Fractional-diffusion solutions for transient local temperature and heat flux

Applying properties of the Laplace transform, the transient heat diffusion equation can be transformed into a fractional (extraordinary) differential equation. This equation can then be modified, using the Fourier Law, into a unique expression relating the local value of the time-varying temperature (or heat flux) and the corresponding transient hear flux (or temperature). We demonstrate that the transformation into a fractional equation requires the assumption of unidirectional heat transport through a semi-infinite do main. Even considering this limitation, the transformed equation leads to a very simple relation between local time-varying temperature and heat flux. When applied along the boundary of the domain, the analytical expression d etermines the local time-variation of surface temperature (or heat flux) wi thout having to solve the diffusion equation within the entire domain. The simplicity of the solution procedure, together with some introductory conce pts of fractional derivatives, is highlighted considering some transient he at transfer problems with known analytical solutions.