Unsteady Flow of Couple Stress Fluid with Suspended Dust Particles in a Porous Medium
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Abstract
The present paper examines the unsteady flow of an in-compressible couple stress fluid carrying uniformly distributed suspended dust particles through a porous medium confined between two parallel porous plates. The couple stress theory of Stokes is employed to account for the polar and micro-rotational character of the suspension, while the dust phase is modelled as a continuum with an in-terphase Stokes drag interaction and the Darcy resistance term represents the porous matrix. The governing dimensional equations of the fluid and particle phases are non-dimensionalised and reduced, through a perturbation scheme valid for a small-amplitude oscillatory pressure gradient superposed on a steady mean gradient, to a set of coupled ordinary differential equations for the steady and unsteady components of velocity. Closed-form analytical solutions are obtained in terms of hyperbolic functions, and expressions for the skin friction coefficient, centreline velocity, volumetric flow rate and the phase lag between the two constituents are derived. A wide-ranging parametric study is presented in seven tables and five graphical illustrations, covering the couple stress parameter, permeability parameter, mass concentration of dust particles, relaxation-time parameter and frequency of oscillation. The results indicate that the couple stress parameter enhances the velocity of both phases and reduces the wall skin friction, whereas an increasing permeability parameter accelerates the flow and the mass concentration of dust particles retards it. The dust phase lags the fluid phase increasingly as the relaxation-time parameter and the frequency of oscillation increase. The limiting Newtonian dusty-fluid case is recovered and compared with the couple stress results, confirming the internal consistency of the analysis. The study is expected to be of value in problems of blood-flow rheology, lubrication with contaminated fluids, filtration, and flow through fibrous or granular porous media encountered in petroleum and chemical engineering.
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References
Chitra, M., & Kavitha, V. (2017). Influence of slip condition on unsteady pulsatile flow through a porous medium in a circular pipe. Research Journal of Science and Technology, 9(3), 441–448.
Devakar, M., & Ramgopal, N. C. (2015). Fully developed flows of two immiscible couple stress and Newtonian fluids through a nonporous and porous medium in a horizontal cylinder. Journal of Porous Media, 18(5), 549–558.
Farhad, A., Muhammad, B., Madeha, G., & Ilyas, K. (2020). A report on fluctuating free convection flow of heat absorbing viscoelastic dusty fluid past in a horizontal channel with MHD effect. Scientific Reports, 10(1), 8523.
Ishaq, M., Ur Rehman, S., Riaz, M. B., & Zahid, M. (2024). Hydrodynamical study of couple stress fluid flow in a linearly permeable rectangular channel subject to Darcy porous medium and no-slip boundary conditions. Alexandria Engineering Journal, 90, 1–14.
Kumar, S., Pundir, R., & Nadian, P. K. (2020). Effect of dust particles on a rotating couple-stress ferromagnetic fluid heated from below. International Journal of Scientific Engineering and Applied Science, 6(2), 1–9.
Ramesh, K. (2015). Effects of heat and mass transfer on the peristaltic transport of MHD couple stress fluid through porous medium in a vertical asymmetric channel. Journal of Fluids, 2015, Article 163832.
Sasikala, R., Govindarajan, A. G., & Gayathri, R. (2018). Unsteady stokes flow of dusty fluid between two parallel plates through porous medium in the presence of magnetic field. Journal of Physics: Conference Series, 1000, 012154.
Srinivas, J., & Murthy, J. V. R. (2016). Flow of two immiscible couple stress fluids between two permeable beds. Journal of Applied Fluid Mechanics, 9(1), 501–507.
Vyas, P., & Gajanand. (2023). Differential transform method for couple stress fluid flow in a channel with a porous base. Heat Transfer, 52(3), 2348–2382.
Yadav, R. K., & Yadav, S. (2023). A study on the flow of couple stress fluid in a porous curved channel. European Journal of Mechanics – B/Fluids, 103, 91–101.
Yitagesu, D. K. (2023). Hydromagnetic flow of two immiscible couple stress fluids through a porous medium in a cylindrical pipe with slip effect. Journal of Applied Mathematics, 2023, Article 1902844.
Yitagesu, D. K., & Gosa, G. (2024). Magnetohydrodynamic flow of two immiscible Jeffrey fluids through a horizontal porous cylinder. Journal of Applied Mathematics, 2024, 1–14.
Parveen, S. R. (2024). Transfer and unsteady MHD flow of a dusty couple stress fluid in a porous medium. International Journal of Intelligent Systems and Applications in Engineering, 12(23s), 2027–2033.
Abbas, Z., Hasnain, J., & Sajid, M. (2015). Hydromagnetic mixed convective two-phase flow of couple stress and viscous fluids in an inclined channel. Zeitschrift für Naturforschung A, 69(9–10), 553–561.
Kumar, N., & Gupta, S. (2019). MHD free convective flow of micropolar and Newtonian fluids through porous medium in a vertical channel. Meccanica, 54(1), 277–291.
Ansari, I. A., & Deo, S. (2017). Effect of magnetic field on the two immiscible viscous fluids flow in a channel filled with porous medium. National Academy Science Letters, 40(3), 211–215.
Rathod, V. P., & Parveen, S. R. (2015). MHD Couette flow and heat transfer of a dusty couple stress fluid with exponential decaying pressure gradient. International Journal of Mathematical Archive, 6(8), 152–158.
Mohanty, B., Mishra, S. R., & Pattnaik, H. B. (2015). Numerical investigation on heat and mass transfer effect of micropolar fluid over a stretching sheet. Alexandria Engineering Journal, 54(2), 223–232.
Gundagani, M., Paul, A., & Babu, N. V. N. (2015). Numerical study of chemical reaction effects on unsteady MHD fluid flow past an infinite vertical plate embedded in a porous medium with variable suction. Electronic Journal of Mathematical Analysis and Applications, 3(2), 179–192.
Eldabe, N. T., & Abouzeid, M. Y. (2022). Thermal micropolar and couple stresses effects on peristaltic flow of biviscosity nanofluid through a porous medium. Frontiers in Physics, 10, 991391.
V P Rathod and Syeda Rasheeda Parveen “Unsteady dusty couple stress fluid flow with heatransfer” Ph.d Theses (2016)
V. P Rathod and Syeda Rasheeda Parveen.“Usteady flow of a dusty magnetic conducting couple stress fluid through apipe”. INT.J.OFMATHS. SCI. &ENGG. APPLS. (IJMSEA) ISSN 0973-9424,Vol.8 , No.II PP.149-160, MARCH ,2014.