The heat storage capacity of a solid spherical body under general periodic thermal excitations

The problem of evaluating the dynamic heat storage capacity of a solid sphere is analysed for the case of general periodic thermal excitation profiles of any form. A general relation to calculate the storage capacity is obtained in closed form for the harmonic case, and in term of Fourier series for the intermittent one, and it is shown that the harmonic heating is not the most efficient heat storage procedure. Equations in frequency domain to calculate the heat storage capacity under general periodic (non-harmonic ) heating are given. A comparison with the results, in terms of storage efficiency, obtainable by lumped capacitance method and by an approximation based on linear combination of first order systems is reported.