Continuously Operated Non-isothermal Ideal Tubular Reactor

3 Continuously Operated Non-isothermal Ideal Tubular Reactor 

The model of a non-isothermal wall-cooled ideal tubular reactor discussed in the following neglects radial gradients of temperature and concentration, and only considers axial gradients. The control space is a slab with the differential length dz in the direction of flow. For steady-state operation, the mass balance for a differential element dVa (= zdAt.im) and a constant volume reaction of reactant A is given by 

Rewriting Eq. (4.10.70) with the internal surface per volume of reactor (dAt.int/ dVR = 4/dint), the superficial fluid velocity us = 4V/ndj ), and substitution of the rate Ta by Cj indK ldr leads to the heat balance in terms of the heat flow per unit volume  

The cooling term Uh has to consider three parameters, (i) radial heat transfer from the fluid to the internal surface of the tube, (ii) conduction of heat through the wall, and (iii) heat transfer from the external surface to the cooling medium. 

These three thermal resistances are combined in the thermal transmission coefficient U, already introduced in Section 3.2.1.2  

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