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Analysis of thermal responses in a two-dimensional porous medium caused by pulse heat flux

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Abstract

In this article, the generalized model for thermoelastic waves with two relaxation times is utilized to compute the increment of temperature, the displacement components, the stress components, and the changes in the volume fraction field in a two-dimensional porous medium. By using the Fourier-Laplace transform and the eigenvalue method, the considered variables are obtained analytically. The derived approach is estimated with numerical outcomes which are applied to the porous media with a geometrical simplification. The numerical results for the considered variables are performed and presented graphically. Finally, the outcomes are represented graphically to display the difference among the classical dynamical (CD) coupled, the Lord-Shulman (LS), and the Green-Lindsay (GL) models.

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References

  1. BIOT, M. A. General theory of three-dimensional consolidation. Journal of Applied Physics, 12(2), 155–164 (1941)

    Article  Google Scholar 

  2. BIOT, M. A. Theory of propagation of elastic waves in a fluid-saturated porous solid II: higher frequency range. The Journal of the Acoustical Society of America, 28(2), 179–191 (1956)

    Article  MathSciNet  Google Scholar 

  3. LORD, H. W. and SHULMAN, Y. A generalized dynamical theory of thermoelasticity. Journal of the Mechanics and Physics of Solids, 15(5), 299–309 (1967)

    Article  Google Scholar 

  4. GREEN, A. and LINDSAY, K. Thermoelasticity. Journal of Elasticity, 2(1), 1–7 (1972)

    Article  Google Scholar 

  5. BIOT, M. A. Thermoelasticity and irreversible thermodynamics. Journal of Applied Physics, 27(3), 240–253 (1956)

    Article  MathSciNet  Google Scholar 

  6. MARIN, M., VLASE, S., ELLAHI, R., and BHATTI, M. On the partition of energies for the backward in time problem of thermoelastic materials with a dipolar structure. Symmetry, 11(7), 863 (2019)

    Article  Google Scholar 

  7. MARIN, M., ELLAHI, R., and CHIRILA, A. On solutions of Saint-Venant’s problem for elastic dipolar bodies with voids. Carpathian Journal of Mathematics, 33(2), 219–232 (2017)

    MathSciNet  MATH  Google Scholar 

  8. KARAGEORGHIS, A., LESNIC, D., and MARIN, L. A moving pseudo-boundary MFS for void detection in two-dimensional thermoelasticity. International Journal of Mechanical Sciences, 88, 276–288 (2014)

    Article  Google Scholar 

  9. SINGH, B. Wave propagation in a generalized thermoelastic material with voids. Applied Mathematics and Computation, 189(1), 698–709 (2007)

    Article  MathSciNet  Google Scholar 

  10. BACHHER, M., SARKAR, N., and LAHIRI, A. Generalized thermoelastic infinite medium with voids subjected to instantaneous heat sources with fractional derivative heat transfer. International Journal of Mechanical Sciences, 89, 84–91 (2014)

    Article  Google Scholar 

  11. ABBAS, I. A. Nonlinear transient thermal stress analysis of thick-walled FGM cylinder with temperature-dependent material properties. Meccanica, 49(7), 1697–1708 (2014)

    Article  Google Scholar 

  12. MOHAMED, R., ABBAS, I. A., and ABO-DAHAB, S. Finite element analysis of hydromagnetic flow and heat transfer of a heat generation fluid over a surface embedded in a non-Darcian porous medium in the presence of chemical reaction. Communications in Nonlinear Science and Numerical Simulation, 14(4), 1385–1395 (2009)

    Article  Google Scholar 

  13. ABBAS, I. A., EL-AMIN, M., and SALAMA, A. Effect of thermal dispersion on free convection in a fluid saturated porous medium. International Journal of Heat and Fluid Flow, 30(2), 229–236 (2009)

    Article  Google Scholar 

  14. ABBAS, I. A. and KUMAR, R. Deformation due to thermal source in micropolar generalized thermoelastic half-space by finite element method. Journal of Computational and Theoretical Nanoscience, 11(1), 185–190 (2014)

    Article  Google Scholar 

  15. ZENKOUR, A. M. and ABBAS, I. A. Magneto-thermoelastic response of an infinite functionally graded cylinder using the finite element method. Journal of Vibration and Control, 20(12), 1907–1919 (2014)

    Article  MathSciNet  Google Scholar 

  16. EZZAT, M., EL-KARAMANY, A., and EL-BARY, A. Modeling of memory-dependent derivative in generalized thermoelasticity. The European Physical Journal Plus, 131(10), 372 (2016)

    Article  Google Scholar 

  17. SARKAR, N. Wave propagation in an initially stressed elastic half-space solids under time-fractional order two-temperature magneto-thermoelasticity. The European Physical Journal Plus, 132(4), 154 (2017)

    Article  Google Scholar 

  18. EZZAT, M. A. State space approach to unsteady two-dimensional free convection flow through a porous medium. Canadian Journal of Physics, 72(5–6), 311–317 (1994)

    Article  Google Scholar 

  19. ZEESHAN, A., ELLAHI, R., MABOOD, F., and HUSSAIN, F. Numerical study on bi-phase coupled stress fluid in the presence of Hafnium and metallic nanoparticles over an inclined plane. International Journal of Numerical Methods for Heat and Fluid Flow, 29(8), 2854–2869 (2019)

    Article  Google Scholar 

  20. SHEIKHOLESLAMI, M., ELLAHI, R., SHAFEE, A., and LI, Z. Numerical investigation for second law analysis of ferrofluid inside a porous semi annulus: an application of entropy generation and exergy loss. International Journal of Numerical Methods for Heat and Fluid Flow, 29(3), 1079–1102 (2019)

    Article  Google Scholar 

  21. ELLAHI, R., SAIT, S. M., SHEHZAD, N., and AYAZ, Z. A hybrid investigation on numerical and analytical solutions of electro-magnetohydrodynamics flow of nanofluid through porous media with entropy generation. International Journal of Numerical Methods for Heat and Fluid Flow, 30(2), 834–854 (2019)

    Article  Google Scholar 

  22. MILANI-SHIRVAN, K., MAMOURIAN, M., MIRZAKHANLARI, S., RAHIMI, A., and ELLAHI, R. Numerical study of surface radiation and combined natural convection heat transfer in a solar cavity receiver. International Journal of Numerical Methods for Heat and Fluid Flow, 27(10), 2385–2399 (2017)

    Article  Google Scholar 

  23. MILANI-SHIRVAN, K., MAMOURIAN, M., and ELLAHI, R. Numerical investigation and optimization of mixed convection in ventilated square cavity filled with nanofluid of different inlet and outlet port. International Journal of Numerical Methods for Heat and Fluid Flow, 27(9), 2053–2069 (2017)

    Article  Google Scholar 

  24. MARIN, M., BALEANU, D., and VLASE, S. Effect of microtemperatures for micropolar ther-moelastic bodies. Structural Engineering and Mechanics, 61(3), 381–387 (2017)

    Article  Google Scholar 

  25. MARIN, M. and CRACIUN, E. Uniqueness results for a boundary value problem in dipolar ther-moelasticity to model composite materials. Composites Part B: Engineering, 126, 27–37 (2017)

    Article  Google Scholar 

  26. RAMESH, K. and OJJELA, O. Entropy generation analysis of natural convective radiative second grade nanofluid flow between parallel plates in a porous medium. Applied Mathematics and Mechanics (English Edition), 40(4), 481–498 (2019) https://doi.org/10.1007/s10483-019-2464-8

    Article  MathSciNet  Google Scholar 

  27. MONDAL, S., SAHU, S., and PANKAJ, K. Transference of Love-type waves in a bedded structure containing a functionally graded material and a porous piezoelectric medium. Applied Mathematics and Mechanics (English Edition), 40(8), 1083–1096 (2019) https://doi.org/10.1007/s10483-019-2505-6

    Article  Google Scholar 

  28. AFIFY, A. and ELGAZERY, N. Effect of double dispersion on non-Darcy mixed convective flow over vertical surface embedded in porous medium. Applied Mathematics and Mechanics (English Edition), 34(10), 1247–1262 (2013) https://doi.org/10.1007/s10483-013-1742-6

    Article  MathSciNet  Google Scholar 

  29. DAS, N. C., LAHIRI, A., and GIRI, R. R. Eigenvalue approach to generalized thermoelasticity. Indian Journal of Pure and Applied Mathematics, 28(12), 1573–1594 (1997)

    MathSciNet  MATH  Google Scholar 

  30. ABBAS, I. A. The effects of relaxation times and a moving heat source on a two-temperature generalized thermoelastic thin slim strip. Canadian Journal of Physics, 93(5), 585–590 (2015)

    Article  Google Scholar 

  31. STEHFEST, H. Algorithm 368: numerical inversion of Laplace transforms [D5]. Communications of the ACM, 13(1), 47–49 (1970)

    Article  Google Scholar 

  32. OTHMAN, M. I. and MARIN, M. Effect of thermal loading due to laser pulse on thermoelastic porous medium under GN theory. Results in Physics, 7, 3863–3872 (2017)

    Article  Google Scholar 

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Acknowledgements

The authors gratefully acknowledge the technical and financial supports from the Deanship of Scientific Research (DSR), King Abdulaziz University, Jeddah.

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Authors and Affiliations

  1. Nonlinear Analysis and Applied Mathematics (NAAM) Research Group, Department of Mathematics, King Abdulaziz University, Jeddah, 21441, Saudi Arabia

    T. Saeed & I. A. Abbas

  2. Department of Mathematics, Faculty of Science, Sohag University, Sohag, 82524, Egypt

    I. A. Abbas

Authors
  1. T. Saeed
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  2. I. A. Abbas
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Correspondence to I. A. Abbas.

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Citation: SAEED, T. and ABBAS, I. A. Analysis of thermal responses in a two-dimensional porous medium caused by pulse heat flux. Applied Mathematics and Mechanics (English Edition), 41(6), 927–938 (2020) https://doi.org/10.1007/s10483-020-2612-8

Project supported by the Deanship of Scientific Research (DSR), King Abdulaziz University, Jeddah (No. DF-782-130-1441)

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Saeed, T., Abbas, I.A. Analysis of thermal responses in a two-dimensional porous medium caused by pulse heat flux. Appl. Math. Mech.-Engl. Ed. 41, 927–938 (2020). https://doi.org/10.1007/s10483-020-2612-8

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  • DOI: https://doi.org/10.1007/s10483-020-2612-8

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