Heat diffusion in a homogenous slab with an arbitrary periodical heat source: The case of heat source with square wave modulation function

As it has been mentioned in a previous work, the starting point in the study of heat transfer problems is the heat diffusion equation, and their solution reflects not only the boundary conditions consistent to the experimental setup, but also the kind of modulation considered for the heat source. There, the solutions of the heat diffusion equation were found for Dirichlet, Neumann and Robin boundary conditions type, and for an arbitrary modulation function, which the only requirement that the modulation function had an expansion in Fourier basis. From these general solutions, the temperature distributions (as function of relative frequency and relative position) were calculated, under the assumption that the heat source had the sinusoidal modulation inherit from the modulation of the optical excitation, and for all three boundary conditions mentioned before, since this kind of modulation is usually used in the standard models in Photothermal Science and Techniques. However, this kind of modulation is in fact an approximation for the real experimental conditions, since mechanical modulators (choppers) are frequently used in Photothermal experiments withmodulated light. In this present work, the temperature distributions are calculated, considering a square wave modulation for Dirichlet, Neumann and Robin boundary conditions, and in the case of Robin boundary conditions, the influence of different Biot numbers in the thermal response, are also presented and discussed.