Fractional heat conduction in a rectangular plate with bending moments

• Autorzy: Warbhe Shrikant

Identyfikatory

DOI

10.17512/jamcm.2020.4.10

• Języki publikacji: EN

Abstrakty

EN

In this research work, we consider a thin, simply supported rectangular plate defined as 0 ≤ x ≤ a, 0 ≤ y ≤ b, 0 ≤ z ≤ c and determine the thermal stresses by using a thermal bending moment with the help of a time dependent fractional derivative. The constant temperature is prescribed on the surface y = 0 and other surfaces are maintained at zero temperature. A powerful technique of integral transform is used to find the analytical solution of initial-boundary value problem of a thin rectangular plate. The numerical result of temperature distribution, thermal deflection and thermal stress component are computed and represented graphically for a copper plate.

Słowa kluczowe

EN

Mittag-Leffler function; integral transform; fractional partial differential equation; fractional derivatives; fractional integrals

PL

ułamkowe równanie różniczkowe cząstkowe; funkcja Mittag-Lefflera; pochodna ułamkowa; naprężenia termiczne; przewodzenia ciepła; transformata całkowa

• Wydawca: Wydawnictwo Politechniki Częstochowskiej
• Czasopismo: Journal of Applied Mathematics and Computational Mechanics
• Rocznik: 2020
• Tom: Vol. 19, nr 4
• Strony: 115--126
• Opis fizyczny: Bibliogr. 20 poz., rys.

Twórcy

autor

Warbhe Shrikant

• Department of Mathematics, Laxminarayan Institute of Technology, R.T.M.N.U. Nagpur 440033 Maharashtra, India

Bibliografia

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• [4] Deshmukh, K.C., Khandait, M.V., & Kumar, R. (2014). Thermal stresses in a simply supported plate with thermal bending moments with heat sources. Materials Physics and Mechanics, 21, 135-146.
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• [12] Raslan, W.E. (2015). Application of fractional order theory of thermoelasticity in a thick plate under axisymmetric temperature distribution. Journal of Thermal Stresses, 38, 733-743.
• [13] Warbhe, S.D., Tripathi, J.J., Deshmukh, K.C., & Verma, J. (2017). Fractional heat conduction in a thin circular plate with constant temperature distribution and associated thermal stresses. Journal of Heat Transfer, 139, 044502-1 to 044502-4.
• [14] Warbhe, S.D., Tripathi, J.J., Deshmukh, K.C., & Verma, J. (2018). Fractional heat conduction in a thin hollow circular disk and associated thermal deflection. Journal of Thermal Stresses, 41(2), 262-270.
• [15] Tripathi, J.J., Warbhe, S.D., Deshmukh, K.C., & Verma, J. (2017). Fractional order thermoelastic deflection in a thin circular plate. Applications and Applied Mathematics: An International Journal, 12, 898-909.
• [16] Tripathi, J.J., Warbhe, S.D., Deshmukh, K.C., & Verma, J. (2018). Fractional order generalized thermoelastic response in a half space due to a periodically varying heat source. Multidiscipline Modeling in Materials and Structures, 14, 2-15.
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• [20] Povstenko, Y. (2015). Linear Fractional Diffusion-Wave Equation for Scientists and Engineers. New York: Birkhäser.

Uwagi

Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2021).