The leading edge effect in a suddenly differentially heated cavity

Abstract

We perform a two dimensional numerical simulation of transient natural convection in a suddenly differentially heated cavity in order to observe the initial transient flows, particularly the leading edge effect. The numerical results show that the pressure plays a key role in the origination and propagation of the leading edge effect and the deviation of the numerical solution from the theoretical solution is due to the neglect of the convection terms in the theoretical solution of the energy equation. Accordingly, the one dimensional conduction solution does not estimate the transport coefficients. References Mahajan, R. L. and Gebhart, B., Leading edge effects in transient natural convection flow adjacent to a vertical surface, J. Heat Transfer, 100, 731--733, 1978. Patterson, J. C., Graham, T., Schˆpf, W. and Armfield, S. W., Boundary layer development on a semi-infinite suddenly heated vertical plate, J. Fluid Mech., 453, 39--55, 2002. doi:10.1017/S0022112001006553 Patterson, J. C. and Imberger, J., Unsteady natural convection in a rectangular cavity, J. Fluid Mech., 100, 65--86, 1980. doi:10.1017/S0022112080001012 Xu, F., Patterson, J. C. and Lei, C., Oscillations of the Horizontal Intrusion in a Side-heated Cavity, 15th Australasian Fluid Mechanics Conference, Sydney, 779--782, 2004. Xu, F., Patterson, J. C. and Lei, C., Shadowgraph observations of the transition of the thermal boundary layer in a side-heated cavity, Exp. Fluids, 38, 770--779, 2005. doi:10.1007/s00348-005-0960-1 Armfield, S. W. and Patterson, J. C., Wave properties of natural-convection boundary layers, J. Fluid Mech., 239, 195--211, 1992. doi:10.1017/S0022112092004373 Armfield, S. W. and Patterson, J. C., Start-up flow on a vertical semi-infinite heated plate, Proc. 7th Australasian Heat and Mass Transfer, Townsville, 37--43, 2000. Gebhart, B., Transient response and disturbance growth in vertical buoyancy-driven flows, J. Heat Transfer, 110, 1166--1174, 1988. Goldstein, R. J. and Briggs, D. G., Transient free convection about vertical plates and cylinders, J. Heat Transfer, 86, 490--500, 1964.