A Variational Principle for Transport Phenomena : II Applications to Several Problems

Abstract

The variational principle formulated in the previous paper was applied to several problems in transport phenomena. The problems of momentum, heat and mass transfer of which exact solutions have been well known were treated and the approximate solution was obtained in order to distinguish the characteristics of the variational principle. It was indicated that the approximate solutions by the variational principle agreed with the exact solutions for the quantities related to the average values in a space or the quantities connected with the functional (flow rate, Nusselt number, Sherwood number), even when the grade of approximation for the profiles of velocities, temperature and concentration was not so good. The method described in this paper could apply to more complex problems which could not be solved exactly.