Transport Phenomena in Eccentric Cylindrical Coordinates |
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| Authors: | P H Gilbert C Saengow A J Giacomin |
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| Affiliation: | 1. Chemical Engineering Department, Polymers Research Group, Queen's University, Kingston, Canada;2. Mechanical and Aerospace Engineering Department, Polymer Research Center, King Mongkut's University of Technology North Bangkok, Bangkok, Thailand;3. Mechanical and Materials Engineering Department, Queen's University, Kingston, ON, Canada |
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| Abstract: | Studies in transport phenomena have been limited to a select few coordinate systems. Specifically, Cartesian, cylindrical, spherical, Dijksman toroidal, and bipolar cylindrical coordinates have been the primary focus of transport work. The lack of diverse coordinate systems, for which the equations of change have been worked out, limits the diversity of transport phenomena problem solutions. Here, we introduce eccentric cylindrical coordinates and develop the corresponding equations of change (continuity, motion, and energy). This new coordinate system is unique, distinct from bipolar cylindrical coordinates, and does not contain cylindrical coordinates as a special case. We find eccentric cylindrical coordinates to be more intuitive for solving transport problems than bipolar cylindrical coordinates. Specific applications are given, in the form of novel exact solutions, for problems important to chemical engineers, in momentum, heat and mass transfer. We complete our analysis of eccentric cylindrical coordinates by using the new equations to solve one momentum, one energy, and one mass transport problem exactly. © 2017 American Institute of Chemical Engineers AIChE J, 63: 3563–3581, 2017 |
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| Keywords: | coordinate systems eccentric cylinders transport phenomena equations of change |
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