Abstract
The recent papers of Glansdorff, Prigogine and Hays have shown that a variational principle may be applied to problems in fluid flow. As examples of the use of a variational formulation, the problems of slow viscous incompressible flow between parallel plates and in a circular tube are solved for the case where the phenomenological coefficients of thermal conductivity and viscosity are functions of temperature. The method of Rayleigh-Ritz is used with the variational form to obtain solutions which are compared with solutions obtained by direct analytical techniques. Close agreement between the two methods of analysis is obtained for both Couette and Poiseuille flow, thus establishing a measure of confidence in the variational solution to problems for which direct solutions cannot be obtained.
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