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https://doi.org/10.1109/MMM.2015.2394020

has been cited by the following article:

• TITLE: Internal Temperature of Skin when Surface Temperature Is Controlled with an Electromagnetic Beam

  AUTHORS: Hongyun Wang, Wesley A. Burgei, Hong Zhou

  KEYWORDS: Electromagnetic Beam of Time-Varying Power, Control of Surface Temperature, Thermal Effect of Beam, Non-Dimensional Analysis

  JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.9 No.3, March 22, 2021

  ABSTRACT: We study the thermal effect on skin exposed to an electromagnetic beam of time-dependent power. We consider two types of beam power time schedules. In the controlled temperature exposure, the skin surface temperature is increased quickly to a prescribed level using a high beam power; then the surface temperature is maintained at the prescribed level by adjusting the beam power adaptively. In the constant power exposure, the applied beam power is relatively low and stays unchanged over the time. We start both types of exposures at the same time and compare their internal temperatures of skin when they have the same surface temperature. In a non-dimensionalized formulation, we show that at the moment when both exposure types reach the same prescribed surface temperature level, the controlled temperature exposure has a higher internal temperature at all depths. This conclusion is mathematically rigorous and is independent of skin material properties.