Thermodynamics and Heat-Flow Analysis by Lagrangian Methods

New procedures for the analysis of heat flow are summarized and further applications are presented. The methods may be considered as a special case of a more general formulation of the thermodynamics of irreversible processes. This formulation is based on the introduction of a new thermodynamic potential, the concept of flow field as a state variable, and the use of Lagrangian techniques and generalized coordinates. A brief account is given of the basic principles and of the more recently developed method of “associated flow.” Application to a one-dimensional problem leads to a simplified scheme for the calculation of transient temperatures in a wall by combining the Lagrangian methods with the boundary-layer techniques along the lines developed in the writer’s earlier work. Another application deals with the calculation of transient temperature in a wing structure under aerodynamic heating. The concept of “effective” flange width is introduced. It represents the region of the flange which is influenced by the presence of a web.