Numerical investigation of the dusty Williamson fluid with the dependency of time has been done in current disquisition. The flow of multiphase liquid/particle suspension saturating the medium is caused by stretching of porous surface. The influence of magnetic field and heat generation/absorption is observed. It is assumed that particle has a spherical shape and distributed uniformly in fluid matrix. The unsteady two-dimensional problems are modeled for both fluid and particle phase using conservation of mass, momentum and heat transfer. The finalized model generates the non-dimensioned parameters, namely Weissenberg number, unsteadiness parameter, magnetic parameter, heat generation/absorption parameter, Prandtl number, fluid particle interaction parameter, and mass concentration parameters. The numerical solution is obtained. Locality of skin friction and Nusselt number is deliberately focused to help of tables and graphs. While inferencing the current article it is clearly observed that increment of Williamson parameter, unsteadiness parameter, magnetic parameter, volume fraction parameter, and mass concentration parameter reduces the velocity profile of fluid and solid particles as well. And increment of Prandtl number, unsteadiness parameter, volume fraction parameter, and mass concentration parameter reduces the temperature profile of fluid and solid particles as well.
Key words
unsteady flow /
multiphase Williamson fluid /
variable magnetic field /
permeable wall /
heat source/sink
{{custom_keyword}} /
{{custom_sec.title}}
{{custom_sec.title}}
{{custom_sec.content}}
References
[1] P. G. Saffmann, J. Fluid Mech. 13 (1962) 120.
[2] S. L. Soo, The Fluid Dynamics of Multiphase System, Blaisdell (1968).
[3] F. E. Marble, Dynamics of a Gas Containing Small Solid Partials, in:Proceeding of the Fifth AGARD Colloquium Combustion and Propulsion, Pergamon Press, Oxford (1963) 175.
[4] J. T. C. Liu, Phys. Fluids 9 (1966) 1716.
[5] D. H. Michael and D. A. Miller, Mathematika 13 (1966) 97.
[6] S. K. Kumar and L. V. K. V. Sarma, Int. J. Eng. Sci. 29 (1991) 123.
[7] E. Valentini and M. Maiellaro, Arch. Mech. 41 (1990) 759.
[8] S. Naramgari and C. Sulochana, Ain Shams Eng. J. 7 (2016) 709.
[9] N. Sandeep, C. Sulochana, and B. R. Kumar, Int. J. Eng. Sci. Tech. 19 (2016) 227.
[10] R. Sivaraj and B. R. Kumar, Int. J. Heat and Mass Transfer 55 (2012) 3076.
[11] S. Mosayebidorcheh, O. D. Makinde, D. D. Ganji, and M. Abedian Chermahini, Ther. Sci. Eng. Progress 2 (2017) 57.
[12] N. Ijaz, A. Zeeshan, M. M. Bhatti, and Rahmat Ellahi, J. Mol. Liq. 250 (2017), DOI:10.1016/j.molliq.2017.11.123.
[13] R. V. Williamson, Ind. Eng. Chem. Res. 11 (1929) 1108.
[14] I. Zehra, M. M. Yousaf, and S. Nadeem, Results in Phys. 5 (2015) 20.
[15] S. Bilal, K. U. Rehman, M. Y. Malik, and M. Khan, Results in Phys. 7 (2017) 204.
[16] M. Y. Malik, M. Bibi, F. Khan, and T. Salahuddin, AIP Adv. 6 (2016) 035101.
[17] T. Hayat, S. Ahmad, M. I. Khan, and A. Alsaedi, Results in Phys. 8 (2018) 545.
[18] A. M. Siddiqui, S. Bhatti, M. A. Rana, and M. Zahid, Results in Phys. 7 (2017) 2845.
[19] K. U. Rehman, A. A. Khan, M. Y. Malik, and U. Ali, Methods X 4 (2017) 429.
[20] M. Ramzan, M. Bilal, and J. D. Chung, J. Mol. Liq. 225 (2017) 856.
[21] S. Bilal, K. U. Rehman, and M. Y. Malik, Results in Phys. 7 (2017) 690.
[22] M. M. Bhatti and M. M. Rashidi, J. Mol. Liq. 221 (2016)567.
[23] K. G. Kumar, N. G. Rudraswamy, B. J. Gireesha, and S. Manjunatha, Results in Phys. 7 (2017) 3196.
[24] M. Khan and A. Hamid, Results in Phys. 7 (2017) 3968.
[25] A. Hamid, Hashim, and M. Khan, Results in Phys. 9 (2018) 479.
[26] B. J. Gireeshaa, G. K. Ramesh, M. S. Abel, and C. S. Bagewadi, Int. J. Multiphase Flow 37 (2011) 977.
[27] A. Zeeshan, A. Majeed, C. Fetecau, and S. Muhammad, Results in Phys. 7 (2017), DOI:10.1016/j.rinp.2017.08.047.
[28] G. K. Ramesh, B. J. Gireesha, and C. S. Bagewadi, Int. J. Heat and Mass Transfer 55 (2012) 4900.
[29] M. Sheikholeslami and M. M. Bhatti, Int. J. Heat and Mass Transfer 109 (2017) 115.
[30] P. Sharma and C. L. Varshney, Int. J. Heat and Mass Transfer 45 (2003) 2511.
[31] S. Manjunatha and B. J. Gireesha, Ain Shams Eng. J. 7 (2016) 505.
[32] Madiha bibi, Khalil-Ur-Rehman, M. Y. Malik, and M. Tahir, Eur. Phys. J. Plus 133 (2018) 154.
[33] S. Manjunatha, B. J. Gireesha, and C. S. Bagewadi, Int. J. Eng. Sci. Tech. 4 (2012) 36.
[34] N. S. Akbar, S. Nadeem, R. Ul. Haq, and Z. H. Khan, Indian J. Phys. 87 (2013) 1121.
[35] M. Fathizadeh, M. Madani, Y. Khan, N. Faraz, A. Yildirim, and S. Tutkun, J. King Saud University 25 (2013) 107.
{{custom_fnGroup.title_en}}
Footnotes
{{custom_fn.content}}
PDF(1202 KB)
