Paper presented at the 9th International Conference on Heat Transfer, Fluid Mechanics and Thermodynamics, Malta, 16-18 July, 2012.
This paper extends the method, in which a Volterra-type
integral equation that relates the local values of temperature and
the corresponding heat flux within a semi-infinite domain, to a
transient heat transfer process in a non-isolated system that has
a memory about its previous state. To model such memory
systems, the apparatus of fractional calculus is used. Based on
the generalized constitutive equation with fractional order
derivative, the fractional heat equation is obtained and solved.
Its analytical solution is given in the form of a Volterra-type
integral equation. It follows from the model, developed in this
study, that the heat wave, generated in the beginning of ultrafast
energy transport processes, is dissipated by thermal
diffusion as the process goes on. The corresponding
contributions of the wave and diffusion into the heat transfer
process are quantified by a fractional parameter, H , which is a
material-dependent constant.
