Geometric Approach to Laminar Convection

摘要

The formal analogy with continuum solid mechanics allows one to develop a semiqualitative theory of laminar convection in tubes of arbitrary cross section, which might be useful in some cases (for instance, in microfluidics). In particular, for a fluid of constant shear viscosity driven by a fixed pressure gradient, the heat transfer rate per unit length across the wall can be expressed in terms of a purely geometric parameter, that is, the torsional rigidity of the tube cross section. As a consequence, the heat transfer rate can be calculated in terms of overall quantities without requiring pointwise solution of the Hagen-Poiseuille problem. Furthermore, a number of mathematical theorems concerning torsional rigidity can be applied straightforward to the heat transfer problem, resulting into the definition of upper or lower bounds for the heat transfer rate through the tube wall.