Calculation of temperature field in a thin moving sheet heated with laser beam

A temperature field in a thin moving sheet heated with a laser beam is calculated. The power density in the beam is distributed according the Gauss function. Cooling effects caused by the free or forced convection in ambient gas is taken into account. The problem becomes two dimensional by averaging the temperature field over the sheet thickness. Two-dimensional integral Fourier transformation on space coordinates is applied to solve the problem. It gives an analytical solution of the problem in the Fourier space. The inverse Fourier transformation is fulfilled and the solution is represented via an integral having exponential asymptotes at infinity.