Chemically Reactive Unsteady Flow of Casson Fluid over a Stretching Surface
DOI:
https://doi.org/10.56532/mjsat.v5i2.509Keywords:
Chemical Reaction, Casson Fluid, Unsteadiness ParameterAbstract
This study aims to investigate the unsteady flow behaviour of Casson fluid over a stretching surface in the presence of a magnetic field. The effects of magnetic field, Casson parameter and chemical reaction are also accounted for in this model. A Casson non-Newtonian constitutive model is utilized to describe the fluid transport. By employing appropriate similarity transformations, the model equations are reformulated as ordinary differential equations. Then the reduced differential equations are solved numerically using the Nachtsheim-Swigert shooting technique along with a sixth-order Runge-Kutta method. The graphical representation illustrates the influence of key physical parameters on flow characteristics. It is indicated that fluid velocity declines with a rise in the unsteadiness parameter and temperature significantly decreases due to this unsteadiness. Moreover, increasing chemical reaction parameter diminishes both velocity and concentration field. Again to validate the accuracy of the developed code, the results are compared with those from earlier research, demonstrating good agreement.
References
N. T. M. Eldabe NTM, G. Saddeck, and A. F. El-Sayed, “Heat transfer of MHD non-Newtonian Casson fluid flow between two rotating cylinders,” Mechanics and Mechanical Engineering, vol. 5, no. 2, pp. 237-251, 2001. doi: https://doi.org/10.4236/am.2024.158034
S. Nadeem, R. U. Haq, and C. Lee, “MHD flow of a Casson fluid over an exponentially shrinking sheet,” Scientia Iranica, vol. 19, no. 6, pp. 1550-1553, 2012. doi: https://doi.org/10.1016/j.scient.2012.10.021
N. Casson, “Flow equation for pigment-oil suspensions of the printing ink-type,” Rheology of disperse systems, Pergamon Press, Oxford, pp. 84-104, 1959.
R. K. Dash, K. N. Mehta, and G. Jayaraman, “Casson fluid flow in a pipe filled with a homogeneous porous medium,” International Journal of Engineering Science, vol. 34, no. 10, pp. 1145-1156, 1996. doi: https://doi.org/10.1016/0020-7225(96)00012-2
P.D. McCormack and L. Crane, “Physics of Fluid Dynamics”, New York, Academic Press, 1973.
T. Hayat, M. Sajid, and I. Pop, “Three-dimensional flow over a stretching surface in a viscoelastic fluid,” Nonlinear Analysis: Real World Applications, vol. 9, no.4, pp. 1811-1822, 2008. doi: https://dx.doi.org/10.1016/j.nonrwa.2007.05.010
E. M. A. Elbashbeshy, and M. A. A. Bazid, “Heat transfer over an unsteady stretching surface,” Heat and mass transfer, vol.41, no. 1, pp. 1-4, 2004. doi: https://doi.org/10.1007/s00231-004-0520-x
S. Sharidan, M. Mahmood, and I. Pop, “Similarity solutions for the unsteady boundary layer flow and heat transfer due to a stretching sheet,” Applied Mechanics and Engineering, vol. 11, no. 3, pp. 647, 2006.doi: https://www.researchgate.net/publication/266493374
P. R. Sharma, and G. Singh, “Unsteady MHD free convective flow and heat transfer along a vertical porous plate with variable suction and internal heat generation,” International Journal of Applied Mathematics and Mechanics, vol. 4, no. 5, pp. 1-8, 2008. doi: https://citeseerx.ist.psu.edu/document?repid=rep1&type=pdf&doi=207ad262ac07e64dc8d30421b64a23b036b18671.
M. S. Alam, M. M. Rahman, and M. A. Samad, “Dufour and Soret effects on unsteady MHD free convection and mass transfer flow past a vertical porous plate in a porous medium,” Nonlinear Analysis: Modelling and Control, vol. 11, no. 3, pp. 217-226, 2006. doi: https://doi.org/10.15388/NA.2006.11.3.14743
H. Bararnia, M. Gorji, G. Domairry, and A. R. Ghotbi, “An analytical study of boundary layer flows on a continuous stretching surface,” Acta applicandae mathematicae, vol. 106, pp.125-133, 2009. link: https://link.springer.com/article/10.1007/s10440-008-9286-3
M. A. El-Aziz, “Viscous dissipation effect on mixed convection flow of a micropolar fluid over an exponentially sheet,” Can. J. Phys., vol.87, pp. 359-368, 2009. doi: http://dx.doi.org/10.1139/P09-047
K. Bhattacharyya, S. Mukhopadhyay, and G. C. Layek, “Slip effects on an unsteady boundary layer stagnation-point flow and heat transfer towards a stretching sheet,” Chinese Physics Letters, vol. 28, no.9, pp. 094702, 2011. doi: https://doi.org/10.1088/0256-307X/28/9/094702
D. Iranian, P. Loganathan, and P. Ganesan, “Unsteady MHD natural convective flow over vertical plate in thermally stratified media with variable viscosity and thermal conductivity,” International Journal of Computer Applications, vol. 121, no. 3, pp.18-24, 2015. doi: https://citeseerx.ist.psu.edu/document?repid=rep1&type=pdf&doi=a145dd7e73c429a7f600611d574eaa1dc193e324
N. C. Mathanti, and P. Gaur, “The effects of varying viscosity and thermal conductivity on steady free convective flow and heat transfer along an isothermal vertical plate in presence of heat sink,” Journal of Applied Fluid Mechanics, vol. 2, no.1, pp. 23-28, 2009. doi: https://www.researchgate.net/publication/26579367
M. Nakamura, and T. Sawada, “Numerical study on the flow of a non-Newtonian fluid through an axisymmetric stenosis,” Journal of Biomechanical Engineering, Vol. 110, no. 137, pp. 137-143,1988. doi: http://dx.doi.org/10.1115/1.3108418
A. Neeraja, R. R. Devi, B. Devika, V. N. Radhika, and M. K. Murthy, “Effects of viscous dissipation and convective boundary conditions on magnetohydrodynamics flow of casson liquid over a deformable porous channel,” Results in Engineering, vol. 4, pp. 100040, 2019. doi: https://doi.org/10.1016/j.rineng.2019.100040
P.R. Nachtsheim,and P. Swigert, “Satisfaction of the asymptotic boundary conditions in numerical solution of the systems of non-linear equations of boundary layer type,” Ph.D. Thesis, National Aeronautics and Space Administration, vol. 3004, 1965.
J.C. Misra, and A. Sinha, “Effect of thermal radiation on MHD flow of blood and heat transfer in a permeable capillary in stretching motion,” Heat Mass Transfer, vol. 49, pp. 617-628, 2013. doi: https://doi.org/10.1007/s00231-012-1107-6
S. Pramanik, “Casson fluid flow and heat transfer past an exponentially porous stretching surface in presence of thermal radiation,” Ain shams engineering journal, vol. 5, no. 1, pp. 205-212, 2014. doi: https://doi.org/10.1016/j.asej.2013.05.003
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2025 Md. Maruf Hasan, M Enamul Karim
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
