Application of Fractional Order Theory of Thermoelasticity in an Elliptical Disk and Associated Thermal Stresses

AbstractIn this article, a time fractional-order theory of thermoelasticity is applied to an isotropic homogeneous elliptical disk. The lower and upper surfaces of the disk are maintained at zero temperature, whereas the sectional heat supply is applied on the outer curved surface. Thermal deflection and associated thermal stresses are obtained in terms of Mathieu function of the first kind of order 2n. Numerical evaluation is carried out for the temperature distribution, Thermal deflection and thermal stresses and results of the resulting quantities are depicted graphically.

Download Full-text

FRACTIONAL ORDER THEORY OF THERMAL STRESSES IN A TWO DIMENSIONAL TRANSVERSELY ISOTROPIC MAGNETO THERMOELASTIC MATERIAL

Journal of Theoretical and Applied Mechanics ◽

10.7546/jtam.50.20.03.02 ◽

2020 ◽

Vol 50 (3) ◽

Author(s):

PARVEEN LATA ◽

IQBAL KAUR

Keyword(s):

Fractional Order ◽

Thermal Stresses ◽

Transversely Isotropic ◽

Order Theory ◽

Two Dimensional ◽

Thermoelastic Material

Download Full-text

2D PROBLEM FOR A SPHERE IN THE FRACTIONAL ORDER THEORY THERMOELASTICITY TO AXISYMMETRIC TEMPERATURE DISTRIBUTION

Advances in Mathematics: Scientific Journal ◽

10.37418/amsj.11.1.1 ◽

2022 ◽

Vol 11 (1) ◽

pp. 1-15

Author(s):

S.G. Khavale ◽

K.R. Gaikwad

Keyword(s):

Temperature Distribution ◽

Fractional Order ◽

Direct Method ◽

Order Theory ◽

Laplace Transform Technique ◽

The Laplace Transform ◽

Copper Material ◽

Mathcad Software ◽

Axisymmetric Temperature ◽

A Direct Method

In the present article, we implement the fractional thermoelasticity theory to a 2D issue for a sphere whose surface is free from traction, subject to a provided axisymmetric temperature distribution of heat. The medium is supposed to be quiescent initially. A direct method is used to get a solution and the Laplace transform technique is used. Mathematical models for copper material are designed as a particular instance. Numerical results are computed with help of Mathcad software and graphically represented and the fractional-order parameter effect has been explained.

Download Full-text

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

Journal of Heat Transfer ◽

10.1115/1.4035442 ◽

2017 ◽

Vol 139 (4) ◽

Cited By ~ 3

Author(s):

S. D. Warbhe ◽

J. J. Tripathi ◽

K. C. Deshmukh ◽

J. Verma

Keyword(s):

Temperature Distribution ◽

Circular Plate ◽

Constant Temperature ◽

Thermal Stresses ◽

Integral Transform ◽

Lower Surface ◽

Order Theory ◽

Displacement Potential ◽

Thin Circular Plate ◽

Static Approach

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.

Download Full-text