Local Thermal Non-equilibrium Convection in a Porous Medium with a Jeffreys Heat Flux in the Solid

• Brian Straughan ^[1]
  1. [1] Durham University

     Durham University

     Reino Unido

     
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 25, Nº 5, 2026
• Idioma: inglés
• Enlaces
  • Texto completo
• Resumen

  • We develop and analyse a theory for thermal convection in a Darcy porous material taking into account the concept of local thermal non-equilibrium whereby the temperature in the solid skeleton may be different from that in the saturating fluid. The thermal microstructure of the solid skeleton is such that we adopt a Jeffreys theory for heat conduction in this part of the continuous medium. The Jeffreys theory in the solid has a mathematical form analogous to that proposed by Sir Harold Jeffreys, F.R.S., for a fluid, although now rather than being a relation between stress and the symmetric part of the velocity gradient as in the original case, the relation is between the heat flux and the temperature gradient. A novel effect is that oscillatory convection requires the Maxwell coefficient to exceed the Jeffreys coefficient, while the precise stationary–oscillatory transition depends separately on both coefficients and on the strength of thermal interaction between the solid and fluid phases.

• Referencias bibliográficas
  • 1. Bhatti, M.M., Anwar Bég, O., Ellahi, R., Abbas, T.: Natural convection non-Newtonian EMHD dissipative flow through a microchannel containing...
  • 2. Zhang, L., Bhatti, M.M., Michaelides, E.E., Ellahi, R.: Characterizing quadratic convection and electromagnetically induced flow of couple...
  • 3. Bhatti, M.M., Marin, M., Ellahi, R.: Effects of quadratic convection and nonlinear heat generation/absorption on granular material flow...
  • 4. Barletta, A.: Routes to Absolute Instability in Porous Media. Springer, New York (2019)
  • 5. Bidin, B., Rees, D.A.S.: Pattern selection for Darcy-Bénard convection with local thermal nonequilibrium. Int. J. Heat Mass Transfer 153,...
  • 6. Combarnous,M.: Description du transfert de chaleur per convection naturelle dans une couche poreuse horizontal á l’aide d’un coefficient...
  • 7. Banu, N., Rees, D.A.S.: Onset of Darcy-Bénard convection using a thermal non-equilibrium model. Int. J. Heat Mass Transfer 45, 2221–2228...
  • 8. Rees, D.A.S., Bassom, A.P., Siddheshwar, P.G.: Local thermal non-equilibrium effects arising from the injection of a hot fluid into a porous...
  • 9. Rees, D.A.S.: Microscopic modelling of the two - temperature model for conduction in heterogeneous three - dimensional media. In: Proc....
  • 10. Rees, D.A.S.: Microscopic modelling of the two-temperature model for conduction in heterogeneous media. J. Porous Media 13, 125–143 (2010)
  • 11. Rees, D.A.S.: The effect of local thermal nonequilibrium on the stability of convection in a vertical porous channel. Trans. Porous Media...
  • 12. Gossler, M.A., Bayer, P., Zosseder, K.: Experimental investigation of thermal retardation and local thermal non-equilibrium effects on...
  • 13. Baek, J.Y., Park, B.H., Rau, G.C., Lee, K.K.: Experimental evidence for local thermal non-equilibrium during heat transport in sand representative...
  • 14. Okasha, M.M., Abbas, M., Formanova, S., Faiz, Z., Ali, A.H., Akgül, A., Mahariq, I., Galal, A.M.: Local thermal non-equilibrium effects...
  • 15. Hasnain,M., Sezer, H., Mason, J.H.: Mathematical modelling of heat andmass transfer inmetal hydride hydrogen storage systems: a comprehensive...
  • 16. Mahfoudh, I., Principi, P., Fioretti, R., Safi, M.: Experimental studies on the effect of using phase change materials in a salinity -...
  • 17. Zhang, W., Yi, Y., Bai, X., Nakayama, A.: A local thermal non-equilibrium analysis for convective and radiative heat transfer in gaseous...
  • 18. Revil, A., Finizola, A., Johnson, T., Ricci, T., Grese, M., Delcher, E., Barde-Cabusson, S., Duvillard, P.A., Ripepe,M.: The thermal plumbing...
  • 19. Arnone, G., Capone, F., Gianfrani, J.A.: Stability of penetrative convection currents in local thermal non-equilibrium. Proc. Roy. Soc....
  • 20. Capone, F., Gentile, M.,Gianfrani, J.A.: Optimal stability thresholds in rotating fully anisotropic porous medium with LTNE. Transp. Porous...
  • 21. Celli, M., Barletta, A., Rees, D.A.S.: Local thermal non-equilibrium analysis of the instability in a vertical porous slab with permeable...
  • 22. Freitas, R.B., Brandão, P.V., Alves, C.S.D.B., Celli, M., Barletta, A.: The effect of local thermal nonequilibrium on the onset of thermal...
  • 23. Pulvirenti, B., Celli, M., Barletta, A.: Flows and convection in metal foams: a survey and new CFD results. Fluids 5, 155 (2020)
  • 24. Saravanan, S., Brindha, D.: Onset of centrifugal convection: departure from thermal equilibrium. Proc. Roy. Soc. London A 469, 20120655...
  • 25. Saravanan, S., Brinda, R.K.: Thermal equilibrium porous convection in a heat generating medium. Int. J. Mech. Sci. 135, 133–145 (2018)
  • 26. Saravanan, S., Meenasaranya, M.: Unconditional stability of an externally controlled medium with thermodynamic non-equilibrium porous....
  • 27. Giovine, P., Mariano, P.M., Mugnaioni, F.: Acceleration waves in thermoelastic complex media with temperature-dependent phase fields....
  • 28. Xu, J., Shao,Y., Feng, X., Zhang, X., Li, H.,Yang, J.,Gao, F.: Lowsintering shrinkage porous ceramics: principles, progress and perspectives....
  • 29. Bisconti, L., Mariano, P.M.: Microstructure-induced finite-speed heat propagation in fluids through porous media: analytical results....
  • 30. Mariano, P.M.: Finite-speed heat propagation as a consequence ofmicrostructural changes. Continuum Mech. Thermodyn. 29, 1241–1248 (2017)
  • 31. Fedorov, A.S., Teplinskaia, A.S.: Thermal properties of porous silicon nanomaterials.Materials (Basel) 15, 8678 (2022)
  • 32. Nar, S.,Kusiak, A., Mareus, R., Stolz, A., Machon, D., Caillard, A., Battaglia, J.L., Boucherif, A., Semmar, N.: Investigation of mesoporous...
  • 33. Joseph, D.D., Preziosi, L.: Heat waves. Rev. Modern Phys. 61, 41–73 (1989)
  • 34. Shomali, Z., Kovács, R., Ván, P., Kudinov, I.V., Ghazanfarian, J.: Lagging heat models in thermodynamics and bioheat transfer: a critical...
  • 35. Kovács, R.: Heat equations beyond Fourier: from heat waves to thermal metamaterials. Phys. Rep. 1048, 1–75 (2024)
  • 36. Giorgi, C., Morro, A., Zullo, F.: Modeling of heat conduction through rate equations. Meccanica 59, 1757–1776 (2024)
  • 37. Giorgi, C., Zullo, F.: Nonlinear and nonlocal models of heat conduction in continuum thermodynamics. Continuum Mech. Thermodyn. 38, 15...
  • 38. Jeffreys, H.: The Earth: Its Origin, History and Physical Constitution, 2nd edn. Cambridge University Press, Cambridge (1929)
  • 39. Tzou, D.Y.: The generalized lagging response in small-scale and high-rate heating. Int. J. Heat Mass Transfer 38, 3231–3240 (1995)
  • 40. Awad, E.: Dual-phase-lag in the balance: sufficiency bounds for the class of Jeffreys’ equations to furnish physical solutions. Int. J....
  • 41. Awad, E., Sandev, T.,Metzler, R., Chechkin, A.: From continuous-time random walks to the fractional Jeffreys equation: solution and applications....
  • 42. Kovács, R.: Interplay of time scales and material nonlinearities in non-Fourier heat conduction. Continuum Mech. Thermodyn. 38, 46 (2026)
  • 43. Chandrasekhar, S.: Hydrodynamic and Hydromagnetic Stability. Dover, New York (1981)
  • 44. Straughan, B.: Stability, andWave Motion in Porous Media. Appl.Math. Sci., vol. 165. Springer, New York (2008)
  • 45. Straughan, B.: Convection with Local Thermal Non-equilibrium and Microfluidic Effects. Advances in Mechanics and Mathematics Series, vol....
  • 46. Jeffreys, H.: The viscosity of the earth. Mon. Not. R. Astron. Soc. 77, 449–456 (1917)
  • 47. Oskolkov, A.P.: Initial - boundary value problems for the equations ofKelvin -Voigt fluids and Oldroyd fluids. Proc. Steklov Inst. Math....
  • 48. Straughan, B.: Oskolkov equations and thermal convection. Adv. Continuum Mech., vol. 56. Birkhäuser, Cham, Switzerland (2026)
  • 49. Straughan, B.: Global nonlinear stability in porous convection with a thermal non-equilibrium model. Proc. Roy. Soc. London A 462, 409–418...