We investigated the boundary-layer flow, heat, and mass transfer characteristics of a third-grade Ellis fluid over a vertical stretching cylinder. The Ellis model was modified with third-grade fluid terms, properly representing the shear-dependent viscosity and higher-order nonlinear stress behaviors characteristic of fluids used for industrial purposes and polymers. Governing equations were derived to account for momentum, thermal, and solutal transport, while emphasizing the coupled influence of the Soret effect (mass flux due to thermal gradients) and the Dufour effect (heat flux induced by concentration gradients). Moreover, the species transport equation incorporated a first-order chemical reaction for modeling. Through the use of similarity transformations, the original nonlinear partial differential equations were converted into a set of coupled ordinary differential equations, which were then solved using numerical techniques. The impacts of various physical factors are presented in both tabular and graphical form. Velocity increased due to an increase in the Ellis fluid factor. The Ellis fluid parameter indicated that the fluid's effective viscosity decreased under shear. As a result, higher values of the Ellis fluid parameter reduce flow resistance, increasing the velocity profile throughout the surface.
Citation: Nadeem Abbas, Wasfi Shatanawi. Thermal and solutal boundary layer of a third grade Ellis fluid over a vertical cylinder with cross-diffusion and reaction effects[J]. AIMS Mathematics, 2026, 11(2): 5006-5028. doi: 10.3934/math.2026205
We investigated the boundary-layer flow, heat, and mass transfer characteristics of a third-grade Ellis fluid over a vertical stretching cylinder. The Ellis model was modified with third-grade fluid terms, properly representing the shear-dependent viscosity and higher-order nonlinear stress behaviors characteristic of fluids used for industrial purposes and polymers. Governing equations were derived to account for momentum, thermal, and solutal transport, while emphasizing the coupled influence of the Soret effect (mass flux due to thermal gradients) and the Dufour effect (heat flux induced by concentration gradients). Moreover, the species transport equation incorporated a first-order chemical reaction for modeling. Through the use of similarity transformations, the original nonlinear partial differential equations were converted into a set of coupled ordinary differential equations, which were then solved using numerical techniques. The impacts of various physical factors are presented in both tabular and graphical form. Velocity increased due to an increase in the Ellis fluid factor. The Ellis fluid parameter indicated that the fluid's effective viscosity decreased under shear. As a result, higher values of the Ellis fluid parameter reduce flow resistance, increasing the velocity profile throughout the surface.
| [1] |
S. Matsuhisa, R. B. Bird, Analytical and numerical solutions for laminar flow of the non‐Newtonian ellis fluid, AIChE J., 11 (1965), 588–595. https://doi.org/10.1002/aic.690110407 doi: 10.1002/aic.690110407
|
| [2] |
Y. Li, B. Yu, J. Chen, C. Wang, Analysis of permeability for Ellis fluid flow in fractal porous media, Chem. Eng. Commun., 195 (2008), 1240–1256. https://doi.org/10.1080/00986440801942018 doi: 10.1080/00986440801942018
|
| [3] |
V. O. Kheyfets, S. L. Kieweg, Gravity-driven thin film flow of an Ellis fluid, J. Non-Newton. Fluid, 202 (2013), 88–98. https://doi.org/10.1016/j.jnnfm.2013.09.010 doi: 10.1016/j.jnnfm.2013.09.010
|
| [4] |
N. Ali, S. Hussain, K. Ullah, O. A. Bég, Mathematical modelling of two-fluid electro-osmotic peristaltic pumping of an Ellis fluid in an axisymmetric tube, Eur. Phys. J. Plus, 134 (2019), 141. https://doi.org/10.1140/epjp/i2019-12488-2 doi: 10.1140/epjp/i2019-12488-2
|
| [5] |
A. Abbasi, S. U. Khan, W. Farooq, F. M. Mughal, M. I. Khan, B. C. Prasannakumara, et al., Peristaltic flow of chemically reactive Ellis fluid through an asymmetric channel: Heat and mass transfer analysis, Ain Shams Eng. J., 14 (2023), 101832. https://doi.org/10.1016/j.asej.2022.101832 doi: 10.1016/j.asej.2022.101832
|
| [6] |
S. Shaheen, H. Huang, F. A. Al-Yarimi, M. B. Arain, Theoretical analysis of Ellis fluid flow in two layers due to metachronal propulsion subject to heat and mass transfer: Application in biological function, Case Stud. Therm. Eng., 59 (2024) 104446. https://doi.org/10.1016/j.csite.2024.104446 doi: 10.1016/j.csite.2024.104446
|
| [7] |
A. Mishra, Analysis of radiative Ellis hybrid nanofluid flow over a stretching/shrinking cylinder embedded in a porous medium with slip condition, Multiscale Multi. Mod., 8 (2025), 282. https://doi.org/10.1007/s41939-025-00871-7 doi: 10.1007/s41939-025-00871-7
|
| [8] |
S. Abdal, M. Ajmal, B. C. Prasannakumara, N. A. Shah, R. M. Zulqarnain, S. J. Yook, Significance of nanoparticles concentration for heat and mass transfer of Ellis fluid dynamics across a stretching wall, J. Therm. Anal. Calorim., 2025, 1–13. https://doi.org/10.1007/s10973-025-14029-7 doi: 10.1007/s10973-025-14029-7
|
| [9] |
B. Sahoo, Hiemenz flow and heat transfer of a third grade fluid, Commun. Nonlinear Sci., 14 (2009), 811–826. https://doi.org/10.1016/j.cnsns.2007.12.002 doi: 10.1016/j.cnsns.2007.12.002
|
| [10] |
T. Hayat, A. Shafiq, A. Alsaedi, M. Awais, MHD axisymmetric flow of third grade fluid between stretching sheets with heat transfer, Comput. Fluids, 86 (2013), 103–108. https://doi.org/10.1016/j.compfluid.2013.07.003 doi: 10.1016/j.compfluid.2013.07.003
|
| [11] |
T. Hayat, A. Shafiq, A. Alsaedi, MHD axisymmetric flow of third grade fluid by a stretching cylinder, Alex. Eng. J., 54 (2015), 205–212. https://doi.org/10.1016/j.aej.2015.03.013 doi: 10.1016/j.aej.2015.03.013
|
| [12] |
A. T. Akinshilo, Steady flow and heat transfer analysis of third grade fluid with porous medium and heat generation, Eng. Sci. Technol., 20 (2017), 1602–1609. https://doi.org/10.1016/j.jestch.2017.11.012 doi: 10.1016/j.jestch.2017.11.012
|
| [13] |
S. Khan, M. M. Selim, A. Khan, A. Ullah, T. Abdeljawad, Ikramullah, et al., On the analysis of the non-Newtonian fluid flow past a stretching/shrinking permeable surface with heat and mass transfer, Coatings, 11 (2021), 566. https://doi.org/10.3390/coatings11050566 doi: 10.3390/coatings11050566
|
| [14] |
N. Fatima, M. Nazeer, M. M. Lashin, M. M. Ghafar, M. R. Gorji, M. K. Hameed, Developments of electro-osmotic two-phase flows of fourth-grade fluid through convergent and divergent channels, Mathematics, 11 (2023), 1832. https://doi.org/10.3390/math11081832 doi: 10.3390/math11081832
|
| [15] | S. Saleem, J. Alzabut, Exact exploration of time fractional-based magnetized flow of a generalized second grade fluid through an oscillating rectangular duct, Int. J. Geom. Methods M., 2024, 2440031. |
| [16] |
X. Xin, I. Khan, A. M. Alqahtani, T. Chinyoka, R. Alroobaea, R. Zulkifli, et al. Numerical simulations of third-grade fluid flow with exothermic reactions in porous media-saturated vertical microchannels, Numer. Heat Tr. B-Fund., 86 (2025), 2473–2493. https://doi.org/10.1080/10407790.2024.2345508 doi: 10.1080/10407790.2024.2345508
|
| [17] | A. Abbas, A. Khan, T. Abdeljawad, N. Becheikh, L. Kolsi, Theoretical analysis of MHD Darcy-Forchheimer porous media for hybrid nanomaterial flow with third-grade fluid over an exponential stretching sheet, Fractals, 2025. |
| [18] |
J. Kim, Y. T. Kang, C. K. Choi, Soret and Dufour effects on convective instabilities in binary nanofluids for absorption application, Int. J. Refrig., 30 (2007), 323–328. https://doi.org/10.1016/j.ijrefrig.2006.04.005 doi: 10.1016/j.ijrefrig.2006.04.005
|
| [19] |
M. B. K. Moorthy, K. Senthilvadivu, Soret and Dufour effects on natural convection flow past a vertical surface in a porous medium with variable viscosity, J. Appl. Math., 2012 (2012), 634806. https://doi.org/10.1155/2012/634806 doi: 10.1155/2012/634806
|
| [20] |
A. Majeed, T. Javed, A. Ghaffari, Numerical investigation on flow of second grade fluid due to stretching cylinder with Soret and Dufour effects, J. Mol. Liq., 221 (2016), 878–884. https://doi.org/10.1016/j.molliq.2016.06.065 doi: 10.1016/j.molliq.2016.06.065
|
| [21] |
M. Y. Malik, O. D. Makinde, Parabolic curve fitting study subject to Joule heating in MHD thermally stratified mixed convection stagnation point flow of Eyring-Powell fluid induced by an inclined cylindrical surface, J. King Saud Univ. Sci., 30 (2018), 440–449. https://doi.org/10.1016/j.jksus.2017.02.003 doi: 10.1016/j.jksus.2017.02.003
|
| [22] |
A. Shojaei, A. J. Amiri, S. S. Ardahaie, K. Hosseinzadeh, D. D. Ganji, Hydrothermal analysis of Non-Newtonian second grade fluid flow on radiative stretching cylinder with Soret and Dufour effects, Case Stud. Therm. Eng., 13 (2019), 100384. https://doi.org/10.1016/j.csite.2018.100384 doi: 10.1016/j.csite.2018.100384
|
| [23] |
A. A. Khan, N. Abbas, S. Nadeem, Q. H. Shi, M. Y. Malik, M. Ashraf, et al., Non-Newtonian based micropolar fluid flow over nonlinear starching cylinder under Soret and Dufour numbers effects, Int. Commun. Heat Mass, 127 (2021), 105571. https://doi.org/10.1016/j.icheatmasstransfer.2021.105571 doi: 10.1016/j.icheatmasstransfer.2021.105571
|
| [24] |
P. Kumar, R. S. Yadav, O. D. Makinde, Numerical study of Williamson fluid flow and heat transfer over a permeable stretching cylinder with the effects of Joule heating and heat generation/absorption, Heat Transfer, 52 (2023), 3372–3388. https://doi.org/10.1002/htj.22832 doi: 10.1002/htj.22832
|
| [25] |
H. Basha, Magnetized dissipative Soret and Dufour effects on thermally radiative Casson fluid flow over a stretching cylinder with Cattaneo–Christov heat and mass flux models, Wave. Random Complex, 2023, 1–29. https://doi.org/10.1080/17455030.2023.2206491 doi: 10.1080/17455030.2023.2206491
|
| [26] |
G. Dharmaiah, S. Dinarvand, J. R. Prasad, S. Noeiaghdam, M. Abdollahzadeh, Non-homogeneous two-component buongiorno model for nanofluid flow toward Howarth's wavy cylinder with activation energy, Results Eng., 17 (2023), 100879. https://doi.org/10.1016/j.rineng.2023.100879 doi: 10.1016/j.rineng.2023.100879
|
| [27] |
P. Thiyagarajan, S. Sathiamoorthy, H. Balasundaram, O. D. Makinde, U. F. Gamiz, S. Noeiaghdam, et al., Mass transfer effects on mucus fluid in the presence of chemical reaction, Alex. Eng. J., 62 (2023), 193–210. https://doi.org/10.1016/j.aej.2022.06.030 doi: 10.1016/j.aej.2022.06.030
|
| [28] |
E. N. Thabet, A. M. A. Alla, H. A. Hosham, S. M. M. El-Kabeir, Entropy generation in peristaltic transport of bio-convective couple stress blood nanofluid with chemotactic microorganisms involving viscous dissipation and slip effects, Alex. Eng. J., 102 (2024), 361–380. https://doi.org/10.1016/j.aej.2024.05.062 doi: 10.1016/j.aej.2024.05.062
|
| [29] |
A. M. Abd‐Alla, E. N. Thabet, H. A. Hosham, S. M. M. El‐Kabeir, Significance of variable thermal conductivity and suction/injection in unsteady MHD mixed convection flow of Casson Williamson nanofluid through heat and mass transport with gyrotactic microorganisms, ZAMM‐J. Appl. Math. Mech., 104 (2024), e202300501. https://doi.org/10.1002/zamm.202300501 doi: 10.1002/zamm.202300501
|
| [30] |
M. Ali, N. Abbas, W. Shatanawi, Soret and Dufour effects on Sutterbynanofluid flow over a Riga stretching surface with variable thermal conductivity, Mod. Phys. Lett. B, 39 (2025), 2450455. https://doi.org/10.1142/S0217984924504554 doi: 10.1142/S0217984924504554
|
| [31] |
B. Ahmed, F. Akbar, A. Ghaffari, S. U. Khan, M. I. Khan, Y. D. Reddy, Soret and Dufour aspects of the third-grade fluid due to the stretching cylinder with the Keller box approach, Wave. Random Complex, 35 (2025), 7236–7248. https://doi.org/10.1080/17455030.2022.2085891 doi: 10.1080/17455030.2022.2085891
|
| [32] |
K. Bhattacharyya, Boundary layer flow and heat transfer over a permeable shrinking cylinder with mass suction, Int. J. Appl. Mech. Eng., 18 (2013). https://doi.org/10.2478/ijame-2013-0062 doi: 10.2478/ijame-2013-0062
|
| [33] |
G. K. Ramesh, S. Manjunatha, G. S. Roopa, A. J. Chamkha, Hybrid (ND-Co3O4/EG) nanoliquid through a permeable cylinder under homogeneous-heterogeneous reactions and slip effects, J. Therm. Anal. Calorim., 146 (2021). https://doi.org/10.1007/s10973-020-10106-1 doi: 10.1007/s10973-020-10106-1
|
Figures(11) / Tables(7)
Nadeem Abbas, Wasfi Shatanawi. Thermal and solutal boundary layer of a third grade Ellis fluid over a vertical cylinder with cross-diffusion and reaction effects[J]. AIMS Mathematics, 2026, 11(2): 5006-5028. doi: 10.3934/math.2026205
DownLoad: