is the dimensionless Brinkman number. To simulate the polymeric behavior of the stress tensor the Simplified Phan-Thien-Tanner model (SPTT) is implemented that the solvent viscosity is neglected. This model is derived from network theory by Phan-Thien and Tanner [24] and is generally used to simulate the rheological behavior of polymeric melts and concentrated solutions. The simplified type of the Phan-Thien-Tanner model (SPTT) becomes: