A Variational Principle for Transport Phenomena : I―Formulation of Principle

Abstract

A new variational principle was formulated to solve the first and second kind of boundary value problems in mometum transprot, heat and mass transfer process. The variational principle formulated in this paper is based on the concept of variational invariant and is applicable to the unsteady state. By deriving Euler's equation from the functional, the equivalence between the variational principle and the boundary value problem was verified. Then, the reciprocal principle was established by verifing that the functional should be a minimum and the reciprocal functional should be a maximum at the stationary point. Finally, the parameters included in the argument functions as the generalized coordinates were defined and Lagrange-Biot's equation which determined these paramtes was derived. Some applications of this principle to the problems of the transport phenomena will be discussed in the following paper.