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In this paper, Modified Divergence Theorem (MDT), known in earlier literature  as Gauss-Ostrogradsky theorem, was formulated and proposed as a general  approach to electromagnetic (EM) radiation, especially ultraviolet (UV)  radiation reactor modeling. Formulated mathematical model, based on MDT, for  multilamp UV reactor was applied to all sources in a reactor in order to  obtain intensity profiles at chosen surfaces inside reactor. Applied  modification of MDT means that intensity at a real opaque or transparent  surface or through a virtual surface, opened or closed, from different sides  of the surface are added and not subtracted as in some other areas of  physics. Derived model is applied to an example of the multiple UV sources  reactor, where sources are arranged inside a cylindrical reactor at the  coaxial virtual cylinder, having the radius smaller than the radius of the  reactor. In this work, optimization of a reactor means maximum transfer of EM  energy sources into the fluid for given fluid absorbance and fluid flow-dose  product. Obtained results, for in advanced known water quality, gives unique  solution for an optimized model of a multilamp reactor geometry. As everyone  can easily verify, MDT is very good starting point for every reactor modeling  and analysis

Modified divergence theorem for analysis and optimization of wall reflecting cylindrical UV reactor