Abstract
This manuscript explores the flow features of the Modified Cross Model in a channel with symmetric trapezoidal cavities in the presence of a circular obstacle. The non-dimensional governing equations and model for different parameters are evaluated via a Galerkin Finite Element Method The system of non-linear algebraic equations is computed by adopting the Newton method. A space involving the quadratic polynomials ( P 2 ) has been selected to compute for the velocity profile while the pressure profile is approximated by a linear ( P 1 ) finite element space of functions. Simulations are performed for a wide range of physical parameters such as modified parameter (from 0.0 to 0.5), power-law index (from 0.5 to 1.5), relaxation parameter (from 1 to 3), and Reynolds number (from 10 to 40). For the case of a modified parameter ( b ) and relaxation parameter ( lambda ), it is observed that the drag coefficient ( C D ) shows an increasing trend while the lift coefficient ( C L ) is changing sign at lower values of ( lambda ), and then becomes positive at lambda = 3 .