Telegraph equation in polar coordinates: Unbounded domain with moving time-harmonic source

Yuriy Povstenko, Martin Ostoja-Starzewski, Tamara Kyrylych

Research output: Contribution to journalArticlepeer-review

Abstract

The telegraph equation with moving time-harmonic source with angular frequency ω is considered in polar coordinates (r,φ). Two problems are studied: the source moving on a straight line with constant velocity v and the source traveling on a circumference of a circle of radius R with a constant orbital frequency Ω. The solutions are obtained using the integral transforms technique. Two limiting cases of the telegraph equation are also analysed: the Fourier heat conduction equation and the linear wave equation. The singularity of the solution to the wave equation at a point r=R+vt, φ=0 in the case of the source moving on a straight line is described. The relationship between the orbital frequency Ω and the polar coordinates at the wave front has been analyzed. The results of numerical simulation are presented graphically for a wide spectrum of nondimensional parameters.

Original languageEnglish (US)
Article number124013
JournalInternational Journal of Heat and Mass Transfer
Volume207
DOIs
StatePublished - Jun 15 2023

Keywords

  • Hankel transform
  • Laplace transform
  • Telegraph equation
  • Time-harmonic impact
  • Wave front

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Mechanical Engineering
  • Fluid Flow and Transfer Processes

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