to main test pagethat they are coupled 'by the interface' Arrhenius
equation. The (exothermal) reaction 'exhibits some conversion' depending on the
rate constant. This produces 'heat of reaction' and a 'rise of the temperature'
(in the reaction mass). The 'new' temperature produces a 'new' rate constant
following the Arrhenius equation. The new rate constant produces the next
conversion step .....and so on, in adiabatic reactors the solution of this
process is comparably simple, cf. the following link (or
the task on an adiabatic
STR ). Here you see the numerical approach of the simultaneous solution of both
balances. Another possibility is the graphical solution which 'derives' from
the 1/r(U)-plot procedure, see an example, - of course finally the same matter!!.
The
procedure can get even a bit more complicated for adiabatic TFRs, where the
calculation 'ends' in the consecutive solution of both balances for a TFR in a
cell compartment model (cf. book of Jens Hagen, Chemische
Reaktionstechnik)
But: Exterior heat and mass transport effects
(e.g. caused by convection or interchange /exchange processes in not adiabatic
and/or continuous reactors) influence (disturb) the two coupled systems and
make the problem even more complex, - e.g. in the case of the calculations for
polytropical (or a bit less difficult: isothermal) process conduction modes, -
or think of the gradients in TFRs with heterogeneous phase flows or
thermostatting jackets with countercurrent or cocurrent flows of two phases or
within the heat exchanging process !
see a blackbord sketch of the various possibilities for the 3 basic reactor types
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