Publication Cover
Numerical Heat Transfer, Part A: Applications
An International Journal of Computation and Methodology
Volume 85, 2024 - Issue 1
99
Views
0
CrossRef citations to date
0
Altmetric
Research Articles

Dual solutions of Williamson-Casson fluid over a heated exponentially shrinking surface with stability analysis: A novel Catteneo-Christov heat flux model combination

&
Pages 114-136 | Received 15 May 2023, Accepted 28 Jul 2023, Published online: 13 Sep 2023

References

  • M. Miklavčič and C. Wang, “Viscous flow due to a shrinking sheet,” Q. Appl. Math., vol. 64, no. 2, pp. 283–290, 2006. DOI: 10.1090/S0033-569X-06-01002-5.
  • H. E. Hafidzuddin, R. Nazar, N. M. Arifin and I. Pop, “Boundary layer flow and heat transfer over a permeable exponentially stretching/shrinking sheet with generalized slip velocity,” JAFM, vol. 9, no. 6, pp. 2025–2036, 2016. DOI: 10.18869/acadpub.jafm.68.235.24834.
  • M. S. Uddin, K. Bhattacharyya, S. Shafie,” Micropolar fluid flow and heat transfer over an exponentially permeable shrinking sheet.” Propuls. Power Res., 5, no. 4 (2016): 310–317. DOI: 10.1016/j.jppr.2016.11.005.
  • S. Ghosh and S. Mukhopadhyay, “Flow and heat transfer of nanofluid over an exponentially shrinking porous sheet with heat and mass fluxes,” Propuls. Power Res., vol. 7, no. 3, pp. 268–275, 2018. DOI: 10.1016/j.jppr.2018.07.004.
  • S. Ghosh and S. Mukhopadhyay, “Stability analysis for model-based study of nanofluid flow over an exponentially shrinking permeable sheet in presence of slip,” Neural Comput. Appl., vol. 32, no. 11, pp. 7201–7211, 2020. DOI: 10.1007/s00521-019-04221.
  • W. Iskandar, A. Ishak and I. Pop, “Hybrid nanofluid flow induced by an exponentially shrinking sheet,” Chin. J. Phys., vol. 68, pp. 468–482, 2020. DOI: 10.1016/j.cjph.2019.12.015.
  • N. A. Zainal, R. Nazar, K. Naganthran and I. Pop, “Heat generation/absorption effect on MHD flow of hybrid nanofluid over bidirectional exponential stretching/shrinking sheet,” Chin. J. Phys., vol. 69, pp. 118–133, 2021. DOI: 10.1016/j.cjph.2020.12.002.
  • N. A. Zainal, R. Nazar, K. Naganthran and I. Pop, “Unsteady MHD stagnation point flow induced by exponentially permeable stretching/shrinking sheet of hybrid nanofluid,” Eng. Sci. Technol. Int. J., vol. 24, no. 5, pp. 1201–1210, 2021. DOI: 10.1016/j.jestch.2021.01.018.
  • A. J. Verma, S. Rajput, K. Bhattacharyya, A. J. Chamkha and D. Yadav, “Comparison between graphene-water and graphene oxide-water nanofluid flows over exponential shrinking sheet in porous medium: dual solutions and stability analysis,” Chem. Eng. J. Adv., vol. 12, no. 2022, pp. 100401, 2022. DOI: 10.1016/j.ceja.2022.100401.
  • A. Rehman, Z. Abbas and J. Hasnain, “Prediction of heat and mass transfer in radiative hybrid nanofluid with chemical reaction using the least square method: a stability analysis of dual solution,” Numer. Heat Transf. A: Appl., vol. 83, no. 9, pp. 958–975, 2023. DOI: 10.1080/10407782.2022.2156410.
  • M. N. Tufail, M. Saleem and Q. A. Chaudhry, “An analysis of Maxwell fluid through a shrinking sheet with thermal slip effect: a Lie group approach,” Indian J. Phys., vol. 95, no. 4, pp. 725–731, 2021. DOI: 10.1007/s12648-020-01745-z.
  • B. M. Triveni, V. Su. Rao, K. Gangadhar and A. J. Chamkha, “Heat transfer analysis of MHD Casson nanofluid flow over a nonlinear stretching sheet in the presence of nonuniform heat source,” Numer. Heat Transf. A: Appl., pp. 1–20, 2023. DOI: 10.1080/10407782.2023.2219831. (In press)
  • G. Mandal and D. Pal, “Mixed convective-quadratic radiative MoS 2–SiO 2/H 2 O hybrid nanofluid flow over an exponentially shrinking permeable Riga surface with slip velocity and convective boundary conditions: entropy and stability analysis,” Numer. Heat Transf. A: Appl., pp. 1–26, 2023. DOI: 10.1080/10407782.2023.2221004. (In press)
  • 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, 2017. DOI: 10.1134/S0021894417030063.
  • N. A. Zainal and R. Nazar, “Ko. Naganthran and I.n Pop,” Viscous dissipation and MHD hybrid nanofluid flow towards an exponentially stretching/shrinking surface,” Neural Comput. Appl., vol. 33, pp. 11285–11295, 2021. DOI: 10.1007/s00521-020-05645-5
  • N. N. Reddy, V. S. Rao and B. R. Reddy, “Chemical reaction impact on MHD natural convection flow through porous medium past an exponentially stretching sheet in presence of heat source/sink and viscous dissipation,” Case Stud. Therm. Eng., vol. 25, no. 2021, pp. 100879, 2021. DOI: 10.1016/j.csite.2021.100879.
  • K. Swain, F. M. Oudina and S. M. Abo-Dahab, “Influence of MWCNT/Fe 3 O 4 hybrid nanoparticles on an exponentially porous shrinking sheet with chemical reaction and slip boundary conditions,” J. Therm. Anal. Calorim., vol. 147, no. 2, pp. 1561–1570, 2022. 022147: DOI: 10.1007/s10973-020-10432-4.
  • D. Dey, O. D. Makinde and R. Borah, “Analysis of dual solutions in MHD fluid flow with heat and mass transfer past an exponentially shrinking/stretching surface in a porous medium,” Int. J. Appl. Comput. Math., vol. 8, no. 2, pp. 66, 2022. DOI: 10.1007/s40819-022-01268-7.
  • J. R. Reddy, V. Sugunamma and N. Sandeep, “Combined effects of frictional and Joule heating on MHD nonlinear radiative Casson and Williamson ferrofluid flows with temperature dependent viscosity,” Int. J. Appl. Comput. Math., vol. 4, no. 6, pp. 1–25, 2018. DOI: 10.1007/s40819-018-0572-0.
  • M. Bhuvaneswari, S. Sivasankaran, H. Niranjan and S. Eswaramoorthi, “Cross diffusion effects on MHD convection of Casson-Williamson fluid over a stretching surface with radiation and chemical reaction,” presented at the Applied Mathematics and Scientific Computing: International Conference on Advances in Mathematical Sciences., 2017. Volume II, pp. 139–146. Springer International Publishing, 2019. DOI: 10.1007/978-3-030-01123-9-15.
  • K. Kumar, V. Anantha, V. Sugunamma, N. Sandeep and J. V. Ramana Reddy, “MHD stagnation point flow of Williamson and Casson fluids past an extended cylinder: a new heat flux model,” SN Appl. Sci., vol. 1, no. 7, pp. 1–11, 2019. | DOI: 10.1007/s42452-019-0743-6.
  • C. S. K. Raju, N. Sandeep, M. E. Ali and A. O. Nuhait, “Heat and mass transfer in 3-D MHD Williamson-Casson fluids flow over a stretching surface with non-uniform heat source/sink,” Therm. Sci., vol. 23, no. 1, pp. 281–293, 2019. DOI: 10.2298/TSCI160426107R.
  • H. A. Ogunseye, S. O. Salawu and E. O. Fatunmbi, “A numerical study of MHD heat and mass transfer of a reactive Casson–Williamson nanofluid past a vertical moving cylinder,” Partial Differ. Equ. Appl. Math., vol. 4, no. 2021, pp. 100148, 2021. DOI: 10.1016/j.padiff.2021.100148.
  • P. P. Humane, V. S. Patil and A. B. Patil, “Chemical reaction and thermal radiation effects on magnetohydrodynamics flow of Casson–Williamson nanofluid over a porous stretching surface,” Proc. Inst. Mech. Eng. E: J. Process Mech. Eng., vol. 235, no. 6, pp. 2008–2018, 2021. DOI: 10.1177/09544089211025376.
  • N. S. Yousef, A. M. Megahed, N. I. Ghoneim, M. Elsafi and E. Fares, “Chemical reaction impact on MHD dissipative Casson-Williamson nanofluid flow over a slippery stretching sheet through porous medium,” Alex. Eng. J., vol. 61, no. 12, pp. 10161–10170, 2022. DOI: 10.1016/j.aej.2022.03.032.
  • B. J. Gireesha and L. Anitha, “Repercussion of Hall effect and nonlinear radiation on Couette-Poiseuille flow of Casson-Williamson fluid through upright microchannel,” Appl. Math. Mech.-Engl. Ed., vol. 43, no. 12, pp. 1951–1964, 2022. DOI: 10.1007/s10483-022-2929-8.
  • M. N. Tufail, M. Saleem and Q. A. Chaudhry, “Chemically reacting mixed convective Casson fluid flow in the presence of MHD and porous medium through group theoretical analysis,” Heat Transf., vol. 49, no. 8, pp. 4657–4677, 2020. DOI: 10.1002/htj.21846.
  • M. Saleem and M. Hussain, “Impression of nonlinear radiation and Stefan blowing on the magneto cross nano-Williamson fluid above exponentially stretching sheet,” Results Eng., vol. 17, pp. 100864, 2023. DOI: 10.1016/j.rineng.2022.100864.
  • Z. Iqbal and M. Saleem, “Convective heat transport features of Darcy Casson fluid flow in a vertical channel: a Lie group approach,” Waves Random Complex Media, pp. 1–14, 2022. DOI: 10.1080/17455030.2022.2142694. (In press)
  • M. N. Nazim Tufail, M. Saleem and Q. A. Chaudhry, “Two-parameter Lie convective Casson fluid scale study with MHD, joule heating and viscous dissipation influences,” Proc. Inst. Mech. Eng. C: J. Mech. Eng. Sci. vol. 235, no. 17, pp. 3199–3212, 2021. DOI: 10.1177/0954406220964843.
  • S. K. Saini, R. Agrawal and P. Kaswan, “Activation energy and convective heat transfer effects on the radiative Williamson nanofluid flow over a radially stretching surface containing Joule heating and viscous dissipation,” Numer. Heat Transf., Part A: Appl., pp. 1–24, 2023. DOI: 10.1080/10407782.2023.2226815. (In press)
  • B. Gebhart, B. Hassard, S. P. Hastings and N. Kazarinoff, “Multiple steady-state solutions for buoyancy-induced transport in porous media saturated with cold pure or saline water,” Numer. Heat Transf., vol. 6, no. 3, pp. 337–352, 1983. DOI: 10.1080/01495728308963091.
  • 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.
  • Q. Zaman, S. Saleem and N. Ali, “Nonsimilar stagnation flow of Williamson fluid over an isothermal linearly stretched sheet,” Numer. Heat Transf. Part A: Appl., pp. 1–17, 2023. DOI: 10.1080/10407782.2023.2206061. (In press)
  • C. Cattaneo, “Sulla conduzione del calore,” Atti Sem. Mat. Fis. Univ. Modena, vol. 3, pp. 83–101, 1948. DOI: 10.1007/978-3-642-11051-1_5.
  • C. I. Christov, “On frame indifferent formulation of the Maxwell–Cattaneo model of finite-speed heat conduction,” Mech. Res. Commun., vol. 36, no. 4, pp. 481–486, 2009. DOI: 10.1016/j.mechrescom.2008.11.003.
  • M. Ciarletta and B. Straughan, “Uniqueness and structural stability for the Cattaneo–Christov equations,” Mech. Res. Commun., vol. 37, no. 5, pp. 445–447, 2010. DOI: 10.1016/j.mechrescom.2010.06.002.
  • V. Tibullo and V. Zampoli, “A uniqueness result for the Cattaneo–Christov heat conduction model applied to incompressible fluids,” Mech. Res. Commun., vol. 38, no. 1, pp. 77–79, 2011. DOI: 10.1016/j.mechrescom.2010.10.008.
  • A. Hafeez, M. Khan and J. Ahmed, “Thermal aspects of chemically reactive Oldroyd-B fluid flow over a rotating disk with Cattaneo–Christov heat flux theory,” J Therm. Anal. Calorim., vol. 144, no. 3, pp. 793–803, 2021. DOI: 10.1007/s10973-020-09421-4.
  • M. N. Sadiq, B. Sarwar, M. Sajid and N. Ali, “Heat transfer in unsteady separated stagnation point flow of a micro-polar fluid: cattaneo–Christov model,” J. Therm. Anal. Calorim., vol. 147, pp. 5199–5209, 2022. DOI: 10.1007/s10973-021-10889-x.
  • S. Bilal, M. I. Shah, N. Z. Khan, A. Akgül and K. S. Nisar, “Onset about non-isothermal flow of Williamson liquid over exponential surface by computing numerical simulation in perspective of Cattaneo Christov heat flux theory,” Alex. Eng. J., vol. 61, no. 8, pp. 6139–6150, 2022. DOI: 10.1016/j.aej.2021.11.038.
  • T. Hayat, A. Fatima, K. Muhammad and A. Alsaedi, “Heat transfer and entropy analysis in squeezing flow of hybrid nanofluid (Au-CuO/NaAlg) with DF (Darcy-Forchheimer) and CC (Cattaneo-Christov) heat flux,” Mater. Sci. Eng.: B, vol. 288, pp. 116150, 2023. DOI: 10.1016/j.mseb.2022.116150.
  • I. Jabeen, S. Ahmad, A. Anjum and M. Farooq, “Analysis of variable mass diffusivity in Maxwell’s fluid with Cattaneo-Christov and nonlinear stratification,” Heliyon, vol. 8, no. 12, pp. e11850, 2022. DOI: 10.1016/j.heliyon.2022.e11850.
  • M. B. Ashraf, A. Tanveer, S. Ulhaq,” Effects of Cattaneo-Christov heat flux on MHD Jeffery nano fluid flow past a stretching cylinder,” J. Magn. Magn. Mater., 565 (2023): 170154. DOI: 10.1016/j.jmmm.2022.170154.
  • T. Oreyeni, A. O. Akindele, A. M. Obalalu, S. O. Salawu and K. Ramesh, “Thermal performance of radiative magnetohydrodynamic Oldroyd-B hybrid nanofluid with Cattaneo–Christov heat flux model: solar-powered ship application,” Numer. Heat Transf., Part A: Appl., pp. 1–19, 2023. DOI: 10.1080/10407782.2023.2213837. (In press)
  • H. Waqas, U. Farooq, S. A. Khan, H. M. Alshehri and M. Goodarzi, “Numerical analysis of dual variable of conductivity in bioconvection flow of Carreau–Yasuda nanofluid containing gyrotactic motile microorganisms over a porous medium,” J. Therm. Anal. Calorim., vol. 145, no. 4, pp. 2033–2044, 2021. DOI: 10.1007/s10973-021-10859-3.
  • M. Hussain, A. Ali, S. W. Yao, A. Ghaffar and M. Inc, “Numerical investigation of ohmically dissipated mixed convective flow,” Case Stud. Therm. Eng., vol. 31, no. 2022, pp. 101809, 2022. DOI: 10.1016/j.csite.2022.101809.
  • M. Hussain, A. Ali, M. Inc, N. Sene and M. Hussan, “Impacts of chemical reaction and suction/injection on the mixed convective williamson fluid past a penetrable porous wedge,” J. Math., vol. 2022, pp. 1–10, 2022. DOI: 10.1155/2022/3233964.
  • S. D. Harris, D. B. Ingham and I. Pop, “Mixed convection boundary-layer flow near the stagnation point on a vertical surface in a porous medium: brinkman model with slip,” Transp. Porous Med., vol. 77, no. 2, pp. 267–285, 2009. DOI: 10.1007/s11242-008-9309-6.
  • L. F. Shampine, I. Gladwell and S. Thompson, Solving ODEs with Matlab. Cambridge University Press, 2003. Doi: 10.1017/CBO9780511615542.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.