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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 PDE are transformed by similarity solution to a system of ODE. 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.

Local thermal non-equilibrium forced convection of a third grade fluid between parallel stretching permeable plates embedded in a porous medium