Heat Generation and Removal in a CSTR

We solved the mass- and energy-balance equations for the CSTR in the previous chapter. The mass balance on species A is 

The first term on the right side of the equation is the rate of heat removal in the inlet and outlet streams, the middle term is the rate of heat generation by reaction, and the third term is the rate of heat removal by cooling. We usually omit the shaft work term Ws in this equation because it is usually much smaller than the other terms. 

We want to find solutions of these equations. It will be convenient to make the energy-balance equation dimensionless before solving it. As introduced in the previous chapter, we define an almost dimensionless rate of heat generation as 

Returning to the mass-balance equation, we write it in terms of fractional conversion (another dimensionless variable) as 

We can now write the preceding energy-balance equation in terms of temperature alone as 

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