A numerical study of boundary layer flow of Williamson nanofluid in the presence of viscous dissipation, bioconvection, and activation energy

References

• M. S. Abel, P. G. Siddheshwar, and M. M. Nandeppanavar, “Heat transfer in a viscoelastic boundary layer flow over a stretching sheet with viscous dissipation and non-uniform heat source,” Int. J. Heat Mass Transf., vol. 50, no. 5–6, pp. 960–966, 2007.
   Web of Science ®Google Scholar
• L. J. Crane, “Flow past a stretching plate,” Z. Angew. Math. Phys., vol. 21, no. 4, pp. 645–647, 1970.
   Web of Science ®Google Scholar
• P. S. Gupta and A. S. Gupta, “Heat and mass transfer on a stretching sheet with suction or blowing,” Can. J. Chem. Eng., vol. 55, no. 6, pp. 744–746, 1977.
   Web of Science ®Google Scholar
• I. Pop and T.-Y. Na, “Unsteady flow past a stretching sheet,” Mech. Res. Commun., vol. 23, no. 4, pp. 413–422, 1996.
   Web of Science ®Google Scholar
• R. V. Williamson, “The flow of pseudoplastic materials,” Ind. Eng. Chem., vol. 21, no. 11, pp. 1108–1111, 1929.
   Google Scholar
• R. Kumar, “MHD boundary layer flow on heat and mass transfer over a stretching sheet with slip effect,” J. Nav. Archit. Mar. Eng., vol. 10, no. 2, pp. 109–118, 2013.
   Google Scholar
• N. S. Kumar, R. Kumar, and A. V. Kumar, “Thermal diffusion and chemical reaction effects on unsteady flow past a vertical porous plate with heat source dependent in slip flow regime,” J. Nav. Archit. Mar. Eng., vol. 13, no. 1, pp. 51–62, 2016.
   Web of Science ®Google Scholar
• A. Ishak, Y. Yian Lok, and I. Pop, “ Stagnation-point flow over a shrinking sheet in a micropolar fluid,” Chem. Eng. Commun., vol. 197, no. 11, pp. 1417–1427, 2010.
   Web of Science ®Google Scholar
• W. Ibrahim and B. Shanker, “Unsteady boundary layer flow and heat transfer due to a stretching sheet by quasilinearization technique,” World J. Mech., vol. 1, no. 6, pp. 288–293, 2011.
   Google Scholar
• K. R. Sekhar, G. V. Ramana Reddy, and B. D. C. N. Prasad, “Chemically reacting on MHD oscillatory slip flow in a planer channel with varying temperature and concentration,” Adv. Appl. Sci. Res., vol. 3, no. 5, pp. 2652–2659, 2012.
   Google Scholar
• E. Haile and B. Shankar, “Heat and mass transfer through a porous media of MHD flow of nanofluids with thermal radiation, viscous dissipation and chemical reaction effects,” Am. Chem. Sci. J., vol. 4, no. 6, pp. 828–846, 2014.
   Google Scholar
• F. Ali, M. Saqib, I. Khan, and N. A. Sheikh, “Application of Caputo-Fabrizio derivatives to MHD free convection flow of generalized Walters’-B fluid model,” Eur. Phys. J. Plus, vol. 131, no. 10, pp. 1–10, 2016.
   Web of Science ®Google Scholar
• V. M. Job, S. R. Gunakala, B. R. Kumar, and R. Sivaraj, “Time-dependent hydromagnetic free convection nanofluid flows within a wavy trapezoidal enclosure,” Appl. Therm. Eng., vol. 115, pp. 363–377, 2017.
   Web of Science ®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, pp. 619–625, 2013.
   Web of Science ®Google Scholar
• R. Kandasamy, K. Periasamy, and K. K. Sivagnana Prabhu, “Effects of chemical reaction, heat and mass transfer along a wedge with heat source and concentration in the presence of suction or injection,” Int. J. Heat Mass Transf., vol. 48, no. 7, pp. 1388–1394, 2005.
   Web of Science ®Google Scholar
• O. D. Makinde, P. O. Olanrewaju, and W. M. Charles, “Unsteady convection with chemical reaction and radiative heat transfer past a flat porous plate moving through a binary mixture,” Afr. Mat., vol. 22, no. 1, pp. 65–78, 2011.
   Google Scholar
• M. Rafiq, H. Yasmin, T. Hayat, and F. Alsaadi, “Effect of Hall and ion-slip on the peristaltic transport of nanofluid: A biomedical application,” Chinese J. Phys., vol. 60, pp. 208–227, 2019.
   Web of Science ®Google Scholar
• I. Tlili, W. A. Khan, and K. Ramadan, “ MHD flow of nanofluid flow across horizontal circular cylinder: Steady forced convection,” J. Nanofluids, vol. 8, no. 1, pp. 179–186, 2019.
   Web of Science ®Google Scholar
• N. A. Alreshidi et al., “Brownian motion and thermophoresis effects on MHD three dimensional nanofluid flow with slip conditions and Joule dissipation due to porous rotating disk,” Molecules, vol. 25, no. 3, pp. 729, 2020.
   PubMed Web of Science ®Google Scholar
• J. U. Rahman et al., “Numerical simulation of Darcy–Forchheimer 3D unsteady nanofluid flow comprising carbon nanotubes with Cattaneo–Christov heat flux and velocity and thermal slip conditions,” Processes, vol. 7, no. 10, pp. 687, 2019.
   Web of Science ®Google Scholar
• Hamid, A. Hashim, M. Khan, and M. Alghamdi, “MHD Blasius flow of radiative Williamson nanofluid over a vertical plate,” Int. J. Mod. Phys. B, vol. 33, no. 22, pp. 1950245, 2019.
   Web of Science ®Google Scholar
• L. A. Lund, Z. Omar, and I. Khan, “Analysis of dual solution for MHD flow of Williamson fluid with slippage,” Heliyon, vol. 5, no. 3, pp. e01345, 2019. DOI: 10.1016/j.heliyon.2019.e01345.
   PubMed Web of Science ®Google Scholar
• A. Hamid and M. Khan, “Transient flow and heat transfer mechanism for Williamson-nanomaterials caused by a stretching cylinder with variable thermal conductivity,” Microsyst. Technol., vol. 25, no. 9, pp. 3287–3297, 2019.
   Web of Science ®Google Scholar
• S. U. Khan and S. A. Shehzad, “Brownian movement and thermophoretic aspects in third-grade nanofluid over oscillatory moving sheet,” Phys. Scr., vol. 94, no. 9, pp. 095202, 2019.
   Web of Science ®Google Scholar
• G. Kalpana, K. R. Madhura, and S. S. Iyengar, “ Numerical computation on Marangoni convective flow of two-phase MHD dusty nanofluids under Brownian motion and thermophoresis effects,” Heat Transf.—Asian Res., vol. 49, no. 1, pp. 626–650, 2020.
   Web of Science ®Google Scholar
• S. A. Khan, Y. Nie, and B. Ali, “ Multiple slip effects on MHD unsteady viscoelastic nano-fluid flow over a permeable stretching sheet with radiation using the finite element method,” SN Appl. Sci., vol. 2, no. 1, pp. 1–14, 2020.
   Web of Science ®Google Scholar
• B. Ali, S. Hussain, S. I. R. Naqvi , D. Habib , and S. Abdal. “Aligned magnetic and bioconvection effects on tangent hyperbolic nanofluid flow across faster/slower stretching wedge with activation energy: Finite element simulation,” Int. J. Appl. Comput. Math., vol. 7, no. 4, pp. 1–20, 2021.
   Google Scholar
• B. Ali, G. Rasool, S. Hussain, D. Baleanu, and S. Bano, “Finite element study of magnetohydrodynamics (MHD) and activation energy in Darcy–Forchheimer rotating flow of Casson Carreau nanofluid,” Processes, vol. 8, no. 9, pp. 1185, 2020.
   Web of Science ®Google Scholar
• B. Ali, Y. Nie, S. Hussain, D. Habib, and S. Abdal, “Insight into the dynamics of fluid conveying tiny particles over a rotating surface subject to Cattaneo–Christov heat transfer, Coriolis force, and Arrhenius activation energy,” Comput. Math. Appl., vol. 93, pp. 130–143, 2021.
   Web of Science ®Google Scholar
• B. Ali, I. Siddique, I. Khan, B. Masood, and S. Hussain, “Magnetic dipole and thermal radiation effects on hybrid base micropolar CNTs flow over a stretching sheet: Finite element method approach,” Res. Phys., vol. 25, pp. 104145, 2021.
   Google Scholar
• K. Sadiq, F. Jarad, I. Siddique, and B. Ali, “Soret and radiation effects on mixture of ethylene glycol-water (50%-50%) based Maxwell nanofluid flow in an upright channel,” Complexity, 2021.
   Web of Science ®Google Scholar
• S. Ershkov and D. Leshchenko, “Solving procedure for the dynamics of charged particle in variable (time-dependent) electromagnetic field,” Z. Angew. Math. Phys., vol. 71, no. 3, pp. 1–8, 2020.
   Web of Science ®Google Scholar
• M. I. Khan, F. Haq, S. A. Khan, T. Hayat, and M. I. Khan, “Development of thixotropic nanomaterial in fluid flow with gyrotactic microorganisms, activation energy, mixed convection,” Comput. Methods Prog. Biomed., vol. 187, pp. 105186, 2020.
   PubMed Web of Science ®Google Scholar
• M. I. Khan, A. Alsaedi, S. Qayyum, T. Hayat, and M. I. Khan, “Entropy generation optimization in flow of Prandtl–Eyring nanofluid with binary chemical reaction and Arrhenius activation energy,” Colloids Surf. A: Physicochem. Eng. Asp., vol. 570, pp. 117–126, 2019.
   Web of Science ®Google Scholar
• M. I. Khan et al., “Salient aspects of entropy generation optimization in mixed convection nanomaterial flow,” Int. J. Heat Mass Transf., vol. 126, pp. 1337–1346, 2018.
   Web of Science ®Google Scholar
• T. Gul et al., “Magnetic dipole impact on the hybrid nanofluid flow over an extending surface,” Sci. Rep., vol. 10, no. 1, pp. 1–13, 2020.
   PubMed Web of Science ®Google Scholar
• A. Khan et al., “Bio-convective micropolar nanofluid flow over thin moving needle subject to Arrhenius activation energy, viscous dissipation and binary chemical reaction,” Case Stud. Therm. Eng., vol. 25, pp. 100989, 2021.
   Web of Science ®Google Scholar
• M. Khan, “On Cattaneo–Christov heat flux model for Carreau fluid flow over a slendering sheet,” Res. Phys., vol. 7, pp. 310–319, 2017.
   Google Scholar
• M. I. Khan, F. Alzahrani, A. Hobiny, and Z. Ali, “ Modeling of Cattaneo-Christov double diffusions (CCDD) in Williamson nanomaterial slip flow subject to porous medium,” J. Mater. Res. Technol., vol. 9, no. 3, pp. 6172–6177, 2020.
   Google Scholar
• R. J. Gowda, R. Naveen Kumar, A. Rauf, B. C. Prasannakumara, and S. A. Shehzad, “Magnetized flow of Sutterby nanofluid through Cattaneo-Christov theory of heat diffusion and Stefan blowing condition,” Appl. Nanosci., vol. 13, pp. 585–594, 2023.
   Web of Science ®Google Scholar
• A. J. Christopher, N. Magesh, R. J. P. Gowda, R. N. Kumar, and R. S. V. Kumar, “Hybrid nanofluid flow over a stretched cylinder with the impact of homogeneous–heterogeneous reactions and Cattaneo–Christov heat flux: Series solution and numerical simulation,” Heat Transf., vol. 50, no. 4, pp. 3800–3821, 2021.
   Google Scholar
• A. U. Yahya et al., “Implication of Bio-convection and Cattaneo-Christov heat flux on Williamson Sutterby nanofluid transportation caused by a stretching surface with convective boundary,” Chinese J. Phys., vol. 73, pp. 706–718, 2021.
   Web of Science ®Google Scholar
• M. Wakeel Ahmad, L. B. McCash, Z. Shah, and R. Nawaz, “Cattaneo-Christov heat flux model for second grade nanofluid flow with Hall effect through entropy generation over stretchable rotating disk,” Coatings, vol. 10, no. 7, pp. 610, 2020.
   Web of Science ®Google Scholar
• M. Waqas, T. Hayat, M. Farooq, S. A. Shehzad, and A. Alsaedi, “Cattaneo-Christov heat flux model for flow of variable thermal conductivity generalized Burgers fluid,” J. Mol. Liq., vol. 220, pp. 642–648, 2016.
   Web of Science ®Google Scholar
• A. Hamid and M. Khan, “Heat and mass transport phenomena of nanoparticles on time-dependent flow of Williamson fluid towards heated surface,” Neural Comput. Appl., vol. 32, no. 8, pp. 3253–3263, 2020.
   Web of Science ®Google Scholar
• A. Hamid and M. Khan, “Impacts of binary chemical reaction with activation energy on unsteady flow of magneto-Williamson nanofluid,” J. Mol. Liq., vol. 262, pp. 435–442, 2018.
   Web of Science ®Google Scholar
• M. Khan and A. Hamid, “Effects of thermal radiation and slip mechanism on mixed convection flow of Williamson nanofluid over an inclined stretching cylinder,” Commun. Theor. Phys., vol. 71, no. 12, pp. 1405, 2019.
   Web of Science ®Google Scholar
• H. D. Hunegnaw, “Unsteady boundary layer flow of Williamson nanofluids over a heated permeable stretching sheet embedded in porous medium in the presence of viscous dissipation,” J. Nav. Archit. Mar. Eng., vol. 18, no. 1, pp. 83–96, 2021.
   Web of Science ®Google Scholar
• R. Sajjad, M. Mushtaq, S. Farid, K. Jabeen, and R. M. A. Muntazir, “Numerical simulations of magnetic dipole over a nonlinear radiative eyring–Powell nanofluid considering viscous and ohmic dissipation effects,” Math. Probl. Eng., vol. 2021, pp. 1–6. 2021.
   Google Scholar
• A. Shaukat, M. Mushtaq, S. Farid, K. Jabeen, and R. M. A. Muntazir, “A study of magnetic/nonmagnetic nanoparticles fluid flow under the influence of nonlinear thermal radiation,” Math. Probl. Eng., vol. 2021, pp. 1–5. 2021.
   Google Scholar
• K. Jabeen, M. Mushtaq, and R. M. Akram Muntazir, “Analysis of magnetic and non magnetic nanoparticles with Newtonian/non-Newtonian base fluids over a nonlinear stretching sheet.” Proc. Inst. Mech. Eng. C: J. Mech. Eng. Sci., 2023.
   Google Scholar
• S. Ashraf, M. Mushtaq, K. Jabeen, S. Farid, and R. M. A. Muntazir, “Heat and mass transfer of unsteady mixed convection flow of Casson fluid within the porous media under the influence of magnetic field over a nonlinear stretching sheet,” Proc. Inst. Mech. Eng. C: J. Mech. Eng. Sci., vol. 237, no. 1, pp. 20–38, 2023.
   Google Scholar
• R. M. Muntazir, M. Mushtaq, and K. Jabeen, “A numerical study of MHD carreau nanofluid flow with gyrotactic microorganisms over a plate, wedge, and stagnation point,” Math. Probl. Eng., 2021.
   Web of Science ®Google Scholar
• K. Sharma, N. Vijay, and S. Kumar, “Significance of geothermal viscosity and heat generation/absorption on magnetic nanofluid flow and heat transfer,” Numer. Heat Transf.: Appl., vol. 82, no. 3, 70–81, 2022.
   Google Scholar
• M. M. Biswal, K. Swain, G. C. Dash, and K. Ojha, “Study of radiative magneto-non-Newtonian fluid flow over a nonlinearly elongating sheet with Soret and Dufour effects,” Numer. Heat Transf.: Appl., vol. 83, no. 4, pp. 331–342.
   Google Scholar
• J. Hasnain and N. Abid, “Numerical investigation for thermal growth in water and engine oil-based ternary nanofluid using three different shaped nanoparticles over a linear and nonlinear stretching sheet,” Numer. Heat Transf.: Appl., Jul 23, pp. 1–2, 2022.
   Google Scholar
• M. I. Khan, S. A. Khan, T. Hayat, M. I. Khan, and A. Alsaedi, “Nanomaterial based flow of Prandtl-Eyring (non-Newtonian) fluid using Brownian and thermophoretic diffusion with entropy generation,” Comput. Methods Prog. Biomed., vol. 180, pp. 105017, 2019.
   Google Scholar