The impact of Beltrami effect on dusty fluid flow through hexagonal channel in presence of porous medium. (English) Zbl 1426.76703
Summary: This paper presents a novel solution to a two-dimensional Beltrami flow through hexagonal channel of a dusty fluid evaluation. The uniqueness of the solution is focused on characterizing the flow behavior of fluid and dust phases by considering the effect of Reynolds number and permeability of porous medium. The governing Navier-Stokes equations are transformed into dimensionless equations and solved using Laplace transform, Fourier transform and Crank-Nicolson techniques. A detailed comparison of analytical and numerical solutions are presented and results are interpreted through performance analysis graphs. Finally, the skin friction at the boundaries are calculated to understand the phase of dusty fluid in the porous medium.
MSC:
| 76T10 | Liquid-gas two-phase flows, bubbly flows |
| 76S05 | Flows in porous media; filtration; seepage |
| 76T15 | Dusty-gas two-phase flows |
Keywords:
dusty fluid; hexagonal channel; laminar flow; velocity of fluid and dust phase; Beltrami flow; porous mediaReferences:
| [1] | Saffman, P. G., On the stability of laminar flow of a dusty gas, J. Fluid Mech., 13, 1, 120-128 (1962) · Zbl 0105.39605 |
| [2] | Marble, F. E., Dynamics of a gas containing small particles, Proceeding of the Fifth AGARD Colliquium Combustion and Propulsion, 175-213 (1963), Pergamon Press: Pergamon Press Oxford |
| [3] | Myint-U, T., Partial Differential Equations of Mathematical physics (1965), American Elsevier Publications Company, 40: American Elsevier Publications Company, 40 New york |
| [4] | Hamdan, M. H.; Sawalha, K. D., Dusty gas flow through porous medium, Appl. Math.Comput., 75, 59-73 (1966) · Zbl 0851.76087 |
| [5] | Liu, J. T., Flow induced by an oscillating infinite flat plate in a dusty gas, Phys. Fluids, 9, 1716-1720 (1966) · Zbl 0147.45802 |
| [6] | Michael, D. H.; Miller, D., Plane parallel flow of a dusty gas, Mathematica, 13, 97-109 (1966) · Zbl 0148.23502 |
| [7] | S.L. Soo, The fluid dynamics of multiphase system, Blaisdell (1968).; S.L. Soo, The fluid dynamics of multiphase system, Blaisdell (1968). |
| [8] | Barron, R. M., Steady Plane Flow of a Viscous Dusty Fluid with Parallel Velocity Fields, Tensor NS, 31, 271-274 (1977) · Zbl 0351.76115 |
| [9] | Rukmangadachari, E.; Arunachalam, P. V., Dusty viscous flow through a cylinder of triangular cross-section, Proc. Indian Acad. Sci., 88, 169-179 (1979) · Zbl 0406.76077 |
| [10] | Kaur, J. P.; Singh, G. D.; Sharma, R. G., Unsteady porous channel flow of a conducting fluid with suspended particles, Def. Sci. J., 138, 13-20 (1988) |
| [11] | singh, K.; singh, K. K., Unsteady flow of adusty visco-elastic liquid through a hexagonal channel, Intl. Cal. Math. Soc., 81, 436-446 (1989) · Zbl 0687.76003 |
| [12] | Ghosh, N. C.; Ghosh, B. C.; Debnath, L., The hydromagnetic flow of a dusty visco-elastic fluid between two infinite parallel plates, Int. J. Comput. Math. Applic., 39, 103-116 (2000) · Zbl 0978.76010 |
| [13] | Ghosh, B. C.; Ghosh, N. C., MHD flow of a visco-elastic fluid through porous medium, Intl. J. Num. Methods Heat Fluid Flow, 11, 7, 682-698 (2001) · Zbl 0995.76098 |
| [14] | Labropulu, F., Generalized beltrami flows and other closed-form solutions of an unsteady viscoelastic fluid, Int. J. Med. Med. Sci., 30, 271-282 (2001) · Zbl 1016.76005 |
| [15] | Changchun, S.; Yongnian, H., Some properties of three-dimensional beltrami flows, Acta Mech. Sin., 7, 289-294 (2001) · Zbl 0753.76034 |
| [16] | Amos, E., Magnetic effect on pulsatile flow in a constricted axis symmetric tube, Indian J. Pure Appl. Math., 34, 1315-1326 (2003) · Zbl 1035.92011 |
| [17] | Bagewadi, C. S.; Gireesha, B. J., A study of two dimensional unsteady fluid flow under varying pressure gradient, Tensor,N.S., 64, 232-240 (2003) · Zbl 1165.76377 |
| [18] | sharma, P.; Varshney, C. L., Thermal dispersion effect on MHD flow of dusty gas and dusty particles through hexagonal channel, Int. J. Heat Mass Transf., 46, 2511-2514 (2003) · Zbl 1032.76702 |
| [19] | Allan, F. M.; Qatanani, N.; Barghouti, I.; Takatka, K. M., Dusty gas model of flow through naturally occurring porous media, Appl. Math. Comput., 148, 809-821 (2004) · Zbl 1049.76067 |
| [20] | Grigioni, M.; Daniele, C.; Morbiducci, U.; Gaudio, C. D.; Avenio, G. D.; Balducci, A.; Barbaro, V., A mathematical description of blood spiral flow in vessel: application to a numerical study of flow in arterial bending, J. Biomech., 38, 1375-1386 (2005) |
| [21] | Gireesha, B. J.; Madhura, K. R.; Bagewadi, C. S., Unsteady flow of a dusty fluid through porous media between annulus of two hexagonal channels, Int. J. Appl. Math. Stat., 27, 20-38 (2012) · Zbl 1348.76148 |
| [22] | Gireesha, B. J.; Bagewadi, C. S.; Vishalakshi, C. S., Beltrami flow of an unsteady dusty fluid between parallel plates in anholonomic co-ordinate system, Electron. J. Theor. Phys., 17, 181-192 (2008) · Zbl 1153.76437 |
| [23] | Jonas, P., Trkalian Flow Fields, 22-24 (2008), Institute of Thermomechanics |
| [24] | Gireesha, B. J.; Bagewadi, C. S.; Prasannakumara, B. C., Pulsatile flow of an unsteady dusty fluid through rectangular channel, Commun. Nonlinear Sci. Numer. Simul., 14, 2103-2110 (2009) · Zbl 1221.76199 |
| [25] | M. Hackert-Oschatzchen, R. Paul, M. Penzil, M. Zinecker, A. Schubert, Simulation of heat transfer on periodic microstructured surfactes for evaporation cooling, Proceedings of 2013 COMSOL Conference.; M. Hackert-Oschatzchen, R. Paul, M. Penzil, M. Zinecker, A. Schubert, Simulation of heat transfer on periodic microstructured surfactes for evaporation cooling, Proceedings of 2013 COMSOL Conference. |
| [26] | Madhura, K. R.; Swetha, D. S., Flow of an unsteady dusty fluid through hexagonal channel in presence of porous medium, Int. J. Appl. Math. Stat., 52, 107-134 (2014) · Zbl 1339.76052 |
| [27] | Asharindavida, F.; Hundewale, N.; Aljahdali, S., Study on hexagonal grid in image processing (2012), Stultan Aljahdali Taif University: Stultan Aljahdali Taif University Saudi Arabia |
| [28] | Prasannakumara, B. C.; Gireesha, B. J.; Manjunatha, P. T., Melting phenomenon in MHD stagnation point flow of dusty fluid over a stretching sheet in the presence of thermal radiation and non-uniform heat source/sink, Int. J. Comput. Methods Eng. Sci. Mech., 16, 1-18 (2015) |
| [29] | Manjunatha, P. T.; Gireesha, B. J.; Prasannakumara, B. C., Effect of radiation on flow and heat transfer of MHD dusty fluid over a stretching cylinder embedded in a porous medium in presence of heat source, Int. J. Appl. Comput. Math., 3, 293-310 (2017) · Zbl 1392.76107 |
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