Transient temperature distribution in a rotating cylinder subject to a surface heat source and convective cooling

In this article, an analytical solution is developed to determine the transient temperature distribution in a rotating finite cylinder subject to a heat source acting on its flat surface with convective cooling. The resolution of the heat conduction problem for the cylinder temperature is carried out by means of the successive application of one-dimensional integral transforms: the finite Fourier transform and the finite Hankel transform. The solution can be applied in different engineering applications such as turning, pin-on-disk devices, bearings and braking systems. Taking this solution into account, a numerical analysis of the transient temperature distribution generated in a rotating cylinder subject to a heat source is performed. In this analysis the effect of the rotation speed and of the convective cooling on the transient temperature distribution of the cylinder and on the time required to reach the quasi-steady state is studied by means of two dimensionless parameters: the Peclet number and the Biot number, which depend on the rotation speed and on the convective heat transfer coefficient, respectively. Finally, different heat source geometries (circular, square and circular trapezoid) are considered.