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Fractional heat conduction equation and associated thermal stresses in an infinite solid with spherical cavity. (English) Zbl 1153.74012

Summary: The temperature distribution and thermal stresses in an infinite medium with a spherical cavity are studied in the framework of a quasi-static uncoupled theory of thermoelasticity based on heat conduction equation with a time fractional derivative of order \(0 < {\alpha} \leqslant 2\). The Caputo fractional derivative is used. As the fractional heat conduction equation in the case \(1 \leqslant {\alpha} \leqslant 2\) interpolates the standard heat conduction equation \(({\alpha} = 1)\) and the wave equation \(({\alpha} = 2)\), the proposed theory interpolates the classical thermoelasticity and the thermoelasticity without energy dissipation introduced by Green and Naghdi. The solution is obtained using the integral transform technique. Numerical results are illustrated graphically.

MSC:

74F05 Thermal effects in solid mechanics
80A20 Heat and mass transfer, heat flow (MSC2010)
26A33 Fractional derivatives and integrals
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