Document Type


Date of Award


Degree Name

Master of Science in Chemical Engineering - (M.S.)


Chemical Engineering and Chemistry

First Advisor

Ernest N. Bart

Second Advisor

Angelo J. Perna

Third Advisor

Hung T. Chen


Solutions to Laplace's equation are obtained by the method of reflections for the problem of heat transfer from two parallel rings of spheres arranged in regular polygonal arrays. The mathematical models developed describe the rate of heat transfer and spatial temperature distribution due to an arbitrary number of identical spheres of equal surface temperature correcting Fourier's heat transfer equation for the interference caused by a multiparticle array. Although the method of solution is quite rigorous and can be used to obtain as accurate a solution as desired, only the second reflection was obtained, yielding a first order correction. The model was compared with an exact solution of Laplace's equation in spherical bipolar coordinates for the case of two spheres in space. The accuracy of the model was shown to be related to the density of the array under consideration becoming more reliable with increased dilution of the system.



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