Asymptotic Methods for Air-Flow Around Fibers
An asymptotic method to determine the air-flow around slender fibers in the case of low Reynolds numbers is presented. Based on the equations for linearized flow, the force acting on a fiber is approximated as the superposition of fundamental solutions. Matching asymptotic expansions valid in different regions of the flow field leads to an integral equation model for the force. The resulting non-standard, strongly singular Fredholm integral equation of the second kind is analyzed theoretically and solved numerically. The application of this model to an industrial melt-spinning process for artificial fibers is discussed.
KeywordsFundamental Solution Asymptotic Method Collocation Point Cool Chamber External Heat Transfer
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