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**Analytical and numerical temperature distribution in a 3-D triple-layer skin tissue subjected to a multi-point laser beam.**
*(English)*
Zbl 1479.78020

Summary: In the present study, the temporal and spatial variation of temperature in a three-dimensional triple-layer skin tissue under the laser heating is determined. Using the method of separation of variables along with the Laplace transform, the so-called Pennes bio-heat equation is analytically solved in a 3D triple-layer tissue in which each layer has its own thermo-physical properties. The laser heating of the skin, with both single and multiple laser beams, is modelled based on time-dependent Gaussian-shaped irradiance distributions with exponential axial attenuation. For the presented solution approach, it can be shown that the laser can be considered as an arbitrary function of time such as pulses with a specified time interval with each desired spatial distribution. Besides the analytical solution, the governing equations are solved numerically by using the standard finite element method and the results are compared with the analytical solution to investigate the effects of laser heating on human skin. The effects of using single and multiple-point laser beams on the temperature increment are investigated. A good agreement between both analytical and numerical solutions is observed. The obtained results indicate that a better temperature distribution in the skin tissue is obtained; whenever, a multi-point laser is employed.

### MSC:

78A60 | Lasers, masers, optical bistability, nonlinear optics |

78A48 | Composite media; random media in optics and electromagnetic theory |

80A19 | Diffusive and convective heat and mass transfer, heat flow |

92C05 | Biophysics |

35Q60 | PDEs in connection with optics and electromagnetic theory |

35Q79 | PDEs in connection with classical thermodynamics and heat transfer |

35Q92 | PDEs in connection with biology, chemistry and other natural sciences |

44A10 | Laplace transform |

78M10 | Finite element, Galerkin and related methods applied to problems in optics and electromagnetic theory |

### Keywords:

analytical solution; biological heat transfer; Laplace transform; multi-layer skin tissue; multi-point laser beam; pulsed laser; Pennes bio-heat equation
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\textit{B. Partovi} et al., J. Eng. Math. 131, Paper No. 13, 14 p. (2021; Zbl 1479.78020)

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