Stability of buoyancy-driven convection in an Oldroyd-B fluid-saturated anisotropic porous layer

doi:10.1007/s10483-018-2329-6

Applied Mathematics and Mechanics (English Edition) ›› 2018, Vol. 39 ›› Issue (5): 653-666.doi: https://doi.org/10.1007/s10483-018-2329-6

Stability of buoyancy-driven convection in an Oldroyd-B fluid-saturated anisotropic porous layer

K. R. RAGHUNATHA, I. S. SHIVAKUMARA, SOWBHAGYA

Department of Mathematics, Bangalore University, Bangalore 560056, India

收稿日期:2017-08-29 修回日期:2017-11-17 出版日期:2018-05-01 发布日期:2018-05-01
通讯作者: I.S.SHIVAKUMARA,E-mail:shivakumarais@bub.ernet.in E-mail:shivakumarais@bub.ernet.in
基金资助:
Project supported by the Innovation in Science Pursuit for the Inspired Research (INSPIRE) Program (No. DST/INSPIRE Fellowship/[IF 150253])

Stability of buoyancy-driven convection in an Oldroyd-B fluid-saturated anisotropic porous layer

K. R. RAGHUNATHA, I. S. SHIVAKUMARA, SOWBHAGYA

Department of Mathematics, Bangalore University, Bangalore 560056, India

Received:2017-08-29 Revised:2017-11-17 Online:2018-05-01 Published:2018-05-01
Contact: I.S.SHIVAKUMARA E-mail:shivakumarais@bub.ernet.in
Supported by:
Project supported by the Innovation in Science Pursuit for the Inspired Research (INSPIRE) Program (No. DST/INSPIRE Fellowship/[IF 150253])

摘要/Abstract

摘要：

The nonlinear stability of thermal convection in a layer of an Oldroyd-B fluid-saturated Darcy porous medium with anisotropic permeability and thermal diffusivity is investigated with the perturbation method. A modified Darcy-Oldroyd model is used to describe the flow in a layer of an anisotropic porous medium. The results of the linear instability theory are delineated. The thresholds for the stationary and oscillatory convection boundaries are established, and the crossover boundary between them is demarcated by identifying a codimension-two point in the viscoelastic parameter plane. The stability of the stationary and oscillatory bifurcating solutions is analyzed by deriving the cubic Landau equations. It shows that these solutions always bifurcate supercritically. The heat transfer is estimated in terms of the Nusselt number for the stationary and oscillatory modes. The result shows that, when the ratio of the thermal to mechanical anisotropy parameters increases, the heat transfer decreases.

关键词: convection, porous medium, Oldroyd-B fluid, elliptic, singular perturbation, difference scheme, uniform convergence, cubic Landau equation

Abstract:

Key words: cubic Landau equation, Oldroyd-B fluid, elliptic, singular perturbation, difference scheme, uniform convergence, porous medium, convection

中图分类号:

K. R. RAGHUNATHA, I. S. SHIVAKUMARA, SOWBHAGYA. Stability of buoyancy-driven convection in an Oldroyd-B fluid-saturated anisotropic porous layer[J]. Applied Mathematics and Mechanics (English Edition), 2018, 39(5): 653-666.

参考文献

[1] McKibbin, R. Convection and heat transfer in layered and anisotropic porous media. ASME 2008 Heat Transfer Summer, American Society of Mechanical Engineers, New York, 327-336(1992)
[2] Nield, D. A. and Bejan, A. Convection in Porous Media, Springer, New York (2013)
[3] Storesletten, L. Effects of anisotropy on convective flow through porous media. Transport Phenomena in Porous Media, Elsevier, the Netherlands, 261-283(1998)
[4] Straughan, B. The Energy Method, Stability and Nonlinear Convection, Springer, New York (2004)
[5] Storesletten, L. Effects of anisotropy on convection in horizontal and inclined porous layers. Emerging Technologies and Techniques in Porous Media, Springer, Dordrecht, 285-306(2004)
[6] Castinel, G. and Combarnous, M. Natural convection in an anisotropic porous layer. International Journal of Chemical Engineering, 17, 605-613(1977)
[7] Epherre, J. F. Criterion for the appearance of natural convection in an anisotropic porous layer. International Journal of Chemical Engineering, 17, 615-616(1977)
[8] Capone, F., Gentile, M., and Hill, A. A. Anisotropy and symmetry in porous media convection. Acta Mechanica, 208, 205-214(2009)
[9] Kvernvold, O. and Tyvand, P. A. Nonlinear thermal convection in anisotropic porous media. Journal of Fluid Mechanics, 90, 609-624(1979)
[10] Govender, S. On the effect of anisotropy on the stability of convection in rotating porous media. Transport in Porous Media, 64, 413-422(2006)
[11] Tyvand, P. A. and Storesletten, L. Onset of convection in an anisotropic porous layer with vertical principal axes. Transport in Porous Media, 108, 581-593(2015)
[12] Malashetty, M. S. and Swamy, M. The onset of convection in a viscoelastic liquid saturated anisotropic porous layer. Transport in Porous Media, 67, 203-218(2007)
[13] Alishaev, M. G. and Mirzadjanzade, A. K. For the calculation of delay phenomenon in filtration theory. Izvestiya Vuzov Neft i Gaz, 6, 71-77(1975)
[14] Rudraiah, N. and Kaloni, P. N. Flow of non-Newtonian fluids. Encyclopedia of Fluid Mechanics, 9, 1-69(1990)
[15] Rudraiah, N., Kaloni, P. N., and Radhadevi, P. V. Oscillatory convection in a viscoelastic fluid through a porous layer heated from below. Rheologica Acta, 28, 48-53(1989)
[16] Shenoy, A. V. Non-Newtonian fluid heat transfer in porous media. Advances in Heat Transfer, 24, 101-190(1994)
[17] Kim, M. C., Lee, S. B., Kim, S., and Chung, B. J. Thermal instability of viscoelastic fluids in porous media. International Journal of Heat and Mass Transfer, 46, 5065-5072(2003)
[18] Malashetty, M. S., Shivakumara, I. S., Sridharkulkarni, and Swamy, M. Convective instability of Oldroyd-B fluid saturated porous layer heated from below using a thermal non-equilibrium model. Transport in Porous Media, 64, 123-39(2006)
[19] Shivakumara, I. S., Malashetty, M. S., and Chavaraddi, K. B. Onset of convection in a viscoelastic fluid saturated sparsely packed porous layer using a thermal non-equilibrium model. Canadian Journal of Physics, 84, 973-90(2006)
[20] Sheu, L. J., Tam, L. M., Chen, J. H., Chen, H. K., Lin, K. T., and Kang, Y. Chaotic convection of viscoelastic fluids in porous media. Chaos, Solitons and Fractals, 37, 113-124(2008)
[21] Wang, S. and Tan, W. Stability analysis of soret-driven double-diffusive convection of Maxwell fluid in a porous medium. International Journal of Heat and Fluid Flow, 32, 88-94(2011)
[22] Raghunatha, K. R., Shivakumara, I. S., and Shankar, B. M. Weakly nonlinear stability analysis of triple diffusive convection in a Maxwell fluid saturated porous layer. Applied Mathematics and Mechanics (English Edition), 39(2), 153-168(2017) https://doi.org/10.1007/s10483-018-2298-6
[23] Cao, L. M., Si, X. H., and Zheng, L. C. Convection of Maxwell fluid over stretching porous surface with heat source/sink in presence of nanoparticles:Lie group analysis. Applied Mathematics and Mechanics (English Edition), 37(4), 433-442(2016) https://doi.org/10.1007/s10483-016-2052-9
[24] Mahanthesh, B., Gireesha, B. J., Shehzad, S. A., Abbasi, F. M., and Gorla, R. S. R. Nonlinear three-dimensional stretched flow of an Oldroyd-B fluid with convective condition, thermal radiation, and mixed convection. Applied Mathematics and Mechanics (English Edition), 38(7), 969-980(2017) https://doi.org/10.1007/s10483-017-2219-6
[25] Makinde, O. D. and Eegunjobi, A. S. Entropy analysis of thermally radiating magnetohydrodynamics slip flow of Casson fluid in a microchannel filled with saturated porous media. Journal of Porous Media, 19, 799-810(2016)
[26] Makinde, O. D. and Rundora, L. Unsteady mixed convection flow of a reactive Casson fluid in a permeable wall channel filled with a porous medium. Defect and Diffusion Forum, 377, 166-179(2017)
[27] Malkus, W. V. R. and Veronis, G. Finite amplitude cellular convection. Journal of Fluid Mechanics, 4, 225-260(1985)
[28] Venezian, G. Effect of modulation on the onset of thermal convection. Journal of Fluid Mechanics, 35, 243-254(1969)
[29] Gupta, V. P. and Joseph, D. D. Bounds for heat transport in a porous layer. Journal of Fluid Mechanics, 57, 491-514(1973)

Stability of buoyancy-driven convection in an Oldroyd-B fluid-saturated anisotropic porous layer

Stability of buoyancy-driven convection in an Oldroyd-B fluid-saturated anisotropic porous layer

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