Outlook of Density Maximum on the Onset of Forchheimer-Bénard Convection with throughflow

Jump To References Section

Authors

  • Sowbhagya .
     Department of Mathematics, Dr. Ambedkar Institute of Technology, Bengaluru ,IN

DOI:

https://doi.org/10.18311/jmmf/2022/32007

Keywords:

Convection, Maximum Density, Porous Medium, Vertical Throughflow, Galerkin Technique.

Abstract

The vertical throughflow effect is investigated on the onset of porous convection by considering a cubic density-temperature relationship and using the Forchheimer-Darcy model. The stability eigenvalue problem is explained numerically using the Galerkin technique. Contrary to the linear density-temperature relationship, the direction of throughflow alters the onset of convection. The throughflow dependent Péclet number is found to stabilize the fluid motion against convection and the upflow is found to be either stabilizing or destabilizing than the downflow depending on the values of thermal condition parameters λ1 and λ2. A destabilizing effect on the onset is observed with increasing λ1 and λ2. The Darcy number Da and the Forchheimer drag co-efficient, cb instability characteristics have been investigated and depicted graphically.

Downloads

Download data is not yet available.

Metrics

Metrics Loading ...

Downloads

Published

2022-12-08

How to Cite

., S. (2022). Outlook of Density Maximum on the Onset of Forchheimer-Bénard Convection with throughflow. Journal of Mines, Metals and Fuels, 70(8A), 32–40. https://doi.org/10.18311/jmmf/2022/32007

Issue

Volume 70, Issue 8A, August 2022

Section

Articles

License

Creative Commons License

This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.

Crossref
Scopus
Google Scholar
Europe PMC

 

References

Barletta, A., Rossi di Schio, E., & Storesletten, L. Convective roll instabilities of vertical throughflow with viscous dissipation in a horizontal porous layer. Transport in porous media, 81(3); 2010:461-477. DOI: https://doi.org/10.1007/s11242-009-9417-y

Brevdo, L., & Ruderman, M. S. On the convection in a porous medium with inclined temperature gradient and vertical throughflow. Part I.Normal modes. Transport in porous media, 80(1); 2009:137-151. DOI: https://doi.org/10.1007/s11242-009-9348-7

Homsy, G. M., & Sherwood, A. E. Convective instabilities in porous media with through flow. AIChE Journal, 22(1); 1976:168-174. DOI: https://doi.org/10.1002/aic.690220121

Horton, C. W., & Rogers Jr, F. T. Convection currents in a porous medium. Journal of Applied Physics, 16(6); 1945:367-370. DOI: https://doi.org/10.1063/1.1707601

Jones, M. C., & Persichetti, J. M. Convective instability in packed beds with throughflow. AIChE journal, 32(9); 1986: 1555-1557. DOI: https://doi.org/10.1002/aic.690320916

Khalili, A., & Shivakumara, I. S. Onset of convection in a porous layer with net through-flow and internal heat generation. Physics of Fluids, 10(1);1998:315-317. DOI: https://doi.org/10.1063/1.869540

Khalili, A., & Shivakumara, I. S. Non-Darcian effects on the onset of convection in a porous layer with throughflow. Transport in porous media, 53(3); 2003: 245-263. DOI: https://doi.org/10.1023/A:1025028508887

Lapwood, E. R.Convection of a fluid in a porous medium. In Mathematical Proceedings of the Cambridge Philosophical Society, 44(4); 1948: 508-521. DOI: https://doi.org/10.1017/S030500410002452X

Moore, D. R. & Weiss, N. O. 1973 J. Fluid Mech. 58, 289. DOI: https://doi.org/10.1017/S0022112073002600

Nield, D. A., & Bejan, A. Forced convection. In Convection in porous media, 2017:85-160. DOI: https://doi.org/10.1007/978-3-319-49562-0_4

Nield,D. A., Convective instability in porous media with throughflow. AIChE journal, 33(7); 1987:1222-1224. DOI: https://doi.org/10.1002/aic.690330719

Nield, D. A., & Joseph, D. D. Effects of quadratic drag on convection in a saturated porous medium. The Physics of fluids, 28(3); 1985: 995-997. DOI: https://doi.org/10.1063/1.865071

Nield, D. A., & Simmons, C. T. (2018). A Brief Introduction to Convection in Porous Media. Transport in Porous Media. doi:10.1007/s11242-018-1163-6 DOI: https://doi.org/10.1007/s11242-018-1163-6

Shivakumara, I. S., & Sureshkumar, S. Convective instabilities in a viscoelastic-fluid- saturated porous medium with throughflow. Journal of Geophysics and Engineering, 4(1); 2007:104-115. DOI: https://doi.org/10.1088/1742-2132/4/1/012

Straughan, B. The energy method, stability, and nonlinear convection (Vol. 91). Springer Science & Business Media. 2013.

Straughan, B. Resonant penetrative convection with an internal heat source/sink. Acta Applicandae Mathematicae, 132(1); 2014:561-581. DOI: https://doi.org/10.1007/s10440-014-9930-z

Straughan, B. Stability and wave motion in porous media, 165; 2008:1-45. DOI: https://doi.org/10.1007/978-0-387-76543-3_4

Straughan, B. Convection with local thermal non-equilibrium and microfluidic effects, 32; 2015:87-93. DOI: https://doi.org/10.1007/978-3-319-13530-4_5

Sutton, F. M. Onset of convection in a porous channel with net through flow. The Physics of Fluids, 13(8); 1970:1931-1934. DOI: https://doi.org/10.1063/1.1693188

Sowbhagya , Effects of quadratic drag and throughflow on the onset of Darcy-BPnard convection in a porous layer using a thermal nonequilibrium model, International journal of Advances in Science, Engineering and Technilogy, 6,2; 2018:(Spl Iss-2)

Raghunatha, K. R., Shivakumara, I. S., & Sowbhagya. Stability of buoyancy-driven convection in an Oldroyd-B fluid-saturated anisotropic porous layer. Applied Mathematics and Mechanics, 39(5); 2018:653–666. DOI: https://doi.org/10.1007/s10483-018-2329-6

N. H. Saeid; I. Pop (2004). Maximum density effects on natural convection from a discrete heater in a cavity filled with a porous medium., 171(3-4), 203–212. doi:10.1007/ s00707-004-0142 DOI: https://doi.org/10.1007/s00707-004-0142-x

Wu, R. S., Cheng, K. C., & Craggs, A. Convective instability in porous media with maximum density and throughflow effects by finite-difference and finite-element methods. Numerical Heat Transfer, Part A: Applications, 2(3); 1979: 303-318. DOI: https://doi.org/10.1080/10407787908913415

Yen, Y.C. (1984) Temperature structure and interface morphology in melting ice-water system. In Frontiers in Hydrology. Water Resources Publications, p. 305-325. DOI: https://doi.org/10.1111/j.1752-1688.1984.tb04698.x

Zhao, C., Hobbs, B. E., & Mühlhaus, H. B.Theoretical and numerical analyses of convective instability in porous media with upward throughflow. International Journal for Numerical and Analytical Methods in Geomechanics, 23(7); 1999: 629- 646. DOI: https://doi.org/10.1002/(SICI)1096-9853(199906)23:7<629::AID-NAG986>3.0.CO;2-K

Capone F, De Luca R, Gentile M. Instability of Vertical Throughflows in Porous Media under the Action of a Magnetic Field. Fluids. 2019; 4(4):191. DOI: https://doi.org/10.3390/fluids4040191