Mixed convective thermal transport in a lid-driven square enclosure with square obstacle

The prime motive of this disquisition is to scrutinize simultaneous aspects of external forcing mechanism and internal volumetric forces on non-Newtonian liquid filled in square enclo-sure. Inertially driven upper lid is assumed by providing constant magnitude of slip velocity whereas thermal equilibrium is disturbed by assuming uniform temperature at lower boundary and by keep-ing rest of walls as cold. To enhance thermal diffusion transport with in the flow domain cold as well as adiabatic temperature situation is provided. In view of velocity constraints all the extremities at no-slip except the upper wall which is moving with ULid. Formulation is attained in dimensional form initially and afterwards variables are used to convert constructed differential system into dimensionless representation. A numerical solution of leading formulation is sought through Galer-kin finite element discretization. Momentum and temperature equations are interpolated by quad-ratic polynomials whereas pressure distribution is approximated by linear interpolating function. Domain discretized version is evaluated in view of triangular and rectangular elements. Newton's scheme is employed to resolve the non-linearly discretized system and a matrix factorization based non-linear solver renowned as PARADISO is used. Validation of results is ascertained by forming agreement with existing studies. In addition, grid independence test is also performed to show credibility of performed computations. Stream lines and isothermal contours patterns are portrayed to evaluate variation in flow distributions. Kinetic energy and local heat flux for uniform and non-uniform heating situations are also divulged in graphical and tabular formats. Increase in Reynold number produces decrease in kinetic energy of fluid. Enhancement in Grashof number causes enrichment of thermal buoyancy forces due to which Nusselt number uplifts. Clock wise rotations increase against upsurge in magnitude of Reynold number which is evidenced form stream lines. Squeezing of secondary vortex against Prandtl number arises due to dominance of viscous forces.(c) 2022 THE AUTHORS. Published by Elsevier BV on behalf of Faculty of Engineering, Alexandria University. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/ licenses/by-nc-nd/4.0/).

Automated summary

The study focuses on the simultaneous effects of external forcing mechanisms and internal volumetric forces on non-Newtonian liquid in a square enclosure. The upper lid is assumed to have a constant magnitude of slip velocity, while thermal equilibrium is disturbed by uniform temperature at the lower boundary and cold walls. The formulation is initially obtained in dimensional form and then converted into a dimensionless representation. Numerical solutions are obtained through Galerkin finite element discretization. The results are validated by comparison with existing studies and grid independence tests. The study shows the variations in flow distributions, kinetic energy, and local heat flux for different heating situations.