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Karmakar T, Barik S, Raja Sekhar GP. Multi-scale analysis of concentration distribution in unsteady Couette–Poiseuille flows through a porous channel. Proc Math Phys Eng Sci 2023. [DOI: 10.1098/rspa.2022.0494] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/26/2023] Open
Abstract
A multiple-scale perturbation analysis is presented to analyse the two-dimensional concentration distribution of passive contaminant released in an incompressible viscous fluid flowing between two parallel plates filled with a porous medium. The flow is driven by the combined effect of the upper plate oscillation in its own plane moving with a constant velocity, and the periodic pressure gradient. Mei’s homogenization technique is used to find the concentration distribution up to third order, complemented with the dispersion coefficients for four different situations, namely, steady, pulsatile, oscillatory and the combined effect of all these. We observe that when the flow is under the combined effect of wall oscillation and pressure pulsation, then the respective frequency (Womersley number) and amplitude parameters oppose each other while influencing the dispersion coefficient. Our analysis reveals that for a fixed amplitude of oscillation and pulsation, the frequency of pressure pulsation has a stronger effect on the dispersion coefficient compared with the wall oscillation. On the other hand, when the Womersley number is kept fixed, amplitude of the wall oscillation dominates the pressure pulsation. This behaviour is more prominent for higher values of the Darcy number. The transverse concentration distribution and its dependency on porous medium parameters are also discussed in detail.
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Affiliation(s)
- Timir Karmakar
- Department of Mathematics, National Institute of Technology Meghalaya, Shillong, Meghalaya 793003, India
| | - Swarup Barik
- Department of Mathematics, SRM Institute of Science and Technology, Kattankulathur, Chennai 603203, Tamil Nadu, India
| | - G. P. Raja Sekhar
- Department of Mathematics, Indian Institute of Technology Kharagpur, Kharagpur 721302, India
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