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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.

The impact of geometric parameters of teeth and lubricating oils to the efficiency of involute internal spur gears, when the transverse contact ratio is 2 < εα ≤ 3, has been analyzed in this paper. The mathematical model and computer program for determining the current and the effective value of the efficiency have been developed. The influence of the character of load distribution and energy losses due to heating effects during the meshing period is included in the factor of load distribution. The results of computer simulation are given in the form of a diagram of the current values of the efficiency during the meshing period. Also, the values of effective efficiency for the considered cylindrical gear pairs have been calculated. [ABSTRACT FROM AUTHOR]