Influence of shear rate on induction period in oligomer curing

The rate of heat generation in shear flow is determined by the power of the work done this is the product of the shear rate and the shear stress. The resulting temperature change can be expressed as  

Then we can rewrite Eq. (2.75) by replacing B with the expression from Eq. (2.76)  

74) and (2.77) give us the principal solution of the problem being discussed, i.e., it is possible to calculate T(t) for different shear rates and then to find the upper limit of the integral in Eq. (2.77) for these rates. The solution becomes clearer if we choose dimensionless variables and transform Eqs. (2.74) and (2.77) into dimensionless form. Let us introduce a dimensionless temperature 0 such that  

The dimensionless time x and dimensionless non-isothermal induction period x are written as follows  

Two additional dimensionless values connected with the activation energies are also used  

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