Unsteady Natural Convection Flow in a Square Cavity Filled with a Porous Medium Due to Impulsive Change in Wall Temperature

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 toT h (T h > T 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.Keywords Unsteady natural convection · Square cavity · Porous medium · Sudden change in wall temperature Nomenclatures 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 (m 2 ) k Thermal conductivity (W m −1 K −1 ) L Height/length of the cavity (m) Nu Local Nusselt number Nu Average Nusselt number Ra Rayleigh number t Time (s)

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Thermal non-equilibrium model subjected to thermal radiation impact and dust particles suspension in a porous square cavity

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