Finite element analysis of bi-viscosity fluid enclosed in a triangular cavity under thermal and magnetic effects

A numerical study is carried out for the mixed convection flow inside a lid-driven triangular cavity quantitatively. The rheological behavior of the fluid inside the cavity is modeled through the constitutive equation of bi-viscosity. The bottom boundary of the cavity is maintained at constant temperature and it is considered as moving with constant speed. The sides of the closed conduit are linearly heated. The governing non-linear partial differential equations are discretized using Galerkin finite element method and pressure is eliminated through the penalty method. The computations are presented graphically for a wide range of the bi-viscosity parameter, thermal radiation parameter, Hartman number, Grashof number, Reynolds number, heat generation/absorption parameter and Prandtl number. The numerical results reveal that the secondary circulation does not appear for small \(\beta\). Moreover, in the convection dominated case, it is observed that a thin boundary layer at the side walls exists for large Hartmann number. The magnitude of the average Nusselt number increases with the Grashof number and \(\beta\) for both values of the Prandtl number \((Pr=0.7,10)\). In contrast, the average Nusselt numbers at both the bottom and side wall decrease with increasing radiation parameter. The results of the present study suggest to tune the rheology of the fluid in the cavity to design a system with improved thermal management.