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

2017 ◽  
Vol 139 (4) ◽  
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.

scholarly journals Thermal stresses induced by a point heat source in a circular plate by quasi-static approach

2011 ◽  
Vol 1 (3) ◽  
pp. 031007
Author(s):  
K.C. Deshmukh ◽  
Y.I. Quazi ◽  
S.D. Warbhe ◽  
V.S. Kulkarni
Keyword(s):  
Heat Source ◽  
Circular Plate ◽  
Thermal Stresses ◽  
Point Heat Source ◽  
Static Approach

scholarly journals Thermoelastic Behavior Inthin Hollow Cylinder using Internal Moving Heat Source

2019 ◽  
Vol 9 (2) ◽  
pp. 2578-2583
Keyword(s):  
Temperature Distribution ◽  
Heat Source ◽  
Boundary Conditions ◽  
Hollow Cylinder ◽  
Infinite Series ◽  
Thermal Stresses ◽  
Integral Transform ◽  
Elastic Problem ◽  
Moving Heat Source ◽  
Integral Transform Technique

A hollow cylinder having cylindrical hole at the center has been examined under the temperature variation condition. This composition deals with study of temperature distribution in thin hollow cylinder and corresponding stresses. The author has worked to carry out the transient thermo elastic problem for evaluation of temperature distribution, displacement and thermal stresses of a thin hollow cylinder. The known non homogeneous boundary conditions are applied to obtain the solution of this problem. The integral transform technique yields the solution to the problem. The analysis contains an infinite series. The variation of said parameters observed and analyzed by using necessary graphs

Analytical solution for thermal stresses in a hollow cylinder under periodic thermal loading

2011 ◽  
Vol 226 (7) ◽  
pp. 1705-1724 ◽  
Author(s):  
Hamid Mahmoudi ◽  
Gholamali Atefi
Keyword(s):  
Temperature Field ◽  
Fourier Series ◽  
Temperature Distribution ◽  
Analytical Solution ◽  
Hollow Cylinder ◽  
Constant Temperature ◽  
Excellent Agreement ◽  
Thermal Loading ◽  
Thermal Stresses ◽  
Time Varying

The aim of this article is to obtain a comprehensive analytical solution for thermal stresses in a hollow cylinder, subjected to periodic time-varying thermal loading on the inner circular and insulated outer circular surfaces, where both lateral surfaces are kept at constant temperature. Temperature distribution as a function of time, and radial, and longitudinal directions is analytically solved using Fourier series and the resulting thermal stresses are obtained. The proposed method is very comprehensive and covers many theoretical and practical problems. The results for both temperature field and thermal stresses have been compared with those obtained in the former works and show excellent agreement for the same conditions.

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

2020 ◽  
Vol 25 (3) ◽  
pp. 169-180
Author(s):  
S. Thakare ◽  
Y. Panke ◽  
K. Hadke
Keyword(s):  
Temperature Distribution ◽  
Fractional Order ◽  
Heat Supply ◽  
Numerical Evaluation ◽  
Thermal Stresses ◽  
Order Theory ◽  
Curved Surface ◽  
Mathieu Function ◽  
Zero Temperature ◽  
Thermal Deflection

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.

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