Energy Balance in a PFTR

For the PFTR we wrote the mass balance on species j by writing a shell balance between position z and z + dz. After letting ds — 0 we obtained the expressions 

0 = [uA pCpT - [uAipCpT +dz + A,(-Afls)r dz - Up (T - Tc) dz In this expression A is the cross-sectional area of the tube nD /A for a cylindrical tube) so the volume dV of this element is At dz. Heat transfer occurs across the external wall of the tube, which has area dA. (subscript c stands for coolant), so that 

Next we assume that the fluid density and the tube diameter are the same at z and Z+ dz to obtain 

For a single reaction in a nonisothermal batch reactor we can write the species and energy-balance equations 

We can also obtain these expressions from the energy-balance equation for the steady-state PFTR by simply transforming dzju dt with A,/ V replacing Pw/At. The solutions of these equations for the batch reactor are mathematically identical to those in the PFTR, although the physical interpretations are quite different. 

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Figure 5-2 Energy balance in a PFTR. A shell balance is made on an element of volume dV between Z and + dz. Species flow Fj and enthalpy flow in and out of this dement of volume are balanced hy species and energy generated by reaction.

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