Influence of Couple Stresses and Thermophoresis on Free Convective Heat and Mass Transfer of Viscoelastic Fluid.

Authors

  • N. T. M. Eldabe Ain Shams University, Heliopolis, Cairo, Egypt
  • Ahmed Refaie Ali Menoufia University, Egypt
  • Gamil Ali Shalaby Menoufia University, Egypt

DOI:

https://doi.org/10.24297/jap.v17i.8637

Keywords:

Viscoelastic fluid, Thermophoresis, Couple stresses

Abstract

A theoretical study has been developed to investigate the influence of thermophoresis and couple stresses on the steady flow of non-Newtonian fluid with free convective heat and mass transfer over a channel bounded by two permeable plates. The considered non-Newtonian fluid follows a viscoelastic model. The problem is modulated mathematically by a system of non-linear differential equations pertaining to describe the continuity, momentum, energy, and concentration. These equations involve the effects of viscous dissipation and chemical reaction. The numerical solutions of the dimensionless equations are found as a function of the physical parameters of this problem. The numerical formulas of the velocity (u), temperature Φ and concentration Θ as well as skin friction coefficient T*, Nusselt number(Nu) and Sherwood number(Sh) are computed. The physical parameter's effects of the problem on these formulas are described and illustrated graphically through some figures and tables. It is observed that any increase in the thermophoretic parameter T leads to reduce in velocity profiles as well as concentration layers. In contrast, the velocity increases with increasing the couple stresses inverse parameter.

Downloads

Download data is not yet available.

Author Biographies

N. T. M. Eldabe, Ain Shams University, Heliopolis, Cairo, Egypt

Department of Mathematics, Faculty of Education

Ahmed Refaie Ali, Menoufia University, Egypt

Assistant lecturer, Department of Mathematics and Computer Science, Faculty of Science

Gamil Ali Shalaby, Menoufia University, Egypt

Department of Mathematics and Computer Science, Faculty of Science

References

R. Piazza. Thermophoresis : moving particles with thermal gradients. Soft Matter - Royal Society of Chemistry, 4, pages 1740 –1744, 2008.

Jashim Uddin and Yeakub Ali. Effects of hydromagnetic and thermophoresis of unsteady forced convection boundary layer flow over flat plates. Journal of Applied Mathematics and Physics, 4, pages 1756–1776, 2016.

U. J. Das. Viscoelastic effects on unsteady two-dimensional and mass transfer of a viscoelastic fluid in a porous channel with radiative heat transfer. Engineering, 5, pages 67 –72, 2013.

C. Sudhakar, N. B. Reddy, B. Vasu and V. R. Prasad. Thermophoresis effect on unsteady free convection heat and mass transfer in a Walters-B fluid past a semi infinite plate. International Journal of Engineering Research and Applications, 2, pages 2080 –2095, 2012.

Nabil T. M. El-dabe, A. Refaie Ali, A. A. El-shekhipy and G. A. Shalaby. Non-linear heat and mass transfer of

second grade fluid flow with hall currents and thermophoresis Effects. Appl. Math. Inf. Sci., 1(11) pages 267–280,

L. Talbot, R.K. Cheng, R.W. Schefer and D.R. Willis. Thermophoresis of particles in a heated boundary layer. J.

Fluid Mech., 101, pages 737 –758, 1980.

G.K. Batchelor and C. Shen. Thermophoretic deposition of particles in gas flowing over cold surfaces. J Colloid

Interface Sci, 107, pages 21 –37, 1985.

C.K. Wu and R. Greif. Thermophoretic deposition including an application to the outside vapor deposition process.

Int. J. Heat. Mass. Tran., 39(7), pages 1429 –1438, 1996.

Stokes, VK. Theories of fluids with mictostructure. Springer Verlag, Berlin, 1984.

Mindlin and Tiersten. HF: Arch. Ration. Mech. Anal., 11, 415, 1962.

N. T. M. Eldabe, A. A. Hassan, and Mona A. A. Mohamed. Effect of couple stresses on the MHD of a non-Newtonian unsteady flow between two parallel porous plates. Z. Naturforsch. 58a), pages 204 –210, 2003.

D. Srinivasacharya and K. Kaladhar. Natural convection flow of a couple stress fluid between two vertical parallel plates with Hall and Ion-slip effects. Acta Mech. Sin., 28(1), pages 41 –50, 2012.

D. Srinivasacharya and K. Kaladhar. Mixed convection flow of couple stress fluid between parallel vertical plates with Hall and Ion-slip effects. Commun Nonlinear Sci Numer Simulat, 17, pages 2447–2462, 2012.

D. Srinivasacharya and K. Kaladhar. Soret and Dufour effects on free convection flow of a couple stress fluid in a vertical channel with chemical reaction. Chemical Industry and Chemical Engineering Quarterly , 19 (1), pages 45–55, 2013.

N.T.M. Eldabe, A.A. Hassan and Mona A.A. Mohamed. Effect of couple stresses on a pulsatile magnetohydrodynamic viscoelastic flow through a channel bounded by two permeable parallel plates. Mechanics and Mechanical Engineering, 1(7), pages 5 –14, 2004.

Samuel O. Adesanya, John A. Falade and Randolph Rach. Effect of couple stresses on Eyring–Powell fluid flow

through a porous channel. Theoretical and applied mechanics , 42, Issue 2, pages 135–150, 2015.

K. Kaladhar, S. S. Motsa and D. Srinivasacharya. Mixed convection flow of couple stress fluid in a vertical channel with radiation and soret effects. Journal of Applied Fluid Mechanics, 9, No. 1, pages 43-50, 2016.

Mohyuddin, Muhammad and Thomas Goetz. Resonance behavior of viscoelastic fluid in Poiseuille flow in the

presence of a transversal magnetic field. International Journal for numerical methods in fluids, 49(8), pages 837–847, 2005.

S.Asghara, Muhammad R.Mohyuddinb and T.Hayat. Effects of Hall current and heat transfer on flow due to a

pull of eccentric rotating disks. International Journal of Heat and Mass Transfer, 48, pages 599–607, 2005.

Javed I. Siddique, Forrest A. Landis and Muhammad R. Mohyuddin. Dynamics of Drainage of Power-Law Liquid into a Deformable Porous Material. Open Journal of Fluid Dynamics, 4, pages 403–414, 2014.

Published

2020-02-07

How to Cite

M. Eldabe, N. T., Ali, A. R., & Ali Shalaby, G. (2020). Influence of Couple Stresses and Thermophoresis on Free Convective Heat and Mass Transfer of Viscoelastic Fluid. JOURNAL OF ADVANCES IN PHYSICS, 17, 50-63. https://doi.org/10.24297/jap.v17i.8637

Issue

Section

Articles