Thermo-diffusive functions

For a wide class of irreversible processes, the fluxes are linear functions of thermodynamic forces determined by phenomenological laws. Some of these laws were briefly discussed earlier, for example, the Fourier and Fick s laws. These laws embrace also the mixed or cross-phenomena, for example, thermo-diffusion, when the diffusion flux linearly depends on both - concentration- and temperature gradients. In general case linear phenomenological relations can be written... 

The two sequential processes that lead to the chemical degradation of a polymer due to oxidation are (1) oxygen diffusion and (2) chemical reaction [15], Researchers [16] have used the so-called unreacted core model to characterize and predict thermo-oxidative degradation in a composite laminate. According to this model, the composite weight loss due to oxidation, q can be expressed as a power law function of time ... 

The macro radicals formed by HPD will be in close proximity and would not be rapidly separated by diffusion, while the cage reaction between them would yield the identified products and confirm some experimental data on the accumulation of functional groups during photo-oxidation (Fig. 3) or thermo-oxidation (Fig. 4). 

In order to monitor the mechanical properties in relation to the microstructure, the knowledge of the precipitation state at the end of a thermo-mechanical treatment is of prime importance. In this purpose, Arcelor develops models that allow for the prediction of the influence of the process parameters on the state of precipitation. The model Multipreci, developed at IRSID is one of them. It (Hedicts the precipitation kinetics of mono- and di-atomic particles in ferrite and austenite as a function of the time-temperature history. It is based on the classical theories for diffusive phase transformation and treats simultaneously the nucleation, growth and ripening phenomena. The state of precipitation that is predicted includes the particle size distribution, their number and volume fraction. From these values, the effect of the precipitates on the mechanical properties can be calculated. 

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