Modeling Diffusion to Thermal Wave Heat Propagation by Using Fractional Heat Conduction Constitutive Model

Document Type: Research Paper


Mechanical Engineering Department, Tarbiat Modarres University, Tehran, Iran


Based on the recently introduced fractional Taylor’s formula, a fractional heat conduction constitutive equation is formulated by expanding the single-phase lag model using the fractional Taylor’s formula. Combining with the energy balance equation, the derived fractional heat conduction equation has been shown to be capable of modeling diffusion-to-Thermal wave behavior of heat propagation by changing the order of fractional differentiation. Finally, finite sine-Fourier and Laplace transforms are employed to find the exact solution of a signaling problem.


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