Asymptotic analysis of axisymmetric plane strain problem involving fractional order heat conduction

ABSTRACT

This work is concerned with the asymptotic solutions of the axisymmetric plane strain problem involving the fractional order heat conduction. The governing equations for the axisymmetric plane strain problem are derived by means of fractional calculus. The Laplace transform technique is used to obtain the general solutions for any set of boundary conditions in the physical domain. The asymptotic solutions for a specific problem of an infinite cylinder with the boundary subjected to a thermal shock is derived by means of the limit theorem of Laplace transform. Utilizing these solutions, the thermoelastic behavior induced by transient thermal shock can be clearly illustrated, and the jumps locating at the position of each wavefront can also be accurately captured. Some comparisons for the predictions of thermoelastic response are conducted to estimate the effect of the fractional order parameter on the thermoelastic behavior.

KEYWORDS:

• generalized thermoelasticity
• fractional order heat conduction
• asymptotic solutions
• axisymmetric plane strain
• thermal shock

Funding

This research was supported by the National Natural Science Foundation of China (Grant Nos. 11102073, 51206062), the National Science Foundation for Post-doctoral Scientists of China (Grant No. 2012M511207), the Research Foundation of Advanced Talents of Jiangsu University (Grant No. 10JDG055), and the Priority Academic Program Development of Jiangsu Higher Education Institutions.