ANALYTICAL AND EXPERIMENTAL STUDY OF THE TRANSIENT LAMINAR NATURAL CONVECTION FLOWS IN PARTIALLY FILLED LIQUID CONTAINERS

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Abstract
An analytical and experimental study is reported of the two-dimensional transient laminar natural convection in a partially filled liquid container. The container walls are subjected to arbitrary time and space dependent temperature variation. The two-dimensional cylindrical momentum and continuity equations are transformed to the vorticity equation and an equation relating the stream function and vorticity. These equations together With the energy equation were solved numerically. An explicit finite-difference technique is developed for this purpose. A method of stability analysis suitable for partial differential equations with variable coefficients is also presented. The calculated temperature transients and the calculated Nusselt number are in good agreement with the experimental results.

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