Essentials of Chemical Reaction Engineering, 2nd Edition

12.7.3 Energy Balance

Using the energy flux, e, to carry out an energy balance on our annulus (Figure 12-15) with system volume 2πrΔrΔz, we have

(Energy flow in at r) = e_r A_cr = e_r · 2πrΔz

(Energy flow in at z) = e_z A_cz = e_z · 2πrΔr

Dividing by 2πrΔrΔz and taking the limit as Δr and Δz → 0

The radial and axial energy fluxes are

Substituting for ...