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Fluid flow and heat transfer through a vertical cylindrical collapsible tube in the presence of magnetic field and an obstacle. (English) Zbl 1468.76077

Summary: In this paper, fluid flow and heat transfer through a Collapsible tube that is vertical with a spherical obstacle and Magnetic fields applied perpendicularly to the main flow has been investigated. The governing equations for this flow are the equations of continuity, motion and energy. The fluid flow through a Collapsible tube present a complex phenomenon due to the interaction of flowing fluid and the tube, hence the equations governing the flow are nonlinear partial differential equations. These equations have been transformed into non-linear ordinary differential equations by introducing a similarity transformation. The resulting equation from the similarity transformation is solved numerically using the Collocation method. The collocation method was implemented in MATLAB by invoking th bvp4c function to obtain the profiles. The simulation results has been presented in form of tables and graphs and also discussed. The effects of varying the Reynolds number, Hartmann number, Eckert number, Unsteadiness parameter, Prandtl number, Grashof number and Thrust constant on fluid temperature, fluid velocity and the rate of heat transfer have been determined. Variation in the various parameters is observed to change the fluid primary velocity, temperature and the rate of heat transfer. This results finds application in physical, biological and applied sciences.

MSC:

76W05 Magnetohydrodynamics and electrohydrodynamics
76M99 Basic methods in fluid mechanics
76M55 Dimensional analysis and similarity applied to problems in fluid mechanics
80A19 Diffusive and convective heat and mass transfer, heat flow

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References:

[1] Marzo and Luo, Numerical Simulation of Three-dimensional Flows Through Collapsible Tubes. PhD thesis, University of Sheffield, 2005
[2] Makinde, Collapsible tube flow: a mathematical model, Romanian Journal of Physics, 50(5/6)(2005) 493.
[3] X.Luo and T.Pedley, The cascade structure of linear instability in collapsible channel flows, Journal of Fluid Mechanics, 600(2008) 45-76. · Zbl 1151.76455
[4] G.Varshney, V. Katiyar and S. Kumar, Effect of magnetic field on the blood flow in artery having multiple stenosis: a numerical study, International Journal of Engineering,Science and Technology, 2(2) (2010) 967-82.
[5] E. Marchandise and Flaud, Accurate modelling of unsteady flows in collapsible tubes, Computer Methods in Biomechanics and Biomedical Engineering, 13(2) (2010) 279-290.
[6] D. Sankar, N. Jaffar, A. Ismail and J. Nagar, Mathematical modeling of a complex system for mhd flow in hemodynamics, Theories and Applications (BIC-TA), 2011 Sixth International Conference on, (2011) 324-328.
[7] J. Prakash and O. Makinde, Radiative heat transfer to blood flow through a stenotic artery in the presence of magnetic field, Latin American applied research, 41(3) (2011) 273-277.
[8] A. Malekzadeh, A. Heydarinasab and Dabir, Magnetic field effect on fluid flow characteristics in a pipe for laminar flow, Journal of Mechanical Science and Technology, 25(2) (2011) 333.
[9] Aminfar, H. Mohammadpourfard and Ghaderi, Two-phase simulation of non-uniform magnetic field effects on biofluid with magnetic nanoparticles through a collapsible tube, Journal of Magnetism and Magnetic Materials, 332 (2013) 172-179.
[10] A. Siviglia and Toffolon, Multiple states for flow through a collapsible tube with discontinuities, Journal of Fluid Mechanics, 761 (2014) 105-122. · Zbl 1308.76347
[11] P. Kozlovsky, Zaretsky, U. Jaffa and Elad, General tube law for collapsible thin and thick-wall tubes, Journal of biomechanics, 47(10) (2014) 2378-2384.
[12] S. Odejide, Fluid flow and heat transfer in a collapsible tube with heat source or sink, Journal of the Nigerian Mathematical Society, 34(1) (2015) 40-49. · Zbl 1349.74114
[13] V. Anand and T. Christov, Steady low reynolds number flow of a generalized newtonian fluid through a slender elastic tube, arXiv preprint arXiv: (2018) 1810.05155.
[14] A. Mehdari, M. Agouzoul and M. Hasnaoui, Analytical modelling for newtonian fluid flow through an elastic tube, Diagnostyka (2018) 19.
[15] F. Ali, A. Imtiaz and N. Sheikh, Flow of magnetic particles in blood with isothermal heating: A fractional model for two-phase flow, Journal of Magnetism and Magnetic Materials, 456 (2018) 413-422.
[16] M. S. Alam, M. M. Haque, M. J. Uddin, Unsteady MHD free convective heat transfer flow along a vertical porous flat plate with internal heat generation, Int. J. Adv. Appl. Math. Mech. 2(2) (2014) 52-61. · Zbl 1359.76328
[17] M. A. Sattar, A local simialrity transformation for the unsteady two-dimensional hydrodynamic boundary layer equations of a flow past a wedge, Int. J. appl. Math. and Mech. 7 (2011) 15-28. · Zbl 1427.76061
[18] A. Rahman, M. Alam and M. Uddin, Influence of magnetic field and thermophoresis on transient forced convective heat and mass transfer flow along a porous wedge with variable thermal conductive and variable thermal conductivity and variable Prandtl number, Int. J. Adv. Appl. Math. Mech., 3(4) (2016) 49-64. · Zbl 1367.76067
[19] J. Surawala and M. Timol, Analysis of thermal boundary layer flow of viscous fluids by new similarity method, Int. J. Adv. Appl. Math. Mech., 6(1) (2018) 69-77. · Zbl 1468.76020
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