Heat Balances for CSTRs

Setting f = Tout, H = //out, and so on, specializes the integral energy balance of Eqnation 5.13 to a perfectly mixed, continnons flow stirred tank  

The simplest, nontrivial version of these equations is obtained when all physical properties (e.g., p and Cp) and process parameters (e.g. gin, a-m, and Tin) are constant. The energy balance for this simplest but still reasonably general case is 

The time derivative is zero at steady state, but it is included so that the method of false transients can be used. The computational procedure in Section 4.3.2 applies directly when the energy balance is given by Equation 5.27. The same basic procedure can be used for Equation 5.24. The enthalpy rather than the temperature is marched ahead as the dependent variable, and then Tout is calculated from //out after each time step. The examples that follow assume constant physical properties and use Equation 5.27. Their purpose is to explore nonisothermal reaction phenomena rather than to present detailed design calculations. 

A CSTR is commonly used for the bulk polymerization of styrene. Assume a mean residence time of 2 h, cold monomer feed (300 K), adiabatic operation (UA i = 0), and a pseudo-first-order reaction with rate constant k = 10 ° exp(—10000/T) h where T is in kelvin. The adiabatic temperature rise for complete conversion is approximately 400 K. Assume constant physical properties and ignore power input form the agitator. 

SOLUTION The component balance for styrene for a first-order reaction in a constant- 

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