Research Papers: Heat and Mass Transfer

A Note on the Generalized Thermoelasticity Theory With Memory-Dependent Derivatives

[+] Author and Article Information
Soumen Shaw

Department of Mathematics,
Indian Institute of Engineering
Science and Technology,
Shibpur 711103, India
e-mail: shaw_soumen@rediffmail.com

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received November 19, 2016; final manuscript received April 11, 2017; published online May 9, 2017. Assoc. Editor: George S. Dulikravich.

J. Heat Transfer 139(9), 092005 (May 09, 2017) (8 pages) Paper No: HT-16-1758; doi: 10.1115/1.4036461 History: Received November 19, 2016; Revised April 11, 2017

In this note, two aspects in the theory of heat conduction model with memory-dependent derivatives (MDDs) are studied. First, the discontinuity solutions of the memory-dependent generalized thermoelasticity model are analyzed. The fundamental equations of the problem are expressed in the form of a vector matrix differential equation. Applying modal decomposition technique, the vector matrix differential equation is solved by eigenvalue approach in Laplace transform domain. In order to obtain the solution in the physical domain, an approximate method by using asymptotic expansion is applied for short-time domain and analyzed the nature of the waves and discontinuity of the solutions. Second, a suitable Lyapunov function, which will be an important tool to study several qualitative properties, is proposed.

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Fig. 1

Displacement distribution versus time (t)

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Fig. 2

Displacement distribution versus distance at t = 0.2

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Fig. 3

Temperature distribution versus time (t)

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Fig. 4

Temperature distribution versus distance at t = 0.2

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Fig. 5

Temperature distribution in a fractured medium: (a) fracture medium, (b) fracture domain, and (c) material domain

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Fig. 6

Stress distribution versus distance at t = 0.2




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