Document Type : Research Paper

**Authors**

Mechanical Engineering Department, Tarbiat Modarres University, Tehran, Iran

**Abstract**

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.

**Keywords**

- Fractional calculus
- Non-Fourier heat conduction
- Generalized Taylor’s Formula
- Diffusion-to-Thermal wave propagation
- Exact solution

**Main Subjects**

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Summer and Autumn 2010

Pages 66-80