Nonsimilar stagnation flow of Williamson fluid over an isothermal linearly stretched sheet

References

• R. V. Williamson, “The flow of pseudoplastic materials,” Ind. Eng. Chem., vol. 21, no. 11, pp. 1108–1111, Nov. 1929. DOI: 10.1021/ie50239a035.
   Google Scholar
• F. Yilmaz and M. Y. Gundogdu, “A critical review on blood flow in large arteries; relevance to blood rheology, viscosity models, and physiologic conditions,” Korea-Aust. Rheol. J., vol. 20, no. 4, pp. 197–211, Dec. 2008.
   Web of Science ®Google Scholar
• H. A. Barnes, J. F. Hutton, and K. Walters, “An introduction to rheology,” in Rheology Series, vol. 3. Elsevier, 1989.
   Google Scholar
• S. Nadeem, S. T. Hussain, and C. Lee, “Flow of a Williamson fluid over a stretching sheet,” Braz. J. Chem. Eng., vol. 30, no. 3, pp. 619–625, Sept. 2013. DOI: 10.1590/S0104-66322013000300019.
   Web of Science ®Google Scholar
• I. Zehra, M. M. Yousaf, and S. Nadeem, “Numerical solutions of Williamson fluid with pressure dependent viscosity,” Res. Phys., vol. 5, no. 1, pp. 20–25, Jan. 2015. DOI: 10.1016/j.rinp.2014.12.002.
   Google Scholar
• T. Salahuddin, M. Y. Malik, A. Hussain, S. Bilal, and M. Awais, “MHD flow of Cattanneo–Christov heat flux model for Williamson fluid over a stretching sheet with variable thickness: Using numerical approach,” J. Magn. Magn. Mater., vol. 401, pp. 991–997, Mar. 2016. DOI: 10.1016/j.jmmm.2015.11.022.
   Web of Science ®Google Scholar
• M. R. Krishnamurthy, B. C. Prasannakumara, B. J. Gireesha, and R. S. R. Gorla, “Effect of chemical reaction on MHD boundary layer flow and melting heat transfer of Williamson nanofluid in porous medium,” Eng. Sci. Technol. Int. J., vol. 19, no. 1, pp. 53–61, Mar. 2016. DOI: 10.1016/j.jestch.2015.06.010.
   Google Scholar
• A. Zaib, K. Bhattacharyya, M. Khalid, and S. Shafie, “Thermal radiation effect on a mixed convection flow and heat transfer of the Williamson fluid past an exponentially shrinking permeable sheet with a convective boundary condition,” J. Appl. Mech. Tech. Phys., vol. 58, no. 3, pp. 419–424, May 2017. DOI: 10.1134/S0021894417030063.
   Web of Science ®Google Scholar
• M. Bibi, M. Y. Malik, M. Tahir, and Khalil-Ur-Rehman, “Numerical study of unsteady Williamson fluid flow and heat transfer in the presence of MHD through a permeable stretching surface,” Eur. Phys. J. Plus, vol. 133, no. 4, pp. 1–15, Apr. 2018. DOI: 10.1140/epjp/i2018-11991-2.
   Web of Science ®Google Scholar
• Y. X. Li et al., “Heat and mass transfer in MHD Williamson nanofluid flow over an exponentially porous stretching surface,” Case Stud. Therm. Eng., vol. 26, no. 1, pp. 100975, Aug. 2021. DOI: 10.1016/j.csite.2021.100975.
   Google Scholar
• K. Ahmed, L. B. McCash, T. Akbar, and S. Nadeem, “Effective similarity variables for the computations of MHD flow of Williamson nanofluid over a non-linear stretching surface,” Processes, vol. 10, no. 6, pp. 1119, Jun. 2022. DOI: 10.3390/pr10061119.
   Web of Science ®Google Scholar
• M. Khan and A. Shahzad, “On stagnation point flow of Sisko fluid over a stretching sheet,” Meccanica, vol. 48, no. 10, pp. 2391–2400, Dec. 2013. DOI: 10.1007/s11012-013-9755-2.
   Web of Science ®Google Scholar
• M. Y. Malik, A. Hussain, T. Salahuddin, and M. Awais, “Effects of viscous dissipation on MHD boundary layer flow of Sisko fluid over a stretching cylinder,” AIP Adv., vol. 6, no. 3, pp. 035009, Mar. 2016. DOI: 10.1063/1.4944347.
   Web of Science ®Google Scholar
• M. KhanHashim, “On Cattaneo–Christov heat flux model for Carreau fluid flow over a slendering sheet,” Res. Phys., vol. 7, no. 1, pp. 310–319, Jan. 2017. DOI: 10.1016/j.rinp.2016.12.031.
   Google Scholar
• A. Pantokratoras, “A common error made in investigation of boundary layer flows,” Appl. Math. Model., vol. 33, no. 1, pp. 413–422, Jan. 2009. DOI: 10.1016/j.apm.2007.11.009.
   Web of Science ®Google Scholar
• A. Pantokratoras, “Four usual errors made in investigation of boundary layer flows,” Powder Technol., vol. 353, no. 15, pp. 505–508, Jul. 2019. DOI: 10.1016/j.powtec.2019.05.060.
   Google Scholar
• A. Pantokratoras, “The nonsimilar laminar wall plume in a constant transverse magnetic field,” Int. J. Heat Mass Transf., vol. 52, no. 15–16, pp. 3873–3878, Jul. 2009. DOI: 10.1016/j.ijheatmasstransfer.2009.03.002.
   Web of Science ®Google Scholar
• A. Pantokratoras, “Non-similar Blasius and Sakiadis flow of a non-Newtonian Carreau fluid,” J. Taiwan Inst. Chem. Eng., vol. 56, no. 1, pp. 1–5, Nov. 2015. DOI: 10.1016/j.jtice.2015.03.021.
   Google Scholar
• A. Pantokratoras, “Blasius and Sakiadis flow with suction and non-linear Rosseland thermal radiation,” Int. J. Thermofluids, vol. 10, no. 1, pp. 100067, May 2021. DOI: 10.1016/j.ijft.2021.100067.
   Google Scholar
• B. S. Goud, P. P. Kumar, and B. S. Malga, “Effect of heat source on an unsteady MHD free convection flow of Casson fluid past a vertical oscillating plate in porous medium using finite element analysis,” Partial Differ. Equ. Appl. Math., vol. 2, pp. 100015, Dec. 2020. DOI: 10.1016/j.padiff.2020.100015.
   Google Scholar
• P. P. Kumar, B. S. Goud, and B. S. Malga, “Finite element study of Soret number effects on MHD flow of Jeffrey fluid through a vertical permeable moving plate,” Partial Differ. Equ. Appl. Math., vol. 1, pp. 100005, Sept. 2020. DOI: 10.1016/j.padiff.2020.100005.
   Google Scholar
• B. S. Goud and M. N. R. Shekar, “Finite element study of Soret and radiation effects on mass transfer flow through a highly porous medium with heat generation and chemical reaction,” Int. J. Comput. Appl. Math., vol. 12, no. 1, pp. 53–64, 2017.
   Google Scholar
• B. S. Goud and M. N. R. Shekar, “Finite element solution of viscous dissipative effects on unsteady MHD flow past a parabolic started vertical plate with mass diffussion and variable temperature,” i-Manag. J. Math., vol. 7, no. 1, pp. 18–25, 2018.
   Google Scholar
• R. J. Moreau, Magnetohydrodynamics, vol. 3. Kluwer Academic Publishers, 1990.
   Google Scholar
• G. R. Rajput, B. P. Jadhav, V. S. Patil, and S. N. Salunkhe, “Effects of nonlinear thermal radiation over magnetized stagnation point flow of Williamson fluid in porous media driven by stretching sheet,” Heat Transf., vol. 50, no. 3, pp. 2543–2557, 2021. DOI: 10.1002/htj.21991.
   Google Scholar
• M. Mustafa, T. Hayat, I. Pop, S. Asghar, and S. Obaidat, “Stagnation-point flow of a nanofluid towards a stretching sheet,” Int. J. Heat Mass Transf., vol. 54, no. 25–26, pp. 5588–5594, 2011. DOI: 10.1016/j.ijheatmasstransfer.2011.07.021.
   Web of Science ®Google Scholar
• S. Larsson and V. Thomee, Partial Differential Equations with Numerical Methods, vol. 45. Berlin: Springer, 2008.
   Google Scholar
• K. W. Morton and D. F. Mayers, Numerical Solution of Partial Differential Equations: An Introduction. Cambridge: Cambridge Univ. Press, 1995.
   Google Scholar
• I. Shingareva and C. Lizarraga-Celaya, Solving Nonlinear Partial Differential Equations with Maple and Mathematica. Wien New York: Springer, 2011.
   Google Scholar
• A. Pantokratoras, “A note on MHD Blasius flow,” Acta Mech., vol. 226, no. 4, pp. 1305–1308, Apr. 2015. DOI: 10.1007/s00707-014-1242-x.
   Web of Science ®Google Scholar
• S. V. Patankar, Numerical Heat Transfer and Fluid Flow. New York, NY, USA: McGraw-Hill, 1980.
   Google Scholar
• P. P. Humane, V. S. Patil, A. B. Patil, M. D. Shamshuddin, and G. R. Rajput, “Dynamics of multiple slip boundaries effect on MHD Casson-Williamson double-diffusive nanofluid flow past an inclined magnetic stretching sheet,” Proc. Inst. Mech. Eng. E: J. Process Mech. Eng., vol. 236, no. 5, pp. 1906–1926, 2022. DOI: 10.1177/09544089221078153.
   Web of Science ®Google Scholar
• T. Srinivasulu and B. S. Goud, “Effect of inclined magnetic field on flow, heat and mass transfer of Williamson nanofluid over a stretching sheet,” Case Stud. Therm. Eng., vol. 23, pp. 100819, 2021. DOI: 10.1016/j.csite.2020.100819.
   Web of Science ®Google Scholar
• S. G. Bejawada, Z. H. Khan, and M. Hamid, “Heat generation/absorption on MHD flow of a micropolar fluid over a heated stretching surface in the presence of the boundary parameter,” Heat Transf., vol. 50, no. 6, pp. 6129–6147, 2021. DOI: 10.1002/htj.22165.
   Google Scholar
• G. B. Shankar and M. M. Nandeppanavar, “Ohmic heating and chemical reaction effect on MHD flow of micropolar fluid past a stretching surface,” Partial Differ. Equ. Appl. Math., vol. 4, pp. 100104, 2021. DOI: 10.1016/j.padiff.2021.100104.
   Google Scholar
• P. P. Humane, V. S. Patil, M. D. Shamshuddin, G. R. Rajput, and A. B. Patil, “Role of bioconvection on the dynamics of chemically active Casson nanofluid flowing via an inclined porous stretching sheet with convective conditions,” Int. J. Model. Simul., pp. 1–20, Jan. 2023. DOI: 10.1080/02286203.2022.2164156.
   Google Scholar