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Chemically reactive species in squeezed flow through modified Fourier’s and Fick’s laws

  • M. Farooq
  • S. AhmadEmail author
  • M. Javed
  • Aisha Anjum
Regular Article

Abstract.

The squeezing flow of a Newtonian fluid with variable viscosity over a stretchable sheet embedded in Darcy porous medium is addressed. Cattaneo-Christov double diffusion models are adopted to disclose the salient features of heat and mass transport via variable thermal conductivity and variable mass diffusivity instead of conventional Fourier’s and Fick’s laws. Further, the concept of heat generation/absorption coefficient and first-order chemical reaction are also imposed to illustrate the characteristics of heat and mass transfer. Highly nonlinear computations are developed in dimensionless form and analyzed via the homotopic technique. The variation of flow parameters on velocity, concentration, and temperature distributions are sketched and disclosed physically. The results found that both concentration and temperature distributions decay for higher solutal and thermal relaxation parameters, respectively. Moreover, a higher chemical reaction parameter results in the reduction of the concentration field whereas the temperature profile enhances for a higher heat generation/absorption parameter.

References

  1. 1.
    M.J. Stefan, Math.-Nat. Wiss. Kl. 69, 713 (1874)Google Scholar
  2. 2.
    P.S. Gupta, A.S. Gupta, Wear 45, 177 (1977)CrossRefGoogle Scholar
  3. 3.
    M. Mustafa, T. Hayat, S. Obaidat, Meccanica 47, 1581 (2012)MathSciNetCrossRefGoogle Scholar
  4. 4.
    M.S. Kumar, N. Sandeep, B.R. Kumar, Glob. J. Pure Appl. Math. 12, 60 (2016)Google Scholar
  5. 5.
    T. Hayat, M. Khan, T. Muhammad, A. Alsaedi, J. Mol. Liq. 237, 447 (2017)CrossRefGoogle Scholar
  6. 6.
    M.M. Rashidi, M. Babu, M. Jayachandra, N. Sandeep, M.E. Ali, J. Comput. Theor. Nanosci. 13, 8700 (2016)CrossRefGoogle Scholar
  7. 7.
    N. Ahmed, U. Khan, S.I. Khan, Saima Bano, S.T. Mohyud-Din, J. King Saud Univ.-Sci. 29, 119 (2017)CrossRefGoogle Scholar
  8. 8.
    A.G. Madaki, R. Roslan, M.S. Rusiman, C.S.K. Kamardan., Alex. Eng. J.,  https://doi.org/10.1016/j.aej.2017.02.011 (2017)
  9. 9.
    C. Cattaneo, Atti Semin. Mat. Fis. Univ. Modena Reggio Emilia 3, 83 (1948)Google Scholar
  10. 10.
    C.I. Christov, Mech. Res. Commun. 36, 481 (2009)CrossRefGoogle Scholar
  11. 11.
    T. Hayat, S. Qayyum, A. Alsaedi, B. Ahmed, Neural Comput. Appl.  https://doi.org/10.1007/s00521-017-3001-0 (2017)
  12. 12.
    J. Sui, L. Zheng, X. Zhang, Int. J. Therm. Sci. 104, 461 (2016)CrossRefGoogle Scholar
  13. 13.
    M.E. Ali, N. Sandeep, Results Phys. 7, 21 (2017)ADSCrossRefGoogle Scholar
  14. 14.
    J. Li, L. Zheng, L. Liu, J. Mol. Liq. 221, 19 (2016)ADSCrossRefGoogle Scholar
  15. 15.
    M. Waqas, T. Hayat, M. Farooq, S.A. Shehzad, A. Alsaedi, J. Mol. Liq. 220, 642 (2016)CrossRefGoogle Scholar
  16. 16.
    M.Y. Malik, M. Khan, T. Salahuddin, I. Khan, Eng. Sci. Technol. Int. J. 19, 1985 (2016)CrossRefGoogle Scholar
  17. 17.
    N. Samyuktha, R. Ravindran, M. Ganapathirao, J. Appl. Mech. Tech. Phys. 58, 116 (2017)ADSCrossRefGoogle Scholar
  18. 18.
    S. Jena, S.R. Mishra, G.C. Dash, Int. J. Appl. Comput. Math. 3, 1225 (2017)MathSciNetCrossRefGoogle Scholar
  19. 19.
    M.I. Khan, T. Hayat, M. Waqas, M.I. Khan, A. Alsaedi, J. Mol. Liq. 233, 465 (2017)CrossRefGoogle Scholar
  20. 20.
    B.K. Jha, D. Daramola, A.O. Ajibade, Transp. Porous Media 111, 681 (2016)MathSciNetCrossRefGoogle Scholar
  21. 21.
    T. Hayat, M.W.A. Khan, A. Alsaedi, M.I. Khan, Collide Polym. Sci. 295, 967 (2017)CrossRefGoogle Scholar
  22. 22.
    S.J. Liao, The proposed homotopy analysis technique for the solution of non-linear problems, PhD Thesis, Shanghai Jiao Tong University, 1992Google Scholar
  23. 23.
    S.J. Liao, Int. J. Non-Linear Mech. 30, 371 (1995)ADSCrossRefGoogle Scholar
  24. 24.
    S.J. Liao, Beyond Perturbation: Introduction to Homotopy Analysis Method (Chapman and Hall, CRC Press, Boca Raton, 2003)Google Scholar
  25. 25.
    S.J. Liao, Appl. Math. Comput. 147, 499 (2004)MathSciNetGoogle Scholar
  26. 26.
    S.J. Liao, Commun. Nonlinear Sci. Numer. Simul. 15, 2003 (2010)ADSMathSciNetCrossRefGoogle Scholar
  27. 27.
    S.J. Liao, Homotopy Analysis Method in Non-linear Differential Equations (Springer and Higher Education Press, Heidelberg, 2012)Google Scholar
  28. 28.
    S.J. Liao, Int. J. Nonlinear Mech. 34, 759 (1999)ADSCrossRefGoogle Scholar
  29. 29.
    S.J. Liao, J. Fluid Mech. 488, 189 (2003)ADSMathSciNetCrossRefGoogle Scholar
  30. 30.
    S.J. Liao, Int. J. Nonlinear Mech. 42, 819 (2007)ADSCrossRefGoogle Scholar
  31. 31.
    D. Theuri, O.D. Makinde, Appl. Comput. Math. 3, 1 (2014)CrossRefGoogle Scholar
  32. 32.
    M. Farooq, M.I. Ijaz, M. Waqas, T. Hayat, A. Alsaedi, M.I. Khan, J. Mol. Liq. 221, 1097 (2016)CrossRefGoogle Scholar
  33. 33.
    Y. Tan, H. Xu, S.J. Liao, Chaos, Solitons Fractals 31, 462 (2007)ADSMathSciNetCrossRefGoogle Scholar
  34. 34.
    J. Cheng, S.J. Liao, R.N. Mohapatra, K. Vajravelu, J. Math. Anal. Appl. 343, 233 (2008)MathSciNetCrossRefGoogle Scholar
  35. 35.
    M. Ramzan, M. Farooq, T. Hayat, J.D. Chung, J. Mol. Liq. 221, 394 (2016)CrossRefGoogle Scholar
  36. 36.
    V. Ananthaswamy, M. Subha, Int. J. Res. -- Granthaalayah 1, 22 (2014)Google Scholar
  37. 37.
    V. Ananthaswamy, S.U. Maheswari, Int. J. Autom. Control Eng. 4, 67 (2015)Google Scholar
  38. 38.
    T. Hayat, M.I. Khan, M. Farooq, A. Alsaedi, M.I. Khan, Int. J. Heat Mass Transfer 106, 289 (2017)CrossRefGoogle Scholar
  39. 39.
    J. Zhu, D. Yang, L. Zheng, X. Zhang, Appl. Math. Lett. 52, 183 (2016)MathSciNetCrossRefGoogle Scholar
  40. 40.
    M. Farooq, Qurat ul ain Anzar, T. Hayat, M.I. Khan, A. Anjum, Results Phys. 7, 3078 (2017)CrossRefGoogle Scholar
  41. 41.
    Y. Lin, L. Zheng, L. Ma, G. Chen, Int. J. Heat Mass Transfer 84, 903 (2015)CrossRefGoogle Scholar
  42. 42.
    T. Hayat, T. Abbas, M. Ayub, M. Farooq, A. Alsaedi, J. Mol. Liq. 222, 854 (2016)CrossRefGoogle Scholar
  43. 43.
    T. Hayat, M. Waqas, S.A. Shehzad, A. Alsaedi, Eur. Phys. J. Plus 131, 253 (2016)CrossRefGoogle Scholar
  44. 44.
    T. Hayat, I. Ullah, A. Alsaedi, M. Farooq, Results Phys. 7, 189 (2017)ADSCrossRefGoogle Scholar
  45. 45.
    B.R. Sharma, Bismeeta Buragohain, Am. J. Heat Mass Transf. 4, 53 (2017)Google Scholar
  46. 46.
    H.M. El-Hawary, M.A.A. Mahmoud, R.G.A. Rahman, A.S. Elfeshawey, Math. Probl. Eng. 2013, e239847 (2013)CrossRefGoogle Scholar

Copyright information

© Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsRiphah International UniversityIslamabadPakistan

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