Abstract
The transient generalized Couette flow through a porous medium of a nonNewtonian viscoelastic fluid between two parallel porous plates is studied with heat transfer. A uniform suction from above and injection from below are applied perpendicular to the plates which are maintained at two fixed, but different, temperatures while the viscosity of the fluid is assumed to vary exponentially with temperature. The fluid is driven by a uniform horizontal exponential decaying pressure gradient. The coupled set of equations of motion and the energy equation is solved numerically using finite differences. The influence of the different physical parameters of the model on the velocity and temperature fields is investigated and presented.
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Abbreviations
 a :

Viscosity exponent (K^{−1})
 c _{p} :

Specific heat at constant pressure (J kg^{−1} K^{−1})
 Ec:

Eckert number
 f _{b} :

Body force (kg m^{−2} s^{−2})
 G :

Pressure gradient (kg m^{−2} s^{−2})
 h :

Separation between the two plates (m)
 k :

Thermal conductivity (J s^{−1} m^{−1} K^{−1})
 k _{1} :

Modulus of rigidity (kg m^{−1} s^{−2})
 K :

Darcy permeability (m^{2} s)
 Pr:

Prandtl number
 M :

Porosity parameter,
 N :

Viscosity exponent
 Q :

Viscoelastic parameter
 Re :

Reynolds number
 S :

Suction parameter
 t :

Time (s)
 T :

Temperature of the fluid (K)
 T _{1} :

Temperature of the lower plate (K)
 T _{2} :

Temperature of the upper plate (K)
 V :

Velocity component of the fluid in the xdirection (m s^{−1})
 U _{o} :

Suction velocity (m s^{−1})
 x :

Axial direction (m)
 y :

Distance in the vertical direction (m)
 z :

Longitudinal direction (m)
 α :

Pressure gradient exponent (s^{−1})
 μ :

Coefficient of viscosity of the fluid (kg m^{−1} s^{−1})
 ρ :

Density of the fluid (kg m^{−3})
 τ :

Shear stress (kg m^{−1} s^{−2})
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Attia, H.A., Abdeen, M.A.M. & ElMeged, W.A. Transient Generalized Couette Flow of Viscoelastic Fluid Through a Porous Medium with Variable Viscosity and Pressure Gradient. Arab J Sci Eng 38, 3451–3458 (2013). https://doi.org/10.1007/s1336901306680
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DOI: https://doi.org/10.1007/s1336901306680