Separable solutions of Cattaneo-Hristov heat diffusion equation in a line segment: Cauchy and source problems

Abstract

The behavior of Cattaneo-Hristov heat diffusion moving in a line segment under the influence of specified initial and source temperatures has been investigated. The Fourier method has been applied to determine the eigenfunctions thus allowing reducing the problem to a set of time-fractional ordinary differential equations. Analytical solutions by applying the Laplace transform method have been developed.

Keywords

• Cattaneo-Hristov heat diffusion
• Laplace transform
• Eigenfunction expansion
• Cauchy problem
• Source problem
• Caputo-Fabrizio fractional derivative