Related Experiment Video
Updated: Jun 8, 2026

Subsurface Defect Localization by Structured Heating Using Laser Projected Photothermal Thermography
Published on: May 15, 2017
Temperature distribution in a uniform medium heated by linear absorption of a Gaussian light beam
Abstract:
The linear-diffusion equation is considered for a positive half-space with heat sources represented by Gaussian functions in the transverse plane and by exponential decay along the longitudinal axis. The exact solution is presented as a single quadrature of the complementary error function (erfc). The approximate solution is suggested in the form of the product of two Gaussian functions and the hyperbolic secant function. Comparison with the exact solution shows that the error of this approximation is near 10%. The approximation may be used in different medical applications, e.g., laser angioplasty.
Related Concept Videos
Absorption of Radiation
Mechanisms of Heat Transfer II
UV–Vis Spectroscopy: Beer–Lambert Law
Gauss's Law
Maxwell-Boltzmann Distribution: Problem Solving
This distribution function f(v) is defined by saying that the expected number N (v1,v2) of particles with speeds between v1 and v2 is given by
Steady, Laminar Flow in Circular Tubes

