Electrokinetics of Dielectric Non-Newtonian Bio Fluids with Heat Transfer Through a Flexible Channel : Numerical Study

• Autorzy: Mekheimer K. S. , Hasona W. M. , El-Shekhipy A. A. , Zaher A. Z.

Identyfikatory

DOI

10.12921/cmst.2017.0000020

• Języki publikacji: EN

Abstrakty

EN

Throughout this paper we investigate the effect of a vertical alternative current AC and heat transfer on the peristaltic flow of a couple stress dielectric fluid (blood flow model) in a symmetric flexible sinusoidal wavy channel. In order to solve the system of coupled non-linear partial differential equations, a program designed by Mathematica software "parametric NDSolve package" is used, which pertains to describe the momentum, the energy, and the electric potential that is obtained from using a regular perturbation method with small amplitude ratio. The numerical formulas of the mean velocity, the mean temperature, and the mean electric field are computed and the phenomenon of reflux (the mean flow reversal) is discussed. Moreover, the physical parameters effects of the problem on these formulas are described and illustrated graphically. The results reveal that the mean time averaged velocity is accelerated in the presence of AC electric field and decelerated for the couple stress fluid model (a special case of non-Newtonian fluid). The mean time averaged temperature is high in the presence of an alternative current AC electric field. This results model imply that the physiological role of AC electric field enhances blood circulation and this might help to eliminate the metabolic waste products and endogenous pains producing.

Słowa kluczowe

EN

peristaltic transport; dielectric fluid; heat transfer; electric field; couple stress fluid

• Wydawca: Institute of Bioorganic Chemistry Scientific Publishers OWN, Polish Academy of Sciences
• Czasopismo: Computational Methods in Science and Technology
• Rocznik: 2017
• Tom: Vol. 23, No. 4
• Strony: 331--341
• Opis fizyczny: Bibliogr. 27 poz., rys.

Twórcy

autor

Mekheimer K. S.

• Math. Dep., Faculty of Sci., Al-Azhar Uni., Nasr City, Egypt

autor

Hasona W. M.

• Math. Dep., Faculty of Sci., Zagazig Uni., Egypt

autor

El-Shekhipy A. A.

• Math. Dep., college of Sci., Imam Abdurrahman Bin Faisal Uni.,P.O.Box 31451, Dammam, Saudi Arabia

autor

Zaher A. Z.

• Eng. Math. Phys. Dep., Faculty of Engineering, - Shubra - Benha Uni., Egypt

Bibliografia

• [1] H.H. Woodson and J.R. Melcher, Electromechanical Dynamics (John Wiley and Sons, New York, 1968).
• [2] M. Takashima, The Stability of a Rotating Layer of the Maxwell Liquid Heated from Below, Journal of the Physical Society of Japan 29, 1061–1068 (1970).
• [3] M. Takashima and A.K. Ghosh, Electrohydrodynamic Instability of Viscoelastic Liquid Layer, Journal of the Physical Society of Japan 47 1717–1722 (1979).
• [4] M.F. El-Sayed, M.H. Harouna, and D.R. Mostapha, Electroconvection peristaltic flow of viscous dielectric liquid sheet in asymmetrical flexible channel, Atomization and Sprays 25 985-1011 (2015).
• [5] M.M. Bhatti, A. Zeeshan, R. Ellahi and N. Ijaz, Heat and mass transfer of two-phase flow with Electric double layer effects induced due to peristaltic propulsion in the presence of transverse magnetic field, Journal of Molecular Liquids (2017), doi:10.1016/j.molliq.2017.01.033.
• [6] N.S. Akbar, S. Nadeem, Thermal and velocity slip effects on the peristaltic flow a six constant Jeffrey’s fluid model, International Journal of Heat Mass Transfer 55, 3964–3970 (2012).
• [7] M. M. Bhatti, A. Zeeshan, R. Ellahi, Heat transfer analysis on peristaltically induced motion of particle-fluid suspension with variable viscosity: clot blood model, Computer Methods and Programs in Biomedicine (2016)
• [8] S. Hina, T. Hayat, S. Asghar and A. A. Hendi, Influence of compliant walls on peristaltic motion with heat/mass transfer and chemical reaction, International Journal of Heat and Mass Transfer 55„ pp.3386-3394 (2012).
• [9] Kh. S. Mekheimer, N. Saleem and T. Hayat, Simultaneous effects of induced magnetic field and heat and mass transfer on the peristaltic motion of second-order fluid in a channel, International Journal for Numerical Methods in Fluids, 70 342–358 (2012).
• [10] T. Hayat, S. Noreen, M. Alhothuali, S. Asghar and A. Alhomaidan, "Peristaltic flow under the effects of an induced magnetic field and heat and mass transfer", International Journal of Heat and Mass Transfer, vol 55, , pp.443-452 (2002).
• [11] V. K. Stokes, Couple stresses in fluids. Physics of Fluids, vol. 9, pp. 1709-1715 (1966).
• [12] Kh. S. Mekheimer, Peristaltic transport of blood in a uniform and non-uniform channel, Applied mathematics and Computation, 153, (2004),763-777.
• [13] M. M. Bhatti, R. Ellahi and A. Zeeshan, Study of variable magnetic fleld on the peristaltic flow of Jeffrey fluid in a nonuniform rectangular duct having compliant walls, Journal of Molecular Liquids, 222 (2016) 101-108.
• [14] R. Ellahi, M. M. Bhatti and I. Pop, Effects of hall and ion slip on MHD peristaltic flow of Jeffrey fluid in a non-uniform rectangular duct, International Journal of Numerical Methods for Heat and Fluid Flow, 26 (2017) 1802-1820.
• [15] A.A. Khan, H. Usman, K. Vafai, R. Ellahi, Study of peristaltic flow of magnetohydrodynamic Walter’s B fluid with slip and heat transfer, Scientia Iranica B 23, 2650–2662 (2016).
• [16] M.M. Bhatti, A. Zeeshan, R. Ellahi, Simultaneous effects of coagulation and variable magnetic fleld on peristaltically induced motion of Jeffrey nanofluid containing gyrotactic microorganism, Microvascular Research 110, 32–42 (2017).
• [17] Kh.S. Mekheimer, A.M. Salem, A.Z. Zaher, Peristatcally induced flow due to a surface acoustic wavy wall, Chinese Journal of Physics 51, 954–968 (2013).
• [18] Kh. S. Mekheimer, A.M. Salem , A.Z. Zaher, Peristatcally induced MHD slip flow in a porous medium due to a surface acoustic wavy wall, Journal of the Egyptian Mathematical Society 22, 143–151 (2014).
• [19] Y. Abd elmaboud, Kh.S. Mekheimer, A.I. Abdellateef, Thermo properties of couple-stress fluid in an asymmetric channel with peristalsis, Journal of Heat Transfer 135 (2013).
• [20] A.M. Abdulhadi, A.W. Saleh, Effects of Couple Stress and Porous Medium on Transient Magneto Peristaltic Flow under the Action of Heat Transfer, IOSR Journal of Mathematics, 12, 71–83 (2016).
• [21] S. Akram, Kh. S. Mekheimer and S. Nadeem, Influence of Lateral Walls on Peristaltic Flow of a Couple Stress Fluid in a Non-Uniform Rectangular Duct, Appl. Math. Inf. Sci. 8, 1127–1133 (2014).
• [22] R. Ellahi, M.M. Bhatti, C. Fetecau, K. Vafai, Peristaltic Flow of Couple Stress Fluid in a Non-Uniform Rectangular Duct Having Compliant Walls, Commun. Theor. Phys. 65, 66–72 (2016).
• [23] S. Hina, M. Mustafa, T. Hayat and A. Alsaedi, Peristaltic flow of couple-stress fluid with heat and mass transfer: An application in biomedicine, Journal of Mechanics in Medicine and Biology 15, 1–17 (2015).
• [24] K. Ramesh and M. Devakar, Effects of heat and mass transfer on the peristaltic transport of MHD couple stress fluid through porous medium in a vertical asymmetric channel, Journal of Fluids, 1–19 (2015).
• [25] A. Govindarajan ,E. P. Siva and M. Vidhya, Combined effect of heat and mass transfer on MHD Peristaltic transport of a couple stress fluid in a inclined asymmetric channel through a porous medium, International Journal of Pure and Applied Mathematics, 105 (2015) 685-707.
• [26] Y.C. Fung, C.S. Yih, Peristaltic Transport, J. Appl. Mech. 35, 669–675 (1968).
• [27] K.H. Wolfgangand, A.M. Phillips, Classical Electricity and Magnetism (Addison-Wesley, 1955).

Uwagi

PL

Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę (zadania 2017).