CASSON FLUID OF A STAGNATION-POINT FLOW (SPF) TOWARDS A VERTICAL SHRINKING/STRETCHING SHEET

Authors

Keywords:

Biot number; Fluid flow; Stream function; RK-Fehlberg integration scheme; Lorentz force

Abstract

This study presents a convectively heated hydromagnetic Stagnation-Point Flow (SPF) of an electrically conducting Casson fluid towards a vertically stretching/shrinking sheet. The Casson fluid model is used to characterize the non-Newtonian fluid behaviour and using similarity variables, the governing partial differential equations are transformed into coupled nonlinear ordinary differential equations. The dimensionless nonlinear equations are solved numerically by Runge-Kutta Fehlberg integration scheme with shooting technique. The effects of the thermophysical parameters on velocity and temperature profiles are presented graphically and discussed quantitatively. The result shows that the flow field velocity decreases with increase in magnetic field parameter and Casson fluid parameter .

Dimensions

Sakiadis, B. C. (1961). Boundary-layer behaviour of continuous solid surfaces: I. boundary-layer equations for two-dimensional and axisymmetric flow. AIChE Journal, 7(1): 26–28. https://doi.org/10.1002/aic.690070108

Makinde, O. D. and Aziz, A. (2010). MHD mixed convection from a vertical plate embedded in a porous medium with a convective boundary condition. Int. J. of Therm. Sci., 49(9): 1813-1820. https://doi.org/10.1016/j.ijthermalsci.2010.05.015

Bachok, N., Ishak, A. and Pop, I. (2012). Boundary layer flow over a moving surface in a nanofluid with suction or injection. Acta Mech. Sin., 28(1): 34-40.

Mutuku, W. N. and Makinde, O. D. (2014). On hydromagnetic boundary layer flow of nanofluids over a permeable moving surface with newtonian heating. Latin American Applied Research, 44(1): 57-62. ISSN 1851-8796

Khan, M. and Khan, W. A. (2016). MHD boundary layer flow of a power-law nanofluid with new mass flux condition. AIP Advances, 6, 025211. https://doi.org/10.1063/1.4942201

Makinde, O. D. (2012). Computational modeling of mhd unsteady flow and heat transfer toward a flat plate with navier slip and newtonian heating. Braz. J. Chem. Eng., 29(2) 159-166.

Crane, L. J. (1970). Flow past a stretching plate. Zeitschrift für Angewandte Mathematik und Physik, 21: 645-647. http://dx.doi.org/10.1007/BF01587695

Chen, C. K. and Char, M. I. (1988). Heat transfer of a continuous stretching surface with suction or blowing. J. Math. Anal. Appl., 135: 568–80.

Chiam, T. C. 1994 “Stagnation-point flow towards a stretching plate. J. Phys. Soc. Japan, 63: 2443–4. http://dx.doi.org/10.1143/JPSJ.63.2443

Layek, G. C., Mukhopadhyay, S. and Samad, S. K. A. (2007). Heat and mass transfer analysis for boundary layer stagnation-point flow towards a heated porous stretching sheet with heat absorption/generation and suction/blowing. Int. Commun. Heat Mass Transfer, 34: 347–56.

Makinde, O. D. and Aziz, A. (2011). Boundary layer flow of a nanofluid past a stretching sheet with a convective boundary condition. Int. J. Therm. Sci., 50: 1326–32.

Gupta, P. S. and Gupta, A. S. (1977). Heat and mass transfer on a stretching sheet with suction or blowing. The Canadian Journal of Chemical Engineering, 55: 744-746. http://dx.doi.org/10.1002/cjce.5450550619

Lun-Shin Yao, Y. and Mamun, M. Md. (2008). Non-Newtonian Fluid Flow on a Flat Plate Part 1: Boundary Layer. Journal of Thermophysics and Heat Transfer, 22(4): 758-761. http://dx.doi.org/10.2514/1.35187

Reddy, B. S., Kishan, N. and Rajasekhar, M. N. (2012). MHD boundary layer flow of a non-newtonian power-law fluid on a moving flat plate. Advances in Applied Science Research, 3(3): 1472-1481.

Xu, H. and Shi-Jun, L. (2009). Laminar flow and heat transfer in the boundary-layer of non-newtonian fluids over a stretching flat sheet. Computers and Mathematics with Applications, 57: 1425–1431.

Fox, V. G., Erickson, L. E. and Fan, L. T. (1969). The laminar boundary layer on a moving continuous flat sheet immersed in a non-newtonian fluid. AIChE Journal, 15: 327-333. http://dx.doi.org/10.1002/aic.690150307

Casson, N. (1959). A flow equation for pigment oil suspensions of the printing ink type. In: Mill, C.C., Ed., Rheology of Disperse Systems. Pergamon Press, Oxford, 84-102.

Bhattacharyya, K. (2013a). Boundary layer stagnation-point flow of casson fluid and heat transfer towards a shrinking/sketching sheet. Frontiers in Heat and Mass Transfer, 4, 023003. https://doi.org/10.5098/hmt.v4.2.3003

Hussain, T., Shehzad, S. A., Alsaedi, A. Hayat, T. and Ramzan, M. (2015). Flow of casson nanofluid with viscous dissipation and convective conditions: a mathematical model. Journal of Central South University, 22: 1132-1140. http://dx.doi.org/10.1007/s11771-015-2625-4

Pramanik, S. (2014). Casson fluid flow and heat transfer past an exponentially porous stretching surface in presence of thermal radiation. Ain Shams Engineering Journal, 5: 205–212.

Mustafa, M., Hayat, T., Pop, I. and Aziz, A. (2011). Unsteady boundary layer flow of a casson fluid due to an impulsively started moving flat plate. Heat Transfer, 40: 563-576. http://dx.doi.org/10.1002/htj.20358

Medikare, M., Joga, S. and Chidem, K. K. (2016). MHD stagnation point flow of a casson fluid over a nonlinearly stretching sheet with viscous dissipation. American J. of Comp. Mathematics, 6: 37-48. http://dx.doi.org/10/4236/ajcm.2016.61005

Mutuku, W. N. (2016). Ethylene glycol (EG) based nanofluids as a coolant for automotive radiator. Asia Pacific Journal for Computational Engineering, 3(1): 1-15. https://doi.org/10.1186/s40540-016-0017-3

Mabood, F., Ibrahim, S. M., Kumar, P. V. and W. A. Khan, (2017). Viscous dissipation effects on unsteady mixed convective stagnation point flow using Tiwari-Das nanofluid model. Results in Physics, 7: 280-287. http://dx.doi.org/10.1016/j.rinp.2016.12.037

Seth, G. S., Tripathi, R. and Mishra, M. K. (2017). Hydromagnetic thin film flow of casson fluid in non-darcy porous medium with joule dissipation and navier's partial slip. Applied Mathematics and Mechanics, 38: 1613-1626. https://doi.org/10.1007/s10483-017-2272-7

Bhattacharyya, K. (2013b). MHD stagnation-point flow of casson fluid and heat transfer over a stretching sheet with thermal radiation. Journal of Thermodynamics. http://dx.doi.org/10.1155.2013/169674

Battacharyya, K. (2011). Dual solution in boundary layer stagnation-point flow and mass transfer with chemical reaction past a stretching/shrinking sheet. International Communications in Heat and Mass Transfer, 38(7): 917-922.

Mahapatra, T. R. and Gupta, A. S. (2001). Magnetohydrodynamic stagnation-point flow towards a stretching sheet. Acta Mechanica, 152(1-4): 191-196.

Mutuku, W. N. and Makinde, O. D. (2017). Double stratification effects on heat and mass transfer in unsteady mhd nanofluid flow over a flat surface. Asia Pac. J. Comput. Engin., 4(2). https://doi.org/10.1186/s40540-017-0021-2

Saidulu, N. and Lakshmi, A. V. (2016). MHD flow of casson fluid with slip effects over an exponentially porous stretching sheet in presence of thermal radiation, viscous dissipation and heat source/sink. American Res. J. of Mathematics, 2: 1-15. ISSN (online) 2378-704X

Ouru, J. O., Mutuku, W. N. and Oke, A. S. (2020). Buoyancy-induced mhd stagnation point flow of williamson fluid with thermal radiation. Journal of Engineering Research and Reports, 11(4): 9-18. https://doi.org/10.9734/jerr/2020/v11i417065

El-Aziz, M. A. and Yahya, A. S. (2017). Perturbation analysis of unsteady boundary layer slip flow and heat transfer of casson fluid past a vertical permeable plate with hall current. Applied Mathematics and Computation, 307: 146-164. https://doi.org/10.1016/j.amc.2017.02.034

Mutuku, W. N. and Makinde, O. D. (2013). Combined effect of buoyancy force and navier slip on mhd flow of a nanofluid over a convectively heated vertical porous plate. The Scientific World Journal, 2013. https://doi.org/10.1155/2013/725643

Mutuku, W. N. (2014). Analysis of hydromagnetic boundary layer flow and heat transfer of nanofluids, Doctoral Thesis, Cape Peninsula University of Technology, South Africa.

Shehzad, S. A., Hayat, T., Qasim, M. and Asghar, S. (2013). Effects of mass transfer on mhd flow of casson fluid with chemical reaction and suction. Brazillian Journal of Chemical Engineering, 30(1). https://doi.org/10.1590/S0104-66322013000100020

Sobamowo, G., Jayesimi, L., Oke, D., Yinusa, A. and Adedibu, O. (2019). Unsteady casson nanofluid squeezing flow between two parallel plates embedded in a porous medium under the influence of magnetic field. Open Journal of Mathematical Sciences, 3: 59-73. https://dx.doi.org/10.30538/oms2019.0049

Ferdom, M., Khaleque, T. S. and Bangalee, M. Z. I. “Heat generation and radiation effects on mhd casson fluid flow over stretching surface through porous medium. European J. of Advances in Engineering and technology, 4(11): 859-857.

Sheikh, M. and Abbas, Z. (2017). Homogeneous-heterogeneous reactions in stagnation point flow of casson fluid due to a stretching/shrinking sheet with uniform suction and slip effects. Ain Shams Engineering Journal, 8(3): 467-474. https://doi.org/10.1016/j.asej.2015.09.10fcombined

Medikare, M., Joga, S. and Chidem, K. K. (2016). MHD stagnation point flow of a casson fluid over a nonlinearly stretching with viscous dissipation. American Journal of Computational Mathematics, 6(1): 37-48. https://dx.doi.org/10.4236/ajcm.ajcm.2016.610005

Singh, M K., Kushvah, B. S., Seth, G. S. and Prakash, J. (2018). Applications of fluid dynamics. In Proceedings of ICAFD 2016 Springer Science and Business Media LLC.

Nandy, S. K. (2013). Analytical solution of mhd stagnation-point flow and heat transfer of casson fluid over a stretching sheet with partial slip. International Scholarly Research Notices, 2013. https://doi.org/10.1155/2013/108264

Bhattacharyya, K., Hayat, T. and Alsaedi, A. (2013). Exact solution for boundary layer flow of casson fluid over a permeable stretching/shrinking sheet. Journal of Applied Mathematics and Mechanics, 94(6). https://doi.org/10.1002/zamm.201200031

Mukhopadhyay, S., Mondal, I. C. and Chamka, A. J. (2013). Casson fluid flow and heat transfer past a symmetric wedge. Heat Transfer, 42(8). https://doi.org/10.1002/htj.21065

Gangadhar, K., Kannan, T., Jayalakshmi P. and Sakthivel, G. (2018). Dual solutions for mhd casson fluid over a shrinking sheet with newtonian heating. International Journal of Ambient Energy, 2018. https://doi.org/10.1080/01430750.2018.1550018

Shateyi, S. and Marewo, G. T. (2014). Numerical analysis of mhd stagnation-point flow of casson fluid, heat and mass transfer over a stretching sheet. Advances in Applied and Pure Mathematics, 128-132.

Bhattacharyya, K. and Vajravelu, K. (2012). Stagnation-point flow and heat transfer over an exponentially shrinking sheet. Communications in Nonlinear Science and Numerical Simulation, 17(7): 2728-2734. https://doi.org/10.1016/j.cnsns.2011.11.011.

Published

14-06-2021

How to Cite

CASSON FLUID OF A STAGNATION-POINT FLOW (SPF) TOWARDS A VERTICAL SHRINKING/STRETCHING SHEET. (2021). FUDMA JOURNAL OF SCIENCES, 5(1), 16-26. https://doi.org/10.33003/fjs-2021-0501-508

Issue

Vol. 5 No. 1 (2021): FUDMA Journal of Sciences - Vol. 5 No. 1

Section

Research Articles
Copyright & Licensing

FUDMA Journal of Sciences

How to Cite

CASSON FLUID OF A STAGNATION-POINT FLOW (SPF) TOWARDS A VERTICAL SHRINKING/STRETCHING SHEET. (2021). FUDMA JOURNAL OF SCIENCES, 5(1), 16-26. https://doi.org/10.33003/fjs-2021-0501-508