Heat Balance with Reactive Material

A dimensionless criterion, the Biot number, is often used in transient heat transfer problems by comparing the heat transfer resistance within the body with 

A high Biot number means that the conductive transfer is small compared to convection and the situation is close to that considered by a Frank-Kamenetskii situation (Section 13.4.1). Inversely, a small Biot number, that is Bi 0.2, means that the convective heat transfer dominates and the situation is close to a Semenov situation. 

Conductive problems described by Equation 13.19 can be solved algebraically or graphically using nomograms based on dimensionless coordinates, where the dimensionless time is given by the Fourier number  

The dimensionless temperature profile is described as a function of the Biot number and Fourier numbers [3, 5]. 

The problem of conductive heat transfer in an inert solid can be solved algebraically, when there is no heat source in the solid. Nevertheless, this problem is not within the scope of our considerations about thermal confinement, since we are interested in the thermal behavior of a reactive solid, that is, a solid comprising a heat source in itself, which requires specific mathematical treatment. 

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During the polymerisation the heat released by the polymerisation reaction can be determined online from temperature measurements, see these references for details about reaction calorimetry - MacGregor (1986), Bonvin et al (1989), Moritz (1989), Schuler and Schmidt (1992). Calorimetric measurements can be used to infer the free amount of monomers in the copolymerisation and also the overall conversion (Urretabizkaia et al, 1993 Gugliotta etal, 1995c Hammouri etal, 1999 Saenz de Buruaga etal, 2000) by means of an observer/estimator. Basically the estimator solves the monomer material balance differential equations using the heat of reaction as input variable instead of the theoretical polymerisation rate. Therefore, the estimator uses the enthalpies of polymerisation of the monomers and the reactivity ratios as parameters. This information is compared with the... 

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