The flow analysis of Williamson nanofluid considering the Thompson and Troian slip conditions at the boundary

References

• R. Saidur, K. Y. Leong, and H. A. Mohammed, “A review on applications and challenges of nanofluids,” Renew. Sustain. Energy Rev., vol. 15, no. 3, pp. 1646–1668, 2011. DOI: 10.1016/j.rser.2010.11.035.
   Web of Science ®Google Scholar
• Z. Said et al., “Recent advances on the fundamental physical phenomena behind stability, dynamic motion, thermophysical properties, heat transport, applications, and challenges of nanofluids,” Phys. Rep., vol. 946, pp. 1–94, 2022. DOI: 10.1016/j.physrep.2021.07.002.
   Web of Science ®Google Scholar
• H.-X. Bao et al., “Boundary-layer flow of heat and mass for tiwari-das nanofluid model over a flat plate with variable wall temperature,” Therm. Sci., vol. 26, no. Spec. Issue 1, pp. 39–47, 2022. DOI: 10.2298/TSCI22S1039B.
   Google Scholar
• A. M. Alqahtani et al., “Thermal analysis of a radiative nanofluid over a stretching/shrinking cylinder with viscous dissipation,” Chem. Phys. Lett., vol. 808, pp. 140133, 2022. DOI: 10.1016/j.cplett.2022.140133.
   Web of Science ®Google Scholar
• V. Puneeth, E. H. Aly, and I. Pop, “Nanofluid flowing over a rotating disk that is stretching and permeable: An unsteady model,” Int. J. Mod. Phys. B, pp. 2350249, 2023. DOI: 10.1142/S0217979223502491.
   Web of Science ®Google Scholar
• F. Wang et al., “Heat and mass transfer of Ag- H2O nano-thin film flowing over a porous medium: A modified Buongiorno’s model,” Chin. J. Phys., 2023. DOI: 10.1016/j.cjph.2023.01.001.
   Web of Science ®Google Scholar
• U. Khan et al., “A novel analysis of heat transfer in the nanofluid composed by nanodimaond and silver nanomaterials: Numerical investigation,” Sci. Rep., vol. 12, no. 1, pp. 1284, 2022. DOI: 10.1038/s41598-021-04658-x.
   PubMed Web of Science ®Google Scholar
• R. Du, D. Jiang, Y. Wang, and K. Wei Shah, “An experimental investigation of CuO/water nanofluid heat transfer in geothermal heat exchanger,” Energy Build., vol. 227, pp. 110402, 2020. DOI: 10.1016/j.enbuild.2020.110402.
   Web of Science ®Google Scholar
• Z. Li, M. Sheikholeslami, A. S. Mittal, A. Shafee, and R. Ul Haq, “Nanofluid heat transfer in a porous duct in the presence of Lorentz forces using the lattice Boltzmann method,” Eur. Phys. J. Plus, vol. 134, no. 1, 2019. DOI: 10.1140/epjp/i2019-12406-8.
   Web of Science ®Google Scholar
• W. Ajeeb, R. R. da Silva, and S. S. Murshed, “Experimental investigation of heat transfer performance of Al2O3 nanofluids in a compact plate heat exchanger,” Appl. Therm. Eng., vol. 218, pp. 119321, 2023. DOI: 10.1016/j.applthermaleng.2022.119321.
   Web of Science ®Google Scholar
• Y. Azizi, M. Bahramkhoo, and A. Kazemi, “Influence of non-uniform magnetic field on the thermal efficiency hydrodynamic characteristics of nanofluid in double pipe heat exchanger,” Sci. Rep., vol. 13, no. 1, pp. 407, 2023. DOI: 10.1038/s41598-022-26285-w.
   PubMed Web of Science ®Google Scholar
• P. Kumar, R. Dwivedi, and K. Pandey, “Numerical investigation of thermo-hydraulic transport characteristics of laminar flow through partially filled porous wavy channel: Effect of Prandtl number,” Numer. Heat Transf., Part A: Appl., pp. 1–20, 2022. DOI: 10.1080/10407782.2021.1969809.
   Google Scholar
• M. Boussoufi and A. Sabeur, “Natural convective nanofluid flow characteristics with Brownian motion effect in an annular space between confocal elliptic cylinders,” Numer. Heat Transf. Part A: Appl., vol. 83, no. 10, pp. 1130–1145, 2023. DOI: 10.1080/10407782.2022.2102396.
   Web of Science ®Google Scholar
• M. Amiri and D. Mikielewicz, “Three-dimensional numerical investigation of hybrid nanofluids in chain microchannel under electrohydrodynamic actuator,” Numer. Heat Transf. Part A: Appl., vol. 83, no. 10, pp. 1146–1173, 2023. DOI: 10.1080/10407782.2022.2150342.
   Web of Science ®Google Scholar
• G. Mandal and D. Pal, “Estimation of entropy generation and heat transfer of magnetohydrodynamic quadratic radiative Darcy–Forchheimer cross hybrid nanofluid (GO + Ag/kerosene oil) over a stretching sheet,” Numer. Heat Transf. Part A: Appl., pp. 1–24, 2023. DOI: 10.1080/10407782.2022.2163944.
   Web of Science ®Google Scholar
• R. Williamson, “The flow of pseudoplastic materials,” Ind. Eng. Chem., vol. 21, no. 11, pp. 1108–1111, 1929. DOI: 10.1021/ie50239a035.
   Google Scholar
• Y. B. Kho, A. Hussanan, M. K. A. Mohamed, and M. Z. Salleh, “Heat and mass transfer analysis on flow of Williamson nanofluid with thermal and velocity slips: Buongiorno model,” Propuls. Power Res., vol. 8, no. 3, pp. 243–252, 2019. DOI: 10.1016/j.jppr.2019.01.011.
   Web of Science ®Google Scholar
• V. S. Patil, P. P. Humane, and A. B. Patil, “Mhd Williamson nanofluid flow past a permeable stretching sheet with thermal radiation and chemical reaction,” Int. J. Model. Simul., pp. 1–15, 2022. DOI: 10.1080/02286203.2022.2062166.
   Google Scholar
• A. Abbas, M. B. Jeelani, A. S. Alnahdi, and A. Ilyas, “MHD Williamson nanofluid fluid flow and heat transfer past a non-linear stretching sheet implanted in a porous medium: Effects of heat generation and viscous dissipation,” Processes, vol. 10, no. 6, pp. 1221, 2022. DOI: 10.3390/pr10061221.
   Web of Science ®Google Scholar
• P. Loganathan and S. Sangeetha, “Effect of Williamson parameter on cu-water Williamson nanofluid over a vertical plate,” Int. Commun. Heat Mass Transf., vol. 137, pp. 106273, 2022. DOI: 10.1016/j.icheatmasstransfer.2022.106273.
   Web of Science ®Google Scholar
• B. Rana et al., “Swimming of microbes in blood flow of nano-bioconvective Williamson fluid,” Therm. Sci. Eng. Prog., vol. 25, pp. 101018, 2021. DOI: 10.1016/j.tsep.2021.101018.
   Google Scholar
• V. Puneeth, M. S. Anwar, and M. R. Khan, “Bioconvective Darcy–Frochherimer flow of the Ree–Eyring nanofluid through a stretching sheet with velocity and thermal slips,” Waves Random Complex Media, pp. 1–22, 2022. DOI: 10.1080/17455030.2022.2157507.
   Google Scholar
• V. Puneeth, F. Ali, M. R. Khan, M. S. Anwar, and N. A. Ahammad, “Theoretical analysis of the thermal characteristics of Ree–Eyring nanofluid flowing past a stretching sheet due to bioconvection,” Biomass Conv. Bioref., pp. 1–12, 2022. DOI: 10.1007/s13399-022-02985-1.
   Web of Science ®Google Scholar
• F. Wang et al., “MHD Williamson nanofluid flow over a slender elastic sheet of irregular thickness in the presence of bioconvection,” Nanomaterials, vol. 11, no. 9, pp. 2297, 2021. DOI: 10.3390/nano11092297.
   Web of Science ®Google Scholar
• V. Puneeth et al., “Stratified bioconvective jet flow of Williamson nanofluid in porous medium in the presence of Arrhenius activation energy,” J. Comput. Biophys. Chem., vol. 22, no. 03, pp. 309–319, 2023. DOI: 10.1142/S2737416523400069.
   Google Scholar
• U. Khan, A. Zaib, I. Pop, S. A. Bakar, and A. Ishak, “Unsteady micropolar hybrid nanofluid flow past a permeable stretching/shrinking vertical plate,” Alex. Eng. J., vol. 61, no. 12, pp. 11337–11349, 2022. DOI: 10.1016/j.aej.2022.05.011.
   Web of Science ®Google Scholar
• U. Khan et al., “Features of magnetic field on biological Williamson fluid in radiated blood flow induced by gold particles through a curved moving surface with buoyancy effect,” Int. J. Mod. Phys. B, vol. 37, no. 03, pp. 2350021, 2023. DOI: 10.1142/S0217979223500212.
   Web of Science ®Google Scholar
• U. Khan et al., “Time-dependent flow of water-based ternary hybrid nanoparticles over a radially contracting/expanding and rotating permeable stretching sphere,” Therm. Sci. Eng. Prog., vol. 36, pp. 101521, 2022. DOI: 10.1016/j.tsep.2022.101521.
   Google Scholar
• P. A. Thompson and S. M. Troian, “A general boundary condition for liquid flow at solid surfaces,” Nature, vol. 389, no. 6649, pp. 360–362, 1997. DOI: 10.1038/38686.
   Web of Science ®Google Scholar
• Z. Abbas, M. Sheikh, J. Hasnain, H. Ayaz, and A. Nadeem, “Numerical aspects of Thomson and Troian boundary conditions in a Tiwari–Das nanofluid model with homogeneous–heterogeneous reactions,” Phys. Scr., vol. 94, no. 11, pp. 115220, 2019. DOI: 10.1088/1402-4896/ab27f0.
   Web of Science ®Google Scholar
• S. Nadeem, S. Ahmad, and M. N. Khan, “Mixed convection flow of hybrid nanoparticle along a Riga surface with Thomson and Troian slip condition,” J. Therm. Anal. Calorim., vol. 143, no. 3, pp. 2099–2109, 2021. DOI: 10.1007/s10973-020-09747-z.
   Web of Science ®Google Scholar
• K. Gangadhar, P. M. Seshakumari, M. V. S. Rao, and A. J. Chamkha, “MHD flow analysis of a Williamson nanofluid due to Thomson and Troian slip condition,” Partial Differ. Equ. Appl. Math., vol. 4, pp. 100108, 2021.
   Google Scholar
• S. Li et al., “Analysis of the Thomson and Troian velocity slip for the flow of ternary nanofluid past a stretching sheet,” Sci. Rep., vol. 13, no. 1, pp. 2340, 2023. DOI: 10.1038/s41598-023-29485-0.
   PubMed Web of Science ®Google Scholar
• N. Fatima et al., “Heat and mass transmission in a boundary layer flow due to swimming of motile gyrotactic microorganisms with variable wall temperature over a flat plate,” Case Stud. Therm. Eng., vol. 45, pp. 102953, 2023. DOI: 10.1016/j.csite.2023.102953.
   Web of Science ®Google Scholar
• M. Arain, A. Zeeshan, M. S. Alhodaly, L. Fasheng, and M. Bhatti, “Bioconvection nanofluid flow through vertical rigid parallel plates with the application of Arrhenius kinetics: A numerical study,” Waves Random Complex Media, pp. 1–18, 2022. DOI: 10.1080/17455030.2022.2123115.
   Web of Science ®Google Scholar
• S. Shaheen et al., “A case study of heat transmission in a Williamson fluid flow through a ciliated porous channel: A semi-numerical approach,” Case Stud. Therm. Eng., vol. 41, pp. 102523, 2023. DOI: 10.1016/j.csite.2022.102523.
   Web of Science ®Google Scholar
• U. Khan et al., “Features of hybridized AA7072 and AA7075 alloys nanomaterials with melting heat transfer past a movable cylinder with Thompson and Troian slip effect,” Arab. J. Chem., vol. 16, no. 2, pp. 104503, 2023. DOI: 10.1016/j.arabjc.2022.104503.
   Web of Science ®Google Scholar
• T. Hussain, S. Shehzad, A. Alsaedi, T. Hayat, and M. Ramzan, “Flow of Casson nanofluid with viscous dissipation and convective conditions: A mathematical model,” J. Cent. South Univ., vol. 22, no. 3, pp. 1132–1140, 2015. DOI: 10.1007/s11771-015-2625-4.
   Web of Science ®Google Scholar
• M. Mahmood, S. Asghar, and M. Hossain, “Transient mixed convection flow arising due to thermal and mass diffusion over porous sensor surface inside squeezing horizontal channel,” Appl. Math. Mech.-Engl. Ed., vol. 34, no. 1, pp. 97–112, 2013. DOI: 10.1007/s10483-013-1656-6.
   Google Scholar
• W. Akaje and B. Olajuwon, “Impacts of nonlinear thermal radiation on a stagnation point of an aligned MHD Casson nanofluid flow with Thompson and Troian slip boundary condition,” J. Adv. Res. Exp. Fluid Mech. Heat Transf., vol. 6, no. 1, pp. 1–15, 2021.
   Google Scholar