To the Calculation of the Unsteady Temperature Field of a Cylindrical Body

Determining the temperature regime of cylindrical bodies in the initial period of time, i.e. at small values of the Fourier number, is a rather time-consuming task. In the calculation process, it is necessary to take into account a large number of members of the series to obtain the result of the required accuracy. In this case, it is required to calculate the eigenvalues of the characteristic equation for each term of this series. The article offers a fairly simple and effective analytical method for determining eigenvalues with high accuracy. The method is based on the use of a special function, the inverse of the relation of the Bessel functions of the first kind of zero and first order. In this case, the procedure for determining eigenvalues is reduced to a simple fast-converging iterative process. Using this procedure allows you to determine any eigenvalue of the characteristic equation with high accuracy required for engineering calculation. The application of this method in engineering practice significantly simplifies the process of determining the temperature regime of cylindrical bodies, and can also be extended to other tasks.