This analysis considers the influence of viscous dissipation and chemical reaction on mixed convection flow of a Jeffrey nanofluid past a stretching plate. The nonlinear partial differential equations modeling the Jeffrey nanofluid flow problem were converted into a dimensionless system of ordinary differential equations by implementing suitable similarity transformations. The spectral quasi-linearization technique was used to solve the transformed system of ordinary differential equations subject to prescribed boundary conditions. The convergence and accuracy of the numerical technique used got tested using the absolute and residual error infinity norms respectively. The skin friction coefficient values obtained using the spectral quasi-linearization method were found to be in excellent agreement with the exact solution. The impact of some physical parameters on the fluid velocity, temperature and concentration profiles were presented graphically. It is noted in this study that for increased values of Eckert number, the fluid temperature profiles and the mass transfer rate are depressed whilst the skin friction coefficient and the heat transfer rate are enhanced. The nanoparticle volume fraction and the heat transfer rate decrease when the chemical reaction rate is increased. The skin friction coefficient and mass transfer rate are increasing functions of the chemical reaction parameter.

Jeffrey nanofluid, viscous dissipation, chemical reaction, spectral quasi-linearization.

Received: September 20, 2024; Accepted: November 7, 2024; Published: January 4, 2025

How to cite this article: H. Muzara and S. Shateyi, On the numerical analysis of the influence of viscous dissipation and chemical reaction on mixed convection flow of a Jeffrey nanofluid past a stretching plate, JP Journal of Heat and Mass Transfer 38(1) (2025), 1-28. https://doi.org/10.17654/0973576325001

This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License

References:
[1] S. U. S. Choi, Z. G. Zhang, W. Yu, F. E. Lockwood and E. A. Grulke, Anomalous thermal conductivity enhancement in nanotube suspensions, Applied Physics Letters 79(14) (2001), 2252-2254. doi:10.1063/1.1408272.
[2] J. Tripathi, B. Vasu, R. Subba Reddy Gorla, A. J. Chamkha, P. V. S. N. Murthy and O. Anwar Bég, Blood flow mediated hybrid nanoparticles in human arterial system: recent research, development and applications, Journal of Nanofluids 10(1) (2021), 1-30. https://doi.org/10.1166/jon.2021.1769.
[3] G. B. Jeffery, The motion of ellipsoidal particles immersed in a viscous fluid, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 102(715) (1922), 161-179. doi:10.1098/rspa.1922.0078.
[4] T. Hayat, A. Aziz, T. Muhammad and A. Alsaedi, Active and passive controls of Jeffrey nanofluid flow over a nonlinear stretching surface, Results in Physics 7 (2017), 4071-4078. doi:10.1016/j.rinp.2017.10.028.
[5] T. Hayat, S. Qayyum and A. Alsaedi, Mechanisms of nonlinear convective flow of Jeffrey nanofluid due to nonlinear radially stretching sheet with convective conditions and magnetic field, Results in Physics 7 (2017), 2341-2351. doi:10.1016/j.rinp.2017.06.052.
[6] R. S. Saif, T. Muhammad, H. Sadia and R. Ellahi, Hydromagnetic flow of Jeffrey nanofluid due to a curved stretching surface, Phys. A 551 (2020), 124060. doi:10.1016/j.physa.2019.12406.
[7] B. J. Gireesha, M. Umeshaiah, B. C. Prasannakumara, N. S. Shashikumar and M. Archana, Impact of nonlinear thermal radiation on magnetohydrodynamic three dimensional boundary layer flow of Jeffrey nanofluid over a nonlinearly permeable stretching sheet, Phys. A 549 (2020), 124051. doi:10.1016/j.physa.2019.124051.
[8] A. Hassan, A. Hussain, M. Arshad, S. Gouadria, J. Awrejcewicz, A. M. Galal, F. M. Alharbi and S. Eswaramoorthi, Insight into the significance of viscous dissipation and heat generation/absorption in magneto-hydrodynamic radiative Casson fluid flow with first-order chemical reaction, Frontiers in Physics 10 (2022), 920372. https://doi.org/10.3389/fphy.2022.920372.
[9] B. Gebhart, Effects of viscous dissipation in natural convection, J. Fluid Mech. 14(2) (1962), 225-232. https://doi.org/10.1017/s0022112062001196.
[10] K. Sharma and S. Gupta, Viscous dissipation and thermal radiation effects in MHD flow of Jeffrey nanofluid through impermeable surface with heat generation/absorption, Nonlinear Engineering 6(2) (2017), 153-166.
doi:10.1515/nleng-2016-0078.
[11] S. Zokri, N. Arifin, M. Salleh, A. Kasim, N. Mohammad and W. Yusoff, MHD Jeffrey nanofluid past a stretching sheet with viscous dissipation effect, Journal of Physics 890 (2017), 012002. https://doi.org/10.1088/1742-6596/890/1/012002.
[12] E. El-Zahar, A. Rashad and L. Seddek, Impacts of viscous dissipation and Brownian motion on Jeffrey nanofluid flow over an unsteady stretching surface with thermophoresis, Symmetry 12(9) (2020), 1450.
https://doi.org/10.3390/sym12091450.
[13] F. Shahzad, W. Jamshed, K. S. Nisar, M. M. Khashan and A.-H. Abdel-Aty, Computational analysis of Ohmic and viscous dissipation effects on MHD heat transfer flow of Cu-PVA Jeffrey nanofluid through a stretchable surface, Case Studies in Thermal Engineering 26 (2021), 101148.
https://doi.org/10.1016/j.csite.2021.101148.
[14] H. Ur Rasheed, A. AL-Zubaidi, S. Islam, S. Saleem, Z. Khan and W. Khan, Effects of Joule heating and viscous dissipation on magnetohydrodynamic boundary layer flow of Jeffrey nanofluid over a vertically stretching cylinder, Coatings 11(3) (2021), 353. https://doi.org/10.3390/coatings11030353.
[15] F. Shahzad, M. Sagheer and S. Hussain, Numerical simulation of magnetohydrodynamic Jeffrey nanofluid flow and heat transfer over a stretching sheet considering Joule heating and viscous dissipation, AIP Advances 8(6) (2018), 065316. https://doi.org/10.1063/1.5031447.
[16] P. Li, A. Abbasi, E. R. El-Zahar, W. Farooq, Z. Hussain, S. U. Khan, M. I. Khan, S. Farooq, M. Y. Malik and F. Wang, Hall effects and viscous dissipation applications in peristaltic transport of Jeffrey nanofluid due to wave frame, Colloid and Interface Science Communications 47 (2022), 100593.
https://doi.org/10.1016/j.colcom.2022.100593.
[17] H. Ge-JiLe, M. Nazeer, F. Hussain, M. I. Khan, A. Saleem and I. Siddique, Two-phase flow of MHD Jeffrey fluid with the suspension of tiny metallic particles incorporated with viscous dissipation and porous medium, Advances in Mechanical Engineering 13(3) (2021), 168781402110059.
https://doi.org/10.1177/16878140211005960.
[18] T. Hussain, S. A. Shehzad, T. Hayat, A. Alsaedi, F. Al-Solamy and M. Ramzan, Radiative hydromagnetic flow of Jeffrey nanofluid by an exponentially stretching sheet, PLoS ONE 9(8) (2014), e103719.
https://doi.org/10.1371/journal.pone.0103719.
[19] S. Maatoug, K. H. Babu, V. V. L. Deepthi, K. Ghachem, K. Raghunath, C. Ganteda and S. U. Khan, Variable chemical species and thermo-diffusion Darcy-Forchheimer squeezed flow of Jeffrey nanofluid in horizontal channel with viscous dissipation effects, Journal of the Indian Chemical Society 100(1) (2023), 100831. https://doi.org/10.1016/j.jics.2022.100831.
[20] Y. Dadhich, N. Alessa, R. Jain, A. R. Kaladgi, K. Loganathan and V. R. Devi, Thermal onsets of viscous dissipation for radiative mixed convective flow of Jeffery nanofluid across a wedge, Symmetry 15(2) (2023), 385.
https://doi.org/10.3390/sym15020385.
[21] A. Haritha, B. Vishali and C. Venkata Lakshmi, Heat and mass transfer of MHD Jeffrey nanofluid flow through a porous media past an inclined plate with chemical reaction, radiation, and Soret effects, Heat Transfer 52(2) (2022), 1178-1197. https://doi.org/10.1002/htj.22735.
[22] M. A. Abbas, M. M. Bhatti and M. Sheikholeslami, Peristaltic propulsion of Jeffrey nanofluid with thermal radiation and chemical reaction effects, Inventions 4(4) (2019), 68. https://doi.org/10.3390/inventions4040068.
[23] N. Sandeep, C. Sulochana and I. L. Animasaun, Stagnation-point flow of a Jeffrey nanofluid over a stretching surface with induced magnetic field and chemical reaction, International Journal of Engineering Research in Africa 20 (2015), 93-111. https://doi.org/10.4028/www.scientific.net/jera.20.93.
[24] T. M. Agbaje and P. G. L. Leach, Numerical investigation of natural convection viscoelastic Jeffrey’s nanofluid flow from a vertical permeable flat plate with heat generation, thermal radiation, and chemical reaction, Abstract and Applied Analysis 2020 (2020), 1-23. https://doi.org/10.1155/2020/9816942.
[25] N. A. Mat Noor, S. Shafie and M. A. Admon, Slip effects on MHD squeezing flow of Jeffrey nanofluid in horizontal channel with chemical reaction, Mathematics 9(11) (2021), 1215. https://doi.org/10.3390/math9111215.
[26] Y.-M. Chu, M. I. Khan, H. Waqas, U. Farooq, S. U. Khan and M. Nazeer, Numerical simulation of squeezing flow Jeffrey nanofluid confined by two parallel disks with the help of chemical reaction: effects of activation energy and microorganisms, International Journal of Chemical Reactor Engineering 19(7) (2021), 717-725. https://doi.org/10.1515/ijcre-2020-0165.
[27] C. S. K. Raju, M. Jayachandra Babu and N. Sandeep, Chemically reacting radiative MHD Jeffrey nanofluid flow over a cone in porous medium, International Journal of Engineering Research in Africa 19 (2015), 75-90.
https://doi.org/10.4028/www.scientific.net/jera.19.75.
[28] I. Ahmad, S. Aziz, N. Ali and S. U. Khan, Radiative unsteady hydromagnetic 3D flow model for Jeffrey nanofluid configured by an accelerated surface with chemical reaction, Heat Transfer 50(1) (2020), 942-966.
https://doi.org/10.1002/htj.21912.
[29] H. Vaidya, C. Rajashekhar, F. Mebarek-Oudina, K. V. Prasad, K. Vajravelu and B. Ramesh Bhat, Examination of chemical reaction on three dimensional mixed convective magnetohydrodynamic Jeffrey nanofluid over a stretching sheet, Journal of Nanofluids 11(1) (2022), 113-124.
https://doi.org/10.1166/jon.2022.1817.
[30] Gossaye Aliy Adem, Analytic treatment for electrical MHD non-Newtonian fluid flow over a stretching sheet through a porous medium, Advances in Mathematical Physics 2020 (2020), 1-14.
[31] R. Mohamed, Abdelraheem Mahmoud Aly, Sameh Ahmed and Mahmoud Soliman, MHD Jeffrey nanofluids flow over a stretching sheet through a porous medium in presence of nonlinear thermal radiation and heat generation, Absorption (2020), 9-22. doi:10.22111/tpnms.2019.29314.1172.
[32] Suresh Goud, Pudhari Srilatha, K. Kumar and S. Devraj, Slip effect on magnetohydrodynamic flow and heat transfer of Jeffrey nanofluid over a stretching sheet in the presence of nonlinear thermal radiation and chemical reaction, Journal of Computational and Theoretical Nanoscience 17 (2020), 1953-1962. doi:10.1166/jctn.2020.8473.
[33] B. Sahoo, Flow and heat transfer of a non-Newtonian fluid past a stretching sheet with partial slip, Commun. Nonlinear Sci. Numer. Simul. 15(3) (2010), 602-615. doi:10.1016/j.cnsns.2009.04.03.
[34] A. Sojoudi, A. Mazloomi, S. C. Saha and Y. T. Gu, Similarity solutions for flow and heat transfer of non-Newtonian fluid over a stretching surface, J. Appl. Math. 2014 (2014), 1-8. doi:10.1155/2014/718319.
[35] S. S. Motsa, P. G. Dlamini and M. Khumalo, Spectral relaxation method and spectral quasilinearization method for solving unsteady boundary layer flow problems, Advances in Mathematical Physics 2014 (2014), 1-12.
[36] N. Rai and S. Mondal, Spectral methods to solve nonlinear problems: a review, Partial Differential Equations in Applied Mathematics 4 (2021), 100043.
https://doi.org/10.1016/j.padiff.2021.100043.
[37] M. S. Ansari, V. M. Magagula and M. Trivedi, Jeffrey nanofluid flow near a Riga plate: spectral quasilinearization approach, Heat Transfer 49 (2020), 1491-1510. doi:10.1002/htj.21673.
[38] N. Acharya, Spectral quasi linearization simulation on the hydrothermal behavior of hybrid nanofluid spraying on an inclined spinning disk, Partial Differential Equations in Applied Mathematics 4 (2021), 100094.
https://doi.org/10.1016/j.padiff.2021.100094.
[39] T. A. Yusuf, Entropy analysis of unsteady MHD nanofluid flow over a stretching surface with effects of variable viscosity and nonuniform heat generation, Numerical Heat Transfer, Part A: Applications 85 (2023), 2754-2771. https://doi.org/10.1080/10407782.2023.2229011.
[40] S. P. Goqo, S. D. Oloniiju, H. Mondal, P. Sibanda and S. S. Motsa, Entropy generation in MHD radiative viscous nanofluid flow over a porous wedge using the bivariate spectral quasi-linearization method, Case Studies in Thermal Engineering 12 (2018), 774-788. https://doi.org/10.1016/j.csite.2018.10.005.
[41] K. Gangadhar, D. Vijayakumar, A. J. Chamkha, T. Kannan and G. Sakthivel, Effects of Newtonian heating and thermal radiation on micropolar ferrofluid flow past a stretching surface: Spectral quasi-linearization method, Heat Transfer 49(2) (2019), 838-857. https://doi.org/10.1002/htj.21641.
[42] M. Magodora, H. Mondal and P. Sibanda, Dual solutions of a micropolar nanofluid flow with radiative heat mass transfer over stretching/shrinking sheet using spectral quasilinearization method, Multidiscipline Modeling in Materials and Structures 16(2) (2019), 238-255.
https://doi.org/10.1108/mmms-01-2019-0028.
[43] N. Acharya, Spectral quasi linearization simulation on the radiative nanofluid spraying over a permeable inclined spinning disk considering the existence of heat source/sink, Appl. Math. Comput. 411 (2021), 126547.
https://doi.org/10.1016/j.amc.2021.126547.
[44] J. Buongiorno, Convective transport in nanofluids, Journal of Heat Transfer 128(3) (2006), 240-250. doi:10.1115/1.2150834.
[45] N. Dalir, Numerical study of entropy generation for forced convection flow and heat transfer of a Jeffrey fluid over a stretching sheet, Alexandria Engineering Journal 53(4) (2014), 769-778. doi:10.1016/j.aej.2014.08.005.
[46] R. E. Bellman and R. E. Kalaba, Quasilinearization and Nonlinear Boundary- value Problems, Elsevier, New York, NY, USA, 1965.
[47] L. N. Trefethen, Spectral Methods in MATLAB, SIAM, Philadelphia, 2000.
[48] T. Hayat, Z. Iqbal, M. Mustafa and A. Alsaedi, Unsteady flow and heat transfer of Jeffrey fluid over a stretching sheet, Thermal Science 18(4) (2014), 1069-1078. doi:10.2298/tsci110907092h.
[49] S. Shateyi and G. T. Marewo, Numerical solution of mixed convection flow of an MHD Jeffery fluid over an exponentially stretching sheet in the presence of thermal radiation and chemical reaction, Open Physics 16(1) (2018), 249-259. https://doi.org/10.1515/phys-2018-0036.
[50] I. Ahmad, S. Aziz, N. Ali and S. U. Khan, Radiative unsteady hydromagnetic 3D flow model for Jeffrey nanofluid configured by an accelerated surface with chemical reaction, Heat Transfer 50(1) (2020), 942-966.
https://doi.org/10.1002/htj.21912.