Date of Award
Master of Science in Chemical Engineering - (M.S.)
Chemical Engineering and Chemistry
Ernest N. Bart
John E. McCormick
Hung T. Chen
This thesis presents a mathematical model of the steady state heat and temperature distributions of a hot sphere located along the midplane of an infinitely long wedge of any arbitrary central angle. The heat and temperature distributions of this geometric configuration are of immense value, since through the use of this model as a wedge shaped unit cell the description of any number of hot spheres, arranged in a regular planar array can be immediately determined.
The method of reflections is used to solve Laplace's equation , V2T=O , analytically using the sphere and the wedge walls as boundary conditions. Only the second reflection was obtained, yielding a first order correction.
The resulting model of an individual sphere within a wedge, and an arbitrary number of spheres arranged in a regular polygonal planar array were obtained. The regular planar array was tested and compared with known exact solutions of Laplace's equation in Bipolar coordinates [ for the solution of two spheres in space ] and Toroidal coordinates [ for the solution approximating an extremely large number of densely packed spheres in a regular planar array ]. The model tested accurately in the comparison with Bipolar coordinates, while the comparison of the developed model with a toroid showed the limitations of a first order correction solution.1
Horwat, David W., "The steady state heat and temperature distribution of a hot sphere within an infinite wedge" (1974). Theses. 2153.