Natural convection in a square porous cavity with an oscillating wall temperature

Abstract EN

A numerical study of the two-dimensional unsteady natural convection flow in a square cavity filled with a porous medium and with sidewall heating is presented in this paper.

The Darcy model is used and the fluid is assumed to be a standard Boussinesq fluid.

The temperature of the hot sidewall oscillates in time about a constant value while the cold wall is held at a constant temperature; the horizontal walls are adiabatic.

The results are presented to demonstrate the temporal variation of the streamlines, the isotherms and the Nusselt number.

When the hot wall temperature oscillates with high amplitude and frequency, it is found that the Nusselt number becomes negative over part of the period for Rayleigh number 103.

Negative values of Nusselt number were found because there will be no enough time to transfer the heat from the hot wall to the cold wall.

A resonance phenomenon is observed when the heating frequency coincides with the frequency of the “flow wheel” circulating within the cavity.

The peak value of the average Nusselt number is observed to occur at the resonance nondimensional frequency of 450 in the range considered (1–2000) for Rayleigh number 103.