Solving the temperature and conversion equations using finite differences

13 Solving the temperature and conversion equations using finite differences 

Here rj k) denotes the rate of reaction j in cell k, which will depend on the cell s temperature, F,  

The temperature differential for the end cell may be written in terms of available cell temperatures as  

Equation (20.64), used together with the known cell temperatures and equation (20.65), enables the molar flows and the concentrations in each cell to be calculated. Putting k = K, m equation (20.65) allows AjiK) to be calculated, which represents the concentrations leaving the reactor. 

The cell temperatures may be updated by solving equation (20.62) numerically. Replacing the space differentials by discrete approximations gives the time differential for cell temperature for every cell except the last as  

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