TEMPERATURE DISTRIBUTION IN A UNIFORM MEDIUM HEATED BY LINEAR ABSORPTION OF A GAUSSIAN LIGHT-BEAM

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 erro r function (erfc). The approximate solution is suggested in the form o f the product of two Gaussian functions and the hyperbolic secant func tion. 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.