Technical Brief

Fractional Heat Conduction in a Thin Circular Plate With Constant Temperature Distribution and Associated Thermal Stresses

[+] Author and Article Information
S. D. Warbhe

Department of Mathematics,
Laxminarayan Institute of Technology,
Nagpur 440033, Maharashtra, India
e-mail: sdwarbhe@rediffmail.com

J. J. Tripathi

Department of Mathematics,
Dr. Ambedkar College,
Nagpur 440010, Maharashtra, India
e-mail: tripathi.jitesh@gmail.com

K. C. Deshmukh

Department of Mathematics,
R.T.M. Nagpur University,
Nagpur 440033, Maharashtra, India
e-mail: kcdeshmukh2000@rediffmail.com

J. Verma

Department of Applied Mathematics,
Pillai HOC College of Engineering and Technology,
Rasayani 410207, Maharashtra, India;
e-mail: jyotiverma.maths@gmail.com

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received May 24, 2016; final manuscript received November 29, 2016; published online January 24, 2017. Editor: Portonovo S. Ayyaswamy.

J. Heat Transfer 139(4), 044502 (Jan 24, 2017) (4 pages) Paper No: HT-16-1296; doi: 10.1115/1.4035442 History: Received May 24, 2016; Revised November 29, 2016

In this work, a fractional-order theory of thermoelasticity by quasi-static approach is applied to the two-dimensional problem of a thin circular plate whose lower surface is maintained at zero temperature, whereas the upper surface is insulated and subjected to a constant temperature distribution. Integral transform technique is used to derive the solution in the physical domain. The corresponding thermal stresses are found using the displacement potential function.

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Grahic Jump Location
Fig. 1

Temperature distribution function

Grahic Jump Location
Fig. 2

Radial stress function σrr/Y

Grahic Jump Location
Fig. 3

Angular stress function σθθ/Y



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