The convection of cold water in the vicinity of its density maximum in a rectangular enclosure is studied in the limit of small Rayleigh number. Results for the stream function (to lowest order) and the first corrections (for convective effects) to the temperature field and heat transfer are obtained. Results are discussed in the context of a single parameter, which fixes the orientation of the wall temperatures with respect to the extremum temperature. The effects of changing the enclosure aspect ratio are also discussed.
Many analytical methods use radial and rectangular systems to interpret unsteady‐state reservoir flow problems. However, there is no information currently available for irregularly shaped aquifers. For many practical cases the aquifer drainage shape is too complicated to be approximated by a circular or rectangular shape. This paper develops an image‐well method for predicting drawdown transient in an aquifer with irregularly shaped boundaries. Previously, the use of the image‐well method to predict drawdown transient was only possible for aquifer boundaries of regular shape.
In this paper, the well function is obtained by superposing the Theis solution of image wells in time. The image‐well method is first applied to regularly shaped aquifers. The validity of the approach is then proved by comparison of the calculated well functions with literature values for various regular drainage shapes. The proven method was applied to interpret a field pumping test and to characterize the reservoir boundaries with irregular shape.
Steady natural convection of water near the density extremum in a vertical annulus is studied numerically. Results for flow in annuli with aspect ratio 1≤A≤8 and varying degrees of curvature are given for 103≤Ra≤105. It is shown that both the density distribution parameter R and the annulus curvature K have a strong effect on the steady flow structure and heat transfer in the annulus. A closed-form solution for the vertical flow in a very tall annulus is compared with numerical results for finite-aspect-ratio annuli.
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