Derivation of Johnson-Segalman Model in Cylindrical Co-ordinates

M. O. Mosa*
*Mathematics Teacher, Sudan International Grammar School, Sudan.
Periodicity:April - June'2019
DOI : https://doi.org/10.26634/jmat.8.2.16389

Abstract

The Johnson-Segalman model is a viscoelastic fluid model for non-affine deformations. However, non-Newtonian fluid is a fluid with properties that differ in any way from Newtonian fluids. The focus of this paper is deriving of Johnson-Segalman model in cylindrical co-ordinates (r, q, z). The continuity equation, momentum equation were derived from vector form to differential form. The Johnson-Segalman model was derived in cylindrical co-ordinates and system of partial differential equations were obtained.

Keywords

Johnson-Segalman model, cylindrical co-ordinates, Cauchy stress tensor, system of partial differential equation.

How to Cite this Article?

Mosa, M. O. (2019). Derivation Of Johnson-Segalman Model In Cylindrical Co-Ordinates. i-manager's Journal on Mathematics, 8(2), 15-24. https://doi.org/10.26634/jmat.8.2.16389

References

[1]. Ahmed, N., Sharma, D., & Deka, H. (2012). MHD mixed convection and mass transfer from an infinite vertical porous plate with chemical reaction in presence of a heat source. Applied Mathematical Sciences, 6(21), 1011-1020.
[2]. Batchelor, G. K. (1967). An Introduction to Fluid Dynamics. Cambridge University Press, Cambridge.
[3]. Bird, R. B., Stewart, W. E., & Lightfoot, E. N. (2007). Transport Phenomena (Revised Second Ed.) John Wiley & Sons, New York.
[4]. Cowling, T. G. (1957). Magnetohydrodynamics. New York: Interscience Pub.
[5]. Hussanan, A., Ismail, Z., Khan, I., Hussein, A. G., & Shafie, S. (2014). Unsteady boundary layer MHD free convection flow in a porous medium with constant mass diffusion and Newtonian heating. The European Physical Journal Plus, 129(3), 46.
[6]. Ibrahim, K. A. Z. (2013). Analytical Solutions of Peristaltic Motion of Magnetohydrodynamic Non-newtonian Fluids (Doctoral Dissertation), Universiti Teknologi Malaysia.
[7]. Johnson Jr, M. W., & Segalman, D. (1977). A model for viscoelastic fluid behavior which allows non-affine deformation. Journal of Non-Newtonian fluid mechanics, 2(3), 255-270. https://doi.org/10.1016/0377-0257(77)80003-7
[8]. Kolkka, R. W., Malkus, D. S., Hansen, M. G., & Ierley, G. R. (1988). Spurt phenomena of the Johnson-Segalman fluid and related models. Journal of Non-Newtonian Fluid Mechanics, 29, 303-335. https://doi.org/10.1016/0377-0257(88)85059-6
[9]. Kundu, P. K., Cohen, I. M., & Dowling, D. R. (2008). Fluid Mechanics, (5th Edi). Academic Press.
[10]. Mohyuddin, M. R., Hayat, T., Mahomed, F. M., Asghar, S., & Siddiqui, A. M. (2004). On solutions of some non-linear differential equations arising in Newtonian and non-Newtonian fluids. Nonlinear Dynamics, 35(3), 229-248.
[11]. Pedlosky, & Joseph (1987). Geophysical Fluid Dynamics. Springer.
[12]. Romig, M. F. (1964). The influence of electric and magnetic fields on heat transfer to electrically conducting fluids. In Advances in Heat Transfer (Vol. 1, pp. 267-354). Elsevier. https://doi.org/10.1016/S0065-2717(08)70100-X
[13]. Vasudev, C., Rao, U. R., Reddy, M. S., & Rao, G. P. (2010). Peristaltic pumping of Williamson fluid through a porous medium in a horizontal channel with heat transfer. American Journal of Scientific and Industrial Research, 1(3), 656-666.
[14]. Wang, Y., Ali, N., & Hayat, T. (2011). Peristaltic Motion of Magneto-hydrodynamic Generalized Second-order Fluid in a Symmetric Channel. Numerical method for partial differential equations. ARPN Journal of Engineering and Applied Sciences, 27(2), 415-435.
[15]. Widodo, B., Siswono, G. O., & Imron, C. (2015). Viscoelastic fluid flow with the presence of magnetic field past a porous circular cylinder. In Proceedings of 5th ISERD International Conference. Bangkok, Thailand.
[16]. Zakaria, K. A., & Amin, N. S. (2014). The Lorentz Force. International Journal of Scientific and Innovative Mathematical Research (IJSIMR), 2(4), 378-380.
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