## 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 language | English (US) |
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Article number | 124013 |

Journal | International Journal of Heat and Mass Transfer |

Volume | 207 |

DOIs | |

State | Published - 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