Asymptotic Effects of Incident Angle and Lateral Conduction in Electromagnetic Skin Heating

TL;DR

This paper develops an asymptotic analytical model for skin heating by electromagnetic beams, accounting for incident angle and lateral conduction effects, providing accurate temperature predictions at moderate depth-to-lateral scale ratios.

Contribution

It derives closed-form expressions for first and second order asymptotic terms, improving temperature distribution predictions by including lateral conduction effects.

Findings

Lateral conduction significantly affects temperature at moderate scale ratios.

The second order term captures lateral conduction effects.

The model accurately predicts temperature distribution considering incident angle and lateral conduction.

Abstract

Previously we derived the leading term asymptotic solution of temperature distribution in skin heating by an electromagnetic beam at an arbitrary incident angle. The asymptotic analysis is based on that the penetration depth of the beam into skin is much smaller than the size of beam cross-section. It allows arbitrary incident angle. We expand the temperature in powers of the small depth to lateral scale ratio. The incident angle affects all terms in the expansion while the lateral heat conduction appears only in terms of positive even powers. The previously obtained leading term solution captures only the main effect of incident angle. The main effect of lateral heat conduction is contained in the second order term, which is mathematically negligible in the limit of small depth to lateral scale ratio. At a moderate length scale ratio (e.g., 0.1), however, the contribution from lateral conduction is quite significant and needs to be included in a meaningful approximate solution. In this study, we derive closed form analytical expressions for the first order and the second order terms in the asymptotic expansion. The resulting asymptotic solution is capable of predicting the temperature distribution accurately including the effects of both incident angle and lateral heat conduction even at a moderate length scale ratio.