Magnetohydrodynamics, 44 (2008), 325–340. doi: 10.22364/mhd.44.3.11
[11]	A. Ghosh, P. Sana, On hydromagnetic channel flow of an Oldroyd-B fluid induced by rectified sine pulses, Comput. Appl. Math., 28 (2009), 365–395. doi: 10.1590/S1807-03022009000300006. doi: 10.1590/S1807-03022009000300006
[12]	M. Husain, T. Hayat, C. Fetecau, S. Asghar, On accelerated flows of an Oldroyd-B fluid in a porous medium, Nonlinear Anal.: Real World Appl., 9 (2008), 1394–1408. doi: 10.1016/j.nonrwa.2007.03.007. doi: 10.1016/j.nonrwa.2007.03.007
[13]	A. Johri, M. Singh, Oscillating flow of a viscous liquid in a porous rectangular duct, Def. Sci. J., 38 (1998), 21–24.
[14]	M. Kamran, Y. Bashir, A. Farooq, A. Shahzad, A. M. Abd Allah, H. Alotaibi, H. Ahmad, Study on the helicoidal flow through cylindrical annuli with prescribed shear stresses, Results Phys., 23 (2021), 103993. doi: 10.1016/j.rinp.2021.103993. doi: 10.1016/j.rinp.2021.103993
[15]	M. Khan, C. Fetecau, T. Hayat, MHD transient flows in a channel of rectangular cross-section with porous medium, Phys. Lett. A, 369 (2007), 44–54. doi: 10.1016/j.physleta.2007.04.076. doi: 10.1016/j.physleta.2007.04.076
[16]	M. Khan, E. Naheed, C. Fetecau, T. Hayat, Exact solutions of starting flows for second grade fluid in a porous medium, Int. J. Non-Linear Mech., 43 (2008), 868–879. doi: 10.1016/j.ijnonlinmec.2008.06.002. doi: 10.1016/j.ijnonlinmec.2008.06.002
[17]	M. Khan, A. Anjum, Some oscillating motions of a burgers fluid, Int. J. Phys. Sci., 7 (2012), 5834–5851. doi: 10.5897/IJPS12.402. doi: 10.5897/IJPS12.402
[18]	M. Khan, Zeeshan, MHD flow of an Oldroyd-B fluid through a porous space induced by sawtooth pulses, Chin. Phys. Lett., 28 (2011), 084701. doi: 10.1088/0256-307X/28/8/084701
[19]	Z. A. Khan, H. Ahmad, Qualitative properties of solutions of fractional differential and difference equations arising in physical models, Fractals, 29 (2011), 2140024. doi: 10.1142/S0218348X21400247. doi: 10.1142/S0218348X21400247
[20]	M. Nazar, C. Fetecau, D. Vieru, C. Fetecau, New exact solutions corresponding to the second problem of stokes for second grade fluids, Nonlinear Anal.: Real World Appl., 11 (2010), 584–591. doi: 10.1016/j.nonrwa.2008.10.055. doi: 10.1016/j.nonrwa.2008.10.055
[21]	M. Nazar, F. Shahid, M. S. Akram, Q. Sultan, Flow on oscillating rectangular duct for maxwell fluid, Appl. Math. Mech., 33 (2012), 717–730. doi: 10.1007/s10483-012-1582-6. doi: 10.1007/s10483-012-1582-6
[22]	A. Siddiqui, T. Hayat, S. Asghar, Periodic flows of a non-Newtonian fluid between two parallel plates, Int. J. Non-Linear Mech., 34 (1999), 895–899, doi: 10.1016/S0020-7462(98)00063-8. doi: 10.1016/S0020-7462(98)00063-8
[23]	Q. Sultan, M. Nazar, I. Ahmad, U. Ali, Flow of second grade fluid between two walls induced by rectified sine pulses shear stress, J. Mech., 31 (2015), 573–582, doi: 10.1017/jmech.2015.22. doi: 10.1017/jmech.2015.22
[24]	Q. Sultan, M. Nazar, U. Ali, M. Imran, Unsteady flow of oldroyd-b fluid through porous rectangular duct, Int. J. Non-Linear Sci., 15 (2013), 195–211.

Reader Comments

your name:*

Email:*
© 2022 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)