Abstract
This note presents a practical approximation method for computing the minimum eigenvalue for a transcendental equation derived from the heat equation with a convective boundary condition. The transcendental equation is approximated by a finite continued fraction equation, which is a quadratic equation. Its solution(the minimum eigenvalue ) is obtained in a closed form depending explicitly on the Biot number. The method is faster than the conventional Newton method and the error is within 0.3%, a level that is quite satisfactory for practical use.
