A NEW METHOD FOR SOLVING THE HEAT CONDUCTIONS IN A HOMOGENOUS CIRCULAR DISK^1)

This paper aims to develop a new method for solving the steady heat conduction in a homogenous circular disk by using the Poisson's formula. This simple and elegant method originates directly from the Cauchy-Riemann equations in combination with the Poisson's formula for a circular region. The solution obtained by the new method is expressed in an integral form, which is further proved to be completely consistent with the classic solution in Fourier series. By establishing the connection between the known Fourier series' solution and the new integral one, this work not only enriches the teaching materials for the course "Methods of Mathematical Physics", but also provides a clear physical interpretation for the corresponding mathematical equation.