Lagrangian Thermodynamics of Heat Transfer in Systems Including Fluid Motior2

The Lagrangian thermodynamic equations of irreversible processes are extended to convective heat transfer. This generalization provides equations for the unified analysis of transient heat flow in complex systems comprising solid structures and moving fluids in either laminar or turbulent flow. The concept of a surface-heat-transfer coefficient is eliminated from the formulation. The theory is developed along two different lines. In one approach a new concept referred to as the “trailing function” is introduced. It represents the surface-heat-transfer properties and may be evaluated by quite simple but remarkably accurate variational procedures. The method of “associated fields” is also generalized to convective phenomena. The second line of approach extends to convective heat transfer the thermodynamic concept of entropy production for both laminar and turbulent flow. The theory amounts to an extension of the thermodynamics of irreversible processes to systems for which Onsager’s relations are not valid.