Electrokinetics of Dielectric Non-Newtonian Bio Fluids with Heat Transfer Through a Flexible Channel: Numerical Study
Mekheimer Kh.S. 1, Hassona W.M. 2, El-Shekhipy A.A. 3, Zaher A.Z. 4
1Math. Dep., Faculty of Sci., Al-Azhar Uni., Nasr City, Egypt
kh_Mekheimer@azhar.edu.eg2 Math. Dep., Faculty of Sci., Zagazig Uni., Egypt
3 Math. Dep., College of Sci., Imam Abdurrahman Bin Faisal Uni.,P.O.Box 31451, Dammam, Saudi Arabia
4 Eng. Math. Phys. Dep., Faculty of Engineering, – Shubra – Benha Uni., Egypt
abdullah.zaher@feng.bu.edu.eg
Received:
Received: 20 March 2017; revised: 06 November 2017; accepted: 08 November 2017; published online: 31 December 2017
DOI: 10.12921/cmst.2017.0000020
Abstract:
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.
Key words:
couple stress fluid, dielectric fluid, electric field, heat transfer, peristaltic transport
References:
[1] H.H. Woodson and J.R. Melcher, Electromechanical Dynam-
ics (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 Insta-
bility 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, Electro-
convection 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. Al-
homaidan, “Peristaltic flow under the effects of an induced
magnetic field and heat and mass transfer”, International Jour-
nal 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 Compu-
tation, 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 non-
uniform 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 mi-
croorganism, 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).
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.
Key words:
couple stress fluid, dielectric fluid, electric field, heat transfer, peristaltic transport
References:
[1] H.H. Woodson and J.R. Melcher, Electromechanical Dynam-
ics (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 Insta-
bility 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, Electro-
convection 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. Al-
homaidan, “Peristaltic flow under the effects of an induced
magnetic field and heat and mass transfer”, International Jour-
nal 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 Compu-
tation, 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 non-
uniform 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 mi-
croorganism, 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).
