Abstract
This chapter aims to discuss the analytical solutions for heat waves
observed in Cattaneo-Hristov heat conduction modelled with Caputo-Fabrizio
fractional derivative. This operator includes a non-singular exponential kernel and
also requires physically interpretable initial conditions for its Laplace transform
property. These provide significant advantages to obtain analytical solutions. Two
different types of harmonic heat sources are assumed to elicit heat waves. The
analytical solutions are obtained by applying Laplace transform with respect to the
time variable and the exponential Fourier transform with respect to spatial coordinate.
The temperature curves for varying values of the fractional parameter, angular
frequency, and the velocity of the moving heat source are drawn using MATLAB.
Keywords: Caputo-Fabrizio fractional derivative, Cattaneo-Hristov heat diffusion model, Exponential fading memory, Fourier transform, Harmonic source effect, Laplace transform, Oscillatory heat transfer.
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