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EFFECT OF NONUNIFORM TEMPERATURE GRADIENTS ON THERMOGRAVITATIONAL CONVECTION IN A POROUS LAYER USING A THERMAL NONEQUILIBRIUM MODEL

卷 14, 册 8, 2011, pp. 659-669
DOI: 10.1615/JPorMedia.v14.i8.10
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Jinho Lee
School of Mechanical Engineering, Yonsei University, Seoul 120-749, Korea
I. S. Shivakumara
Department of Mathematics, Bangalore University, Bangalore-560 056, India
A. L. Mamatha
Department of Mathematics, UGC-Center for Advanced Studies in Fluid Mechanics, BangaloreUniversity, Bangalore 560001, India

摘要

The effect of various forms of nonuniform basic temperature gradients on the onset of convection in a Newtonian fluid-saturated isotropic porous layer is investigated when the fluid and solid phases are not in local thermal equilibrium. A two-field model that represents the fluid and solid phase temperature fields separately is used for energy equation and the Forchheimer-extended Darcy model is used to describe the flow. The eigen value problem is solved numerically using the Galerkin technique. Comparisons are also made of the critical stability parameters between the present results and published ones for the linear basic temperature profile case, and the agreement is found to be good. The possibility of delaying or hastening the on set of convection by the basic state temperature gradients along with the influence of parameters representing the local thermal non-equilibrium effect is analyzed in detail. When compared with the nonuniform temperature gradients, it is found that the linear temperature profile indicates a reinforcement of stability. In addition, the role of thermal depth on the critical conditions is assessed in the case of piecewise linear temperature profiles.

键词: convection, nonuniform temperature gradient, porous medium, thermal nonequilibrium model
对本文的引用

  1. Shivakumara I. S., Lee Jinho, Ravisha M., Gangadhara Reddy R., The effects of local thermal nonequilibrium and MFD viscosity on the onset of Brinkman ferroconvection, Meccanica, 47, 6, 2012. Crossref

  2. Scott Nicola L., Straughan B., A Nonlinear Stability Analysis of Convection in a Porous Vertical Channel Including Local Thermal Nonequilibrium, Journal of Mathematical Fluid Mechanics, 15, 1, 2013. Crossref

  3. Haddad S. A. M., Straughan B., Porous convection and thermal oscillations, Ricerche di Matematica, 61, 2, 2012. Crossref

  4. Saravanan S., Brindha D., Onset of centrifugal filtration convection: departure from thermal equilibrium, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 469, 2154, 2013. Crossref

  5. Shivakumara I.S., Ravisha M., Ng Chiu-On, Varun V.L., A thermal non-equilibrium model with Cattaneo effect for convection in a Brinkman porous layer, International Journal of Non-Linear Mechanics, 71, 2015. Crossref

  6. Siddheshwar P. G., Siddabasappa C., Linear and Weakly Nonlinear Stability Analyses of Two-Dimensional, Steady Brinkman–Bénard Convection Using Local Thermal Non-equilibrium Model, Transport in Porous Media, 120, 3, 2017. Crossref

  7. Shivakumara I.S., Lee Jinho, Ravisha M., Gangadhara Reddy R., Effects of MFD viscosity and LTNE on the onset of ferromagnetic convection in a porous medium, International Journal of Heat and Mass Transfer, 54, 11-12, 2011. Crossref

  8. Dayananda R. N., Shivakumara I. S., Impact of Thermal Non-equilibrium on Weak Nonlinear Rotating Porous Convection, Transport in Porous Media, 130, 3, 2019. Crossref

  9. Shivakumara I. S., Lee Jinho, Mamatha A. L., Ravisha M., Boundary and thermal non-equilibrium effects on convective instability in an anisotropic porous layer, Journal of Mechanical Science and Technology, 25, 4, 2011. Crossref

  10. Hema M., Shivakumara I.S., Impact of Cattaneo law of heat conduction on an anisotropic Darcy-Bénard convection with a local thermal nonequilibrium model, Thermal Science and Engineering Progress, 19, 2020. Crossref

  11. Shivakumara I.S., Shankar B.M., Kumar S.B. Naveen, On the stability of thermosolutal rotating porous convection subject to a lack of thermal equilibrium, International Communications in Heat and Mass Transfer, 133, 2022. Crossref

  12. Aouf Zakaria, Seladji Chakib, Thermosolutal Convection in a Porous Medium Cavity Subjected to Heat and Mass Flux: A Discrete Fracture Effect, Acta Universitatis Sapientiae, Electrical and Mechanical Engineering, 12, 1, 2020. Crossref

  13. Nield Donald A., Bejan Adrian, Internal Natural Convection: Heating from Below, in Convection in Porous Media, 2017. Crossref

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