Lin, Wenxian, and Armfield, SW (2005) Scaling laws for unsteady natural convection cooling of fluid with Prandtl number less than one in a vertical cylinder. Physical Review E (Statistical, Nonlinear, and Soft Matter Physics), 72 (1). 016306.

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Abstract

The flow behavior associated with cooling an initially quiescent isothermal Newtonian fluid with the Prandtl number (Pr) less than one in a vertical cylinder by unsteady natural convection with an imposed lower temperature on vertical sidewalls is investigated by scaling analysis and direct numerical simulation. The flow is dominated by three distinct stages of development, i.e., the boundary-layer development stage adjacent to the sidewall, the stratification stage, and the cooling-down stage, respectively. The first stage can be further divided into three distinct sub-stages, i.e., the start-up stage, the transitional stage, and the boundary-layer steady-state stage, respectively. A scaling analysis is carried out to obtain scaling laws for the basic flow features in terms of the flow control parameters, i.e. the Rayleigh number Ra, Pr, and the aspect ratio of the cylinder A, respectively. A series of direct numerical simulation with selected values of A, Ra, and Pr in the ranges of 1/3<= A<= 3, 10^6 <= Ra <= 10^{10}, and 0.01 <= Pr <= 0.5 are carried out, and it is found that the numerical results agree well with the scaling laws. These numerical results are further used to quantify these scaling laws for Ra, A and Pr in the above mentioned ranges.

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