Stability and Nusselt number scaling for inclined differentially heated cavity flow

Williamson, N.;Armfield, S.W.;Lin, Wenxian;Kirkpatrick, M.P.

Abstract

The flow within inclined differentially side heated square cavities is investigated with two-dimensional numerical simulations. The cavity is inclined such that the heated wall is below the cooled wall. The angle of inclination is varied from theta=0°, which produces the standard differentially heated cavity flow, up to 90° where Rayleigh Bernard flow exists. The variation in flow structure, flow stability and heat transfer is presented with angle of inclination and the Rayleigh number. Results have been obtained over Ra=10⁴ – 10⁸ with Pr=7. It is shown that when the cavity is inclined the flow structure is changed with attached jet/plumes forming adjacent to the adiabatic walls, rather than diffuse intrusions as for the non-inclined side heated cavity. At a specific angle of inclination, the flow undergoes a bifurcation so that the fully developed flow is unsteady and single mode, with a further increase in inclination leading to multimodal flow. The critical transition angle is shown to vary inversely with the Rayleigh number. A scaling relationship for the Nusselt number is proposed which approximates the effect of cavity inclination on total heat transfer.

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International Journal of Heat and Mass Transfer

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1879-2189

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Elsevier

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DOI

10.1016/j.ijheatmasstransfer.2016.02.053