Abstract
Unsteady natural convection flow in a two-dimensional square cavity filled with a porous material has been studied. The flow is initially steady where the left-hand vertical wall has temperature T h and the right-hand vertical wall is maintained at temperature T c (T h > T c) and the horizontal walls are insulated. At time t > 0, the left-hand vertical wall temperature is suddenly raised to \({{\bar{T}}_{\rm h}\,({\bar{T}}_{\rm h} > T_{\rm h})}\) which introduces unsteadiness in the flow field. The partial differential equations governing the unsteady natural convection flow have been solved numerically using a finite control volume method. The computation has been carried out until the final steady state is reached. It is found that the average Nusselt number attains a minimum during the transient period and that the time required to reach the final steady state is longer for low Rayleigh number and shorter for high Rayleigh number.
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Abbreviations
- c p :
-
Specific heat at constant pressure (J kg−1 K−1)
- g :
-
Acceleration due to gravity (m s−2)
- K :
-
Permeability of the porous medium (m2)
- k :
-
Thermal conductivity (W m−1 K−1)
- L :
-
Height/length of the cavity (m)
- Nu :
-
Local Nusselt number
- \({\overline{Nu}}\) :
-
Average Nusselt number
- Ra :
-
Rayleigh number
- t :
-
Time (s)
- t * :
-
Dimensionless time
- T :
-
Fluid temperature (K)
- T h :
-
Temperature of the left-hand vertical wall at t = 0 (K)
- \({\bar{T}_{\rm h}}\) :
-
Temperature of the left-hand vertical wall at t > 0 (K)
- T c :
-
Temperature of the right-hand vertical wall at t≥ 0 (K)
- T 0 :
-
Average temperature at t = 0 (K)
- u, v:
-
Velocity components along x and y directions, respectively (m s−1)
- U, V:
-
Dimensionless velocity components along x and y directions, respectively
- x, y:
-
Cartesian coordinates (m)
- X, Y:
-
Dimensionless Cartesian coordinates
- α e :
-
Effective thermal diffusivity (m2 s−1)
- β :
-
Coefficient of thermal expansion (K−1)
- \({\epsilon}\) :
-
Dimensionless constant
- θ :
-
Dimensionless temperature
- υ :
-
Kinematic viscosity (m2 s−1)
- ρf, ρm:
-
Density of the fluid and porous medium, respectively (kg m−3)
- σ :
-
Ratio of composite material heat capacity to convective fluid heat capacity
- ψ :
-
Dimensionless stream function
- ψ * :
-
Stream function (m2 s−1)
- f:
-
Fluid
- i:
-
Initial condition
- m:
-
Porous medium
References
Aldabbagh L.B.Y., Manesh H.F., Mohamad A.A.: Unsteady natural convection inside a porous enclosure heated from the side. J. Porous Media. 11, 73–83 (2007)
Banu, N., Rees, D.A., Pop, I.: Steady and unsteady free convection in porous cavities with internal heat generation. In: Heat Transfer 1998, Proceedings of 11th IHTC, vol. 4, pp. 375–380, Kyongju (1998)
Baytas A.C., Pop I.: Free convection in a square porous cavity using a thermal nonequilibrium model. Int. J. Therm. Sci. 41, 861–870 (2002)
Bejan A.: On the boundary layer regime in a vertical enclosure filled with a porous medium. Lett. Heat Mass Transf. 6, 93–102 (1979)
Bejan, A., Kraus, A.D. (eds.): Heat Transfer Handbook. Wiley, New York (2003)
Gross, R.J., Bear, M.R., Hickox, C.E.: The application of flux-corrected transport (FCT) on high Rayleigh number natural convection in a porous medium. In: Proceedings of the 8th International Heat Transfer Conference, San Francisco (1986)
Ingham, D.B., Pop, I. (eds): Transport Phenomena in Porous Media, vol III. Pergamon, Oxford (2005)
Khashan S.A., Al-Amiri A.M., Pop I.: Numerical simulation of natural convection heat transfer in a porous cavity heated from below using a non-Darcian and thermal non-equilibrium model. Int. J. Heat Mass Transf. 49, 1039–1049 (2006)
Kumar B.V.R., Singh P., Murthy P.V.S.N.: Effect of surface undulations on natural convection in a porous square cavity. ASME J. Heat Transf. 119, 848–851 (1997)
Manole, D.M., Lage, J.L.: Numerical benchmark results for natural convection in a porous medium cavity. In: HTD—vol. 216, Heat and Mass Transfer in Porous Media, ASME Conference, pp. 55–60 (1992)
Misirlioglu A., Baytas A.C., Pop I.: Free convection in a wavy cavity filled with a porous medium. Int. J. Heat Mass Transf. 48, 1840–1850 (2005)
Nield D.A., Bejan A.: Convection in Porous Media, 3rd edn. Springer, New York (2006)
Patankar S.V.: Numerical Heat Transfer and Fluid Flow. Hemisphere Publishing Corporation, Washington (1980)
Prasad V., Kulacki F.A.: Convective heat transfer in a rectangular porous cavity—effect of aspect ratio on flow structure and heat transfer. ASME J. Heat Transf. 106, 158–165 (1984)
Pop I., Ingham D.B.: Convective Heat Transfer, Mathematical and Computational Modelling of Viscous Fluids and Porous Media. Pergamon Press, Oxford (2001)
Saeid N.H.: Natural convection in porous cavity with sinusoidal bottom wall temperature variation. Int. Commun. Heat Mass Transf. 32, 454–463 (2005)
Saeid N.H., Pop I.: Transient free convection in a porous cavity filled with a porous medium. Int. J. Heat Mass Transf. 47, 1917–1924 (2004)
Vafai, K. (eds): Handbook of Porous Media, 2nd edn. Taylor and Francis, Boca Raton (2005)
Walker, K.L., Homsy, G.M.: Convection in a porous cavity. J. Fluid Mech. 87, 449–474 (1978)
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Kumari, M., Nath, G. Unsteady Natural Convection Flow in a Square Cavity Filled with a Porous Medium Due to Impulsive Change in Wall Temperature. Transp Porous Med 77, 463–474 (2009). https://doi.org/10.1007/s11242-008-9285-x
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DOI: https://doi.org/10.1007/s11242-008-9285-x