Genera Zized Variationa I Prhcz $ Zes for Convective Heat Transfer and Irreversz ’ b k Thermodynamics
Variational principles for convective heat transfer are extended to nonhomogeneous fluids and to fluids with thermal expansion. The results apply to nonlinear problems with temperature dependent properties. The context is restricted to heat transfer but the derivation and a discussion of the physics brings out the general validity of the variational principles for a large category of irreversible processes.
Lagrangian thermodynamics of heat transfer in systems including fluid motion
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.
Thermodynamics and Heat-Flow Analysis by Lagrangian Methods
Summary 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. ARIATIONAL AND LAGRANGIAN METHODS in the analysis of steady and transient heat flow were the object of earlier publications3-5 They may be considered . as a particular application of more general principles of the thermodynamics of irreversible processes. 1-3j g Our purpose here is to give a brief outline of the theory and methods which were developed in more detail in previous publications.4’5 Also, we have added some new examples of application of the theory. One such example is the derivation in section 2 of an equation for the penetration depth under variable temperature at a boundary by using the boundary-layer techniques as introduced by the writer in heat-transfer problems.4 Another example treated in section 4 is an application of the method of associated fields to calculate the temperature in a wing structure under conditions of aerodynamic heating. The method is applied to a steady-state and a transient problem. The treatment of this problem by the method of associated fields leads naturally to the concept of an “effective” flange width. This effective width is a characteristic length representing the region of the flange which is influenced by the web. Section 2 is a simplified outline of the general theory.4 Section 3 summarizes further developments of the method which introduces the concept of associated field5