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Портал Begell Электронная Бибилиотека e-Книги Журналы Справочники и Сборники статей Коллекции
Computational Thermal Sciences: An International Journal
ESCI SJR: 0.249 SNIP: 0.434 CiteScore™: 1.4

ISSN Печать: 1940-2503
ISSN Онлайн: 1940-2554

Computational Thermal Sciences: An International Journal

DOI: 10.1615/ComputThermalScien.2020033642
pages 233-248

MATHEMATICAL MODEL FOR THERMOELASTIC POROUS SPHERICAL REGION PROBLEMS

Eman M. Hussein
Department of Mathematics, Faculty of Science, University of Damanhur, Damanhur, Egypt

Краткое описание

This study investigates the thermal stresses and temperatures during a porous spherical region hydrous with liquid. The general solution is obtained within the Laplace transform domain. The resulting formulation is used to resolve two issues for a solid sphere and a thick spherical shell. The impact of time on a solid sphere and the impact of porosity on a thick spherical shell are analyzed through graphs. A comparison is formed with a solid sphere with identical configuration within absence of the fluid. It was found that the existence of fluid decreased the temperature and displacement, whereas the opposite behavior is observed for stress.

ЛИТЕРАТУРА

  1. Alzahran, F. and Abbas, I., Fractional Order Photo-Thermoelastic Interaction in a Semiconducting Media Containing a Spherical Cavity Subjected to Pulse Heat Flux, J. Adv. Phys, vol. 6, pp. 470-476,2017.

  2. Biot, M., General Solutions of the Equations of Elasticity and Consolidation of a Porous Material, J. Appl. Mech, vol. 23, pp. 91-103,1956.

  3. Biot, M., Theory of Elasticity and Consolidation for a Porous Anisotropic Solid, J. Appl. Phys., vol. 26, pp. 182-198,1955.

  4. Biot, M., Theory of Propagation of Elastic Waves in Fluid-Saturated Porous Solid, J. Acoust. Soc. Am., vol. 28, pp. 168-171,1956.

  5. Ehlers, N. andBluhm, J., Porous Media Theory Experiments and Numerical Application, Berlin, Germany: Springer, 2002.

  6. George, F. and William, G., Essentials of Multiphase Flow and Transport in Porous Media, New York: John Wiley and Sons, Inc., 2008.

  7. Hasheminejad, M., Modal Impedances for a Spherical Source in a Fluid-Filled Spherical Cavity Embedded within a Fluid-Infiltrated Elastic Porous Medium, Int. J. Solid Struct., vol. 35, pp. 129-148,1998.

  8. Hussein, E., Effect of the Porosity on a Porous Plate Saturated with a Liquid and Subjected to a Sudden Change in Temperatures, Acta Mech., vol. 229, pp. 2431-2444,2018.

  9. Hussein, E., Problem in Poroelastic Media for an Infinitely Long Solid Circular Cylinder with Thermal Relaxation, Transp. Porous Media, vol. 106, pp. 145-161,2015.

  10. Mercer, G. and Barry, S., Flow and Deformation in Poroelasticity-II Numerical Method, Math. Comput. Modell, vol. 30, pp. 31-38,1999.

  11. Mittal, G. and Kulkarni, S., Two Temperature Fractional Order Thermoelasticity Theory in a Spherical Domain, J. Therm. Stresses, vol. 42, pp. 1136-1152,2019.

  12. Pecker, C. and Deresiewicz, H., Thermal Effects on Wave Propagation in Liquid-Filled Porous Media, Acta Mech., vol. 16, pp. 45-64,1973.

  13. Raslan, E., Application of Fractional Order Theory of Thermoelasticity to a 1D Problem for a Spherical Shell, J. Theoretical and Appl. Mech, vol. 54, pp. 295-304,2016.

  14. Reddy, P. and Tajuddin, M., Exact Analysis of the Plane-Strain Vibrations of Thick-Walled Hollow Poroelastic Cylinders, Int. J. Solid Struct., vol. 37, pp. 3439-3456,2000.

  15. Shahani, A. and Bashusqeh, S., Analytical Solution of the Thermoelasticity Problem in a Pressurized Thick-Walled Sphere Subjected to Transient Thermal Loading, Math. Mech. Solids, vol. 19, pp. 135-151,2012.

  16. Shanker, B., Manoj, J., Shah, S., and Nath, N., Radial Vibrations of an Infinitely Long Poroelastic Composite Hollow Circular Cylinder, Int. J. of Eng. Sci. and Tech., vol. 4, pp. 17-33,2012.

  17. Sherief, H. and Dhaliwal, R., A Generalized One-Dimensional Thermal Shock Problem for Small Times, J. Therm. Stresses, vol. 4, pp. 407-420,1981.

  18. Sherief, H. and Hamza, F., Axisymmetric Generalized Thermoelasticity Problems in Spherical Regions, in Encyclopedia of Thermal Stresses, Berlin, Germany: Springer Verlag, pp. 281-289,2014.

  19. Sherief, H. and Hamza, F., Generalized Two-Dimensional Thermoelastic Problems in Spherical Regions under Axisymmetric Distributions, J. Therm. Stresses, vol. 19, pp. 55-76,1996.

  20. Sherief, H. and Hussein, E., A Mathematical Model for Short-Time Filtration in Poroelastic Media with Thermal Relaxation and Two Temperatures, Transp. Porous Media, vol. 91, pp. 199-223,2012.

  21. Sherief, H. and Hussein, E., Contour Integration Solution for a Thermoelastic Problem of a Spherical Cavity, Appl. Math. Comput., vol. 320, pp. 557-571,2018.

  22. Sherief, H. and Hussein, E., Fundamental Solution of Thermoelasticity with Two Relaxation Times for an Infinite Spherically Symmetric Space, Z. Angew. Math. Phys, vol. 68, pp. 1-14,2017.

  23. Sherief, H. and Hussein, E., The Effect of Fractional Thermoelasticity on Two-Dimensional Problems in Spherical Regions under Axisymmetric Distributions, J. Therm. Stresses, vol. 43, pp. 440-455,2020.

  24. Sherief, H. and Megahed, F., Two-Dimensional Problems for Thermoelasticity with Two Relaxation Times in Spherical Regions under Axisymmetric Distributions, Int. J. Eng. Sci., vol. 37, pp. 299-314,1999.

  25. Singh, B. and Kumar, R., Reflection and Refraction of Micropolar Elastic Waves at an Interface between Liquid-Saturated Porous Solid and Micropolar Elastic Solid, Proc. Nat. Acad. Sci, vol. 70, pp. 397-410,2000.

  26. Spiegel, M., Mathematical Handbook, New York: McGraw-Hill, 1956.

  27. Tajuddin, M. and Shah, S., Longitudinal Shear Vibrations of Composite Poroelastic Cylinders, Int. J. Eng. Sci. and Tech., vol. 3, pp. 22-33,2011.

  28. Tajuddin, M., Nageswara, N., and Manoj, J., Axial-Shear Vibrations of an Infinitely Long Poroelastic Composite Circular Cylinder, Special Topics and Rev. in Porous Media, An Int. J, vol. 2, pp. 133-143,2011.

  29. Xiong, X., Xiao, R., and Tian, O., Effect of Initial Stress on a Fiber-Reinforced Thermoelastic Porous Media without Energy Dissipation, Transp. Porous Media, vol. 111, pp. 81-95,2016.


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