Equal Average End Temperature

Geometric and kinematic similarity follows from a combination of this equation with Equahons 13.1, 13.3 and 13.4, resulting in 

It should be realized that this equation does not include the power needed to transport the solid bed however, this last item is not important for the thermal considerations in the next paragraphs. 

Two types of thermal similarities can be used equal average end temperatures and similar temperature profiles. The concept of equal average end temperatures can be applied if the extruder operates adiabatically or if Br 1. In this case scaling-up has to proceed according to equal motor power per unit throughput  

With Equations 13.1 and 13.5 this leads for equal viscosities (y/= 0) to 

In this case various degrees of freedom are still retained. 

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For an equal average heat flux, the local maximum tube skin temperature is somewhat lower for the one-row arrangement than for the two-row, staggered arrangement. This is of importance especially in the hot part (at the end) of the cracking coil. 

The calculation is performed in terms of degrees Celsius, including values both above and below zero. It is not convenient, therefore, to use the relative increment of temperature as a test for step size in subroutine CHECKSTEP. I use absolute increments instead. At the end of subroutine SPECS, I set incind equal to 3 for all equations, limiting the absolute increment in temperature to 3° per time step. Zonally averaged heat capacity as a function of latitude is calculated in subroutine CLIMINP in terms of land fraction and the heat capacity parameters specified in SPECS. It is returned in the array heap. 

Calculate the root-mean-square end-to-end distance of a polypropylene chain with number average molecular weight equal to 100,000 g mol. Consider the bond length to be 2.52 A and that the chain is freely jointed. A vulcanized polyisoprene sample has a shear modulus of 0.392 MN m" at room temperature. Determine the average number of monomers between cross-links (p = 1.00 g cm ). 

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