## THERMAL SCIENCE

International Scientific Journal

### LOCAL THERMAL NON-EQUILIBRIUM FORCED CONVECTION OF A THIRD GRADE FLUID BETWEEN PARALLEL STRETCHING PERMEABLE PLATES EMBEDDED IN A POROUS MEDIUM

**ABSTRACT**

The aim of this paper is the numerical investigation of local thermal non-equilibrium effects in the boundary layer forced convection of a third grade fluid flowing in a porous medium confined by two parallel permeable stretching isothermal plates. The horizontal velocity of stretching walls is proportional to the longitudinal distance from origin while its vertical suction component is uniform. The porous medium obey the Brinkman extended Darcy momentum equation. The boundary layer non-linear partial differential equations are transformed by similarity solution to a system of ordinary differential equations. The numerical investigation make known that a flow reversal come about the symmetry line of the channel attributable to the stretching plate boundary which diminished in highly Darcy numbers. The fluid flow field and temperature distribution of the solid and fluid phases are studied based on the conductivity ratio, Darcy number, Prandtl number, Reynolds number, and third order fluid parameters.

**KEYWORDS**

PAPER SUBMITTED: 2016-04-07

PAPER REVISED: 2017-09-03

PAPER ACCEPTED: 2017-09-12

PUBLISHED ONLINE: 2017-10-07

**THERMAL SCIENCE** YEAR

**2019**, VOLUME

**23**, ISSUE

**Issue 2**, PAGES [475 - 484]

- Abdollahzadeh Jamalabadi, M.Y. et al., Influence of radiative heat transfer and transverse magnetic field on peristaltic flow of a third order fluid in a planar channel, Journal of Chemical and Pharmaceutical Research 7 (2015) 12, pp. 788-799.
- Abdollahzadeh Jamalabadi, M.Y., Effects of micro and macro scale Viscous Dissipations with Heat Generation and Local Thermal Non-Equilibrium on Thermal Developing Forced Convection in saturated porous media, Journal of Porous Media 18 (2015) 9, pp.843-860.
- Abdollahzadeh Jamalabadi, M.Y.,Keikha, A.J., Fluid-Solid interaction modeling of cerebrospinal fluid absorption in arachnoid villi, Journal of Chemical and Pharmaceutical Research 8 (2016) 2, pp. 428-442.
- Ghasemi S. E. et al., Study on blood flow containing nanoparticles through porous arteries in presence of magnetic field using analytical methods, Physica E, 70 (2015), pp. 146-156
- Moyers-Gonzalez, M.A. et al., A non-homogeneous constitutive model for human blood. Part III: oscillatory flow, J. Non-Newton. Fluid Mech., 155 (2008), pp. 161-173
- Massoudi, M. , Phuoc T.X., Pulsatile flow of blood using a modified second-grade fluid model, Comput. Math. Appl., 56 (2008), pp. 199-211
- Misra, J.C., Flow and heat transfer of a MHD viscoelastic fluid in a channel with stretching walls: some applications to haemodynamics, Comp. Fluids, 37 (2008), pp. 1-11
- Misra, J.C., Shit G.C., Flow of a biomagnetic viscoelastic fluid in a channel with stretching walls, ASME, J. Appl. Mech., 76 (2009), p. 061006
- Craciunescu, O.I. , Clegg ,S.T., Pulsatile blood flow effects on temperature distribution and heat transfer in rigid vessels, J. Biomech. Eng., 123 (2001), pp. 500-505
- Crane, L.J., Flow past a stretching plate,Z Angew Math Phys, 21 (1970), pp. 645-647
- Ghani, F., et al., Unsteady magnetohydrodynamics thin film flow of a third grade fluid over an oscillating inclined belt embedded in a porous medium, Thermal science, 5 (2016), pp. 875-887
- Hayat, T., et al., Magnetohydrodynamic Flow of Nanofluid over permeable stretching sheet with convective boundary conditions, Thermal science, 20 (2016), pp. 1835-1845
- Klamkin, M. S., Transformation of boundary value problems into initial value problems, J Math Anal Appl., 32 (1970), pp. 308-330