Numerical Computations of Non-Newtonian Fluid Flow in Hexagonal Cavity With a Square Obstacle: A Hybrid Mesh–Based Study - Khan, Y.; Majeed, Afraz Hussain; Shahzad, Hasan; Awan, Farah Jabeen; Iqbal, Kaleem; Ajmal, Muhammad; Faraz, N. (Frontiers in Physics, 2022)
Thermal flow phenomena in a double lid-driven enclosure has many potential applications in numerous engineering domains. The present article theoretically investigates the heat transfer analysis of power-law fluid in a hexagonal cavity embedded with a square obstacle. The upper and lower lid walls of the cavity are considered heated along with the walls of the centered embedded square, whilst the rest of the cavity walls are thermally insulated. In addition, the horizontal lid walls of the cavity are uniformly moving in opposite horizontal directions. The mathematical modeling of the non-linear fluid has been developed considering the continuity, momentum, and energy equations subjected to the appropriate boundary conditions. Due to the nonlinearity of the governing partial differential equations and of the viscosity models, we employ the numerical scheme based on the Finite Element Method (FEM). The stable finite element pair (P_2/P_1) has been selected for the discretization purpose. The discretized non-linear system is solved with the Newton method in conjunction with a direct linear solver in the inner iterations. The thermal flow features are exposed via streamlines and temper ture contours for a set of governing parameters such as Reynolds number (Re), Prandtl number (Pr) and Grashof number (Gr) along with the power-law index (n). The values of local and average Nusselt numbers are calculated for involved parameters. It is noted that the square obstacle has a strong impact for the formulation of streamlines and isotherms. Moreover, the power-law index has strong impact on the values of average Nusselt number and kinetic energy. The kinetic energy of the system increases with an increasing value of Gr and n. While Reynolds has opposite effects on kinetic energy.