Thermomechanical coupling

Example 4.4 Thermomechanical coupling in a circular Couette flow For a circular Couette flow (Figure 4.5), the entropy production rate for an incompressible Newtonian fluid held between two coaxial cylinders is... 

An example of this type of thermomechanical coupling appears to have been observed by Lehmann in cholesteric liquid crystals very soon after their discovery. He found that droplets of the material when heated from below seemed to be rotating violently, but from optical studies he concluded that it was not the drops themselves but the structure that was rotating. Fig. 4.4.1 shows a few of the many sketches that he made depicting his observations. Leslie s equations offer a simple explanation of the phenomenon because of the absence of mirror symmetry, an applied field, which is a polar vector, can result in a torque, which is an axial vector. 

As an example for a bulk metal forming process with thermomechanical coupling, we present the forming process under induction heating. For a more detailed treatment, the reader is referred to Okman et al. 2006. For hollow shafts made of material X5CrNil89 with initial dimensions as Dq = 30 mm, Dj = 22 mm Lo = 60 mm Lj/Lo = 0.75, the numerical predictions and their comparison with the experiments are given in Fig. 4 for heating time 27 s. 

Arruda E.M., and M.C. Boyce. 1995. Effects of strain rate, temperature and thermomechanical coupling on the finite strain deformation of glassy polymers. Mech Mater 19 193-212. 

Example 4.4 Thermomechanical coupling in a Circular Couette flow... 

For example, in the case of a steam engine machine in which the phenomena involved are heating and changes in the state of water, the following thermomechanical couples ate used temperature-entropy (T, S) and opposed pressure-volume (-P, V). To study a chemical transformation in condensed phases at atmospheric pressure, incapable of varying or even influencing the phenomenon, the couple temperature-entropy is chosen and, for each component, the couple quantity of matter and chemical potential. 

We show this change in variables with both thermomechanical couples by choosing the set ... 

This function is confused with Gibbs energy if, as well as the amount of matter, only the thermomechanical couples S, T and V, -P ate considered. In the case where an electrical potential is added, the function is called electrochemical Gibbs energy and its variables ate temperatute, pressure, electrical potential and amount of matter. For surface phenomena, we encounter capillary Gibbs energy which involves the following variables temperature, pressure, surface tension and amount of matter. 

The first recorded example of thermomechanical coupling, as explained in the Les-... 

Fitzgerald, J. E., "Thermomechanical Coupling in Viscoelastic Materials," Presentation at the International Conference on Structure, Solid Mechanics and Engineering Design in Civil Engineering Materials, Southampton, England (1969), Discussion to be published by John Wiley and Sons, Inc.,... 

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