LAMINAR FREE-CONVECTION INDUCED BY A LINE HEAT-SOURCE, AND HEAT-TRANSFER FROM WIRES AT SMALL GRASHOF NUMBERS

The buoyancy-induced laminar flow and temperature fields associated wi th a line source of heat in an unbounded environment are described by numerically solving the non-dimensional Boussinesq equations with the appropriate boundary conditions. The solution is given for values of t he Prandtl number, the single parameter, ranging from zero to infinity . The far-field form of the solution is well known, including a self-s imilar thermal plume above the source. The analytical description clos e to the source involves constants that must be evaluated with the num erical solution. These constants are used when calculating the free co nvection heat transfer from wires (or cylinders of non-circular shape) at small Grashof numbers. We find two regions in the how field: an in ner region, scaled with the radius of the wire, where the effects of c onvection can be neglected in first approximation, and an outer region where, also in first approximation, the flow and temperature fields a re those due to a line source of heat. The cases of large and small Pr andtl numbers are considered separately. There is good agreement betwe en the Nusselt numbers given by the asymptotic analysis and by the num erical analysis, which we carry out for a wide range of Grashof number s, extending to very small values the range of existing numerical resu lts, there is also agreement with the existing correlations of the exp erimental results. A correlation expression is proposed for the relati on between the Nusselt and Grashof numbers, based on the asymptotic fo rms of the relation for small and large Grashof numbers.