The steady state magnetohydrodynamic flow of Jeffrey nanofluid with nonlinear thermal radiation, over a porous plate together with prescribed boundary conditions of interest was carried out via Lie symmetry group alteration. The all-inclusive flow of the present model incorporates the Jeffrey parameters, nonlinear thermal radiation, heat generation, Brownian motion, chemical reaction, thermophoresis and porosity parameter. The derived governing equations of the problem are highly nonlinear coupled partial differential equations. The Lie group approach was used to convert the system partial differential equations to a system of ordinary differential equations which was solved numerically with the help of a matlab solver called bvp4c. The established numerical results were discussed with help of line graph. The Rayleigh number and porosity parameter enriched the velocity fluid. The rise of the temperature ratio parameter and heat generation parameter improved the temperature contours and is reduced by boosting the Prandtl number. Lewis number, chemical reaction parameter diminished the concentration profile and took the opposite direction for Biot number. Equally, by improving Jeffrey parameter and Hartmann number weakened skin friction profile. Also, Sherwood number, and the Nusselt number were also expanded. The recent outcome will be useful in the automobile industry, polymer industry and so on.
| Published in | International Journal of Theoretical and Applied Mathematics (Volume 9, Issue 3) |
| DOI | 10.11648/j.ijtam.20230903.11 |
| Page(s) | 23-34 |
| Creative Commons |
This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited. |
| Copyright |
Copyright © The Author(s), 2023. Published by Science Publishing Group |
Nonlinear Thermal Radiation, Heat Source-Sink, Porosity Parameter and Jeffrey Parameter
| [1] | B. Ahmad, A. Nawaz, S. U. Khan, M. I. Khan, T. Abbas, Y. D. Reddy, K. Guedri, M. Y. Malik, B. S. Goud, A. M. Galal, “Thermal diffusion of Maxwell nanoparticles with diverse flow features: Lie group simulations,” International Communication in Heat and Mass Transfer. vol. 136, p. 106-164, 2022. |
| [2] | B. K. Jha, and G. Samaila, “Nonlinear approximation for buoyancy-driven mixed convection heat and mass transfer flow over an inclined porous plate with Joule heating, nonlinear thermal radiation, viscous dissipation and thermophoresis effects,” Numerical Heat Transfer, Part B: Fundamentals, 2022, DOI: 10.1080/10407790.2022.2150341. |
| [3] | M. I. Khan, M. Waqas, T. Hayat, A. Alsaedi, M. I. Muhammad Imran Khan, “Significance of nonlinear radiation in mixedconvection flow of magneto Walter-B nanoliquid,” International Journal of Hydrogen Energy vol. 42, 26408–26416, 2017. |
| [4] | M. R. Ilias, N. S. Aidah Ismail, A. Raji, N. A. Rawi, S. Shafie, “Unsteady aligned MHD boundary layer flow and heat transfer of a magnetic nanofluids past an inclined plate,” International Journal Mechanical Engineering, vol. 9, no. 2, p. 197-206, 2020. |
| [5] | M. O. Lawal, K. B. Kasali, H. A. Ogunseye, M. O. Oni, Y. O. Tijani, Y. T. Lawal “On the mathematical model of Eyring–Powell nanofluid flow with non-linearradiation, variable thermal conductivity and viscosity,” Partial Differential Equations in Applied Mathematics, vol. 5, p. 1-11, 2022. |
| [6] | O. F. Bidemi and M. S. S. Ahamed “Soret and Dufour effects on unsteady casson magneto-nanofluid flow over an inclined plate embedded in a porous medium,” World Journal of Engineering, https//dio. Org/10.1108/WJE-04-2018-0144, 2019. |
| [7] | S. Aman, I. Khan, Z. Ismail, M. Z. Salleh, A. S. Alshomrani, M. S. Alghamdi, “Magnetic field effect on Poiseuille flow and heat transfer of carbon nanotubes along a vertical channel filled with Casson fluid,” AIP Advances, vol. 7 no. 1, p. 1-18, 2017. |
| [8] | S. Aman, I. Khan, Z. Ismail, M. Z. Sallah, I. Tlili “A new Caputo time fractional model for heat transfer enhancement of water based graphene nanofluid: An application to solar energy” Results in Physics, vol. 9, p. 1352-1362, 2018. |
| [9] | Z. Abbas, S. Hussain, M. Y. Rafiq, J. Hasnain, “Oscillatory slip flow of Fe3O4 and Al2O3 nanoparticles in a vertical porous channel using Darcy's law with thermal radiation,” Heat Transfer, 2020, https://doi.org/10.1002/htj.21771,. |
| [10] | M. G. Sobamowo, “Combined effects of thermal radiation and nanoparticles on free convection flow and heat transfer of casson fluid over a vertical plate,” International Journal of Chemical Engineering, 2018, https://doi.org/10.1155/2018/7305973. |
| [11] | K. Das, A. Sarkary, P. K. Kunduz, “Nanofluid Flow over a Stretching Surface in Presence of Chemical Reaction and Thermal Radiation: An Application of Lie Group Transformation,” Journal of Siberian Federal University. Mathematics & Physics, vol. 10, no 2, p. 146–157, 2017. |
| [12] | T. Muhammad, H. Waqas, U. Manzoor, U. Farooq, Z. F. Rizvi, “On doubly stratified bioconvective transport of Jeffrey nanofluid with gyrotactic motile microorganisms,” Alexandria Engineering Journal vol. 61, p. 1571-1583, 2021. |
| [13] | T. Hayat, S. Qayyum, 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 vol. 7, 2341–2351, 2017. |
| [14] | M. G. Reddy, and O. D. Makinde, “Magnetohydrodynamic peristaltic transport of Jeffrey nanofluid in an asymmetric channel,” Journal of Molecular Liquids vol. 223, p. 1242–1248, 2016. |
| [15] | M. Waqas, S. A. Shehzad, T. Hayat, M. Ijaz Khan, A. Alsaedi, “Simulation of magnetohydrodynamic and radiation heat transport in convectively heated stratified flow of Jeffrey nanofluid.” Journal of Physics and Chemistry of Solids, vol. 133, p. 45-51, 2019. |
| [16] | F. M. Abbasi, S. Shehzad, A. T. Hayat1, M. S. Alhuthali, (2016) Mixed convection flow of Jeffrey nanofluid with thermal radiation and double stratification. Journal of Hydrodynamic, vol. 28, no. 5, p. 840-849, 2016. |
| [17] | G. C. Rana, “Effects of rotation on Jeffrey nanofluid flow saturated by a porous medium” Journal of Applied Mathematics and Computational Mechanics, vol. 20 no. 3, p. 17-29, 2021. |
| [18] | M. A. N. Zin, I. Khan, S. Shafie, A. S. Alshomrani, “Analysis of heat transfer for unsteady MHD free convection flow of rotating Jeffrey nanofluid saturated in a porous medium,” Result in Physics, vol. 7, p. 288-309, 2017. |
| [19] | S. U. Khan, S. A. Shehzad,” Flow of Jeffrey nanofluids over convectively heated oscillatory moving sheet with magnetic field and porosity effects,” Journal of Porous Media vol. 23, no. 6, 907-922, 2020. |
| [20] | T. Hayat, M. Mustafa, I. Pop, “Heat and mass transfer for Soret and Dufours effect on mixed convection boundary layer flow over a stretching vertical surface in a porous medium filled with a viscoelastic fluid” Communication Nonlinear Science Numerical Simulation, vol. 15, p. 1183-1196, 2010. |
| [21] | M. Turkyilmazoglu,” The analytical solution of mixed convection heat transfer and fluid flow of a MHD viscoelastic fluid over a permeable stretching surface,” International Journal mechical science, vol. 77 p. 263-268, 2013. |
| [22] | X. Y. Li, S. R. Mishra, P. K. Pattnaik, S. Baag, M. Y. Li, I. M. Khan, B. N. Khan, K. M. Alaoui, U.S. Khan, (2022) Numerical treatment of time dependent magnetohydrodynamic nanofluid flow of mass and heat transport subject to chemical reaction and heat source, Alexendrial Engineering Journal. 61: (3) 2484–2491. |
APA Style
Williams, M., Bala Yabo, I., Mustafa, A., Audu, A. (2023). Analyzing Steady State Heat and Mass Transfer in Jeffrey Nanofluid with Nonlinear Thermal Radiation. International Journal of Theoretical and Applied Mathematics, 9(3), 23-34. https://doi.org/10.11648/j.ijtam.20230903.11
ACS Style
Williams, M.; Bala Yabo, I.; Mustafa, A.; Audu, A. Analyzing Steady State Heat and Mass Transfer in Jeffrey Nanofluid with Nonlinear Thermal Radiation. Int. J. Theor. Appl. Math. 2023, 9(3), 23-34. doi: 10.11648/j.ijtam.20230903.11
AMA Style
Williams M, Bala Yabo I, Mustafa A, Audu A. Analyzing Steady State Heat and Mass Transfer in Jeffrey Nanofluid with Nonlinear Thermal Radiation. Int J Theor Appl Math. 2023;9(3):23-34. doi: 10.11648/j.ijtam.20230903.11
Share This Article
Twitter
Linked In
Facebook
Copy
Download@article{10.11648/j.ijtam.20230903.11,
author = {Michael Williams and Isah Bala Yabo and Aminu Mustafa and Ahmed Audu},
title = {Analyzing Steady State Heat and Mass Transfer in Jeffrey Nanofluid with Nonlinear Thermal Radiation},
journal = {International Journal of Theoretical and Applied Mathematics},
volume = {9},
number = {3},
pages = {23-34},
doi = {10.11648/j.ijtam.20230903.11},
url = {https://doi.org/10.11648/j.ijtam.20230903.11},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijtam.20230903.11},
abstract = {The steady state magnetohydrodynamic flow of Jeffrey nanofluid with nonlinear thermal radiation, over a porous plate together with prescribed boundary conditions of interest was carried out via Lie symmetry group alteration. The all-inclusive flow of the present model incorporates the Jeffrey parameters, nonlinear thermal radiation, heat generation, Brownian motion, chemical reaction, thermophoresis and porosity parameter. The derived governing equations of the problem are highly nonlinear coupled partial differential equations. The Lie group approach was used to convert the system partial differential equations to a system of ordinary differential equations which was solved numerically with the help of a matlab solver called bvp4c. The established numerical results were discussed with help of line graph. The Rayleigh number and porosity parameter enriched the velocity fluid. The rise of the temperature ratio parameter and heat generation parameter improved the temperature contours and is reduced by boosting the Prandtl number. Lewis number, chemical reaction parameter diminished the concentration profile and took the opposite direction for Biot number. Equally, by improving Jeffrey parameter and Hartmann number weakened skin friction profile. Also, Sherwood number, and the Nusselt number were also expanded. The recent outcome will be useful in the automobile industry, polymer industry and so on.
},
year = {2023}
}
TY - JOUR T1 - Analyzing Steady State Heat and Mass Transfer in Jeffrey Nanofluid with Nonlinear Thermal Radiation AU - Michael Williams AU - Isah Bala Yabo AU - Aminu Mustafa AU - Ahmed Audu Y1 - 2023/12/22 PY - 2023 N1 - https://doi.org/10.11648/j.ijtam.20230903.11 DO - 10.11648/j.ijtam.20230903.11 T2 - International Journal of Theoretical and Applied Mathematics JF - International Journal of Theoretical and Applied Mathematics JO - International Journal of Theoretical and Applied Mathematics SP - 23 EP - 34 PB - Science Publishing Group SN - 2575-5080 UR - https://doi.org/10.11648/j.ijtam.20230903.11 AB - The steady state magnetohydrodynamic flow of Jeffrey nanofluid with nonlinear thermal radiation, over a porous plate together with prescribed boundary conditions of interest was carried out via Lie symmetry group alteration. The all-inclusive flow of the present model incorporates the Jeffrey parameters, nonlinear thermal radiation, heat generation, Brownian motion, chemical reaction, thermophoresis and porosity parameter. The derived governing equations of the problem are highly nonlinear coupled partial differential equations. The Lie group approach was used to convert the system partial differential equations to a system of ordinary differential equations which was solved numerically with the help of a matlab solver called bvp4c. The established numerical results were discussed with help of line graph. The Rayleigh number and porosity parameter enriched the velocity fluid. The rise of the temperature ratio parameter and heat generation parameter improved the temperature contours and is reduced by boosting the Prandtl number. Lewis number, chemical reaction parameter diminished the concentration profile and took the opposite direction for Biot number. Equally, by improving Jeffrey parameter and Hartmann number weakened skin friction profile. Also, Sherwood number, and the Nusselt number were also expanded. The recent outcome will be useful in the automobile industry, polymer industry and so on. VL - 9 IS - 3 ER -
Department of Mathematics, Usmanu Danfodiyo University, Sokoto, Nigeria
Information