A variational principle for fully developed laminar heat transfer in uniform channels I

Summary

A variational principle for forced convection in laminar flow in uniform channels is formulated. The concepts of thermal potential, dissipation function and thermal force have been introduced and a Lagrangian formulation of the thermal flow field using generalized coordinates is given. Special consideration is given to heat transfer in plug flow when the thermal field is a linear function of the generalized coordinates. The concept of normal and ignorable coordinates is introduced. An example showing the use of Lagrangian equations is worked out.