Mixed convective heat transfer in a power-law fluid in a square enclosure: Higher order finite element solutions

Abstract

Incorporation of momentum gradients produced due to inertial motion of the lid along with the presence of temperature differences in the configuration make the physical problem more significant. The joint variation of momentum and thermal diffusion in diversified natural liquids is recognized as mixed convection. Valuable attention has been received by such a phenomenon in different areas of science and technology such as in wind current–based solar receivers, electronic instruments, control of emergency shutdown in reactors, thermal exchangers, oceanic currents, control of atmospheric pollution, and so on. So, the main focus is to contemplate hydrothermal characteristics of a power-law fluid contained in a square cavity with the movement of the upper lid and being thermally adiabatic. The other extremities are considered to be at rest, and the base wall is prescribed with uniform/non-uniform temperature distributions. The governing formulation of the problem is handled by executing a finite element approach. Hybrid meshing is performed for domain discretization, and weak variational formulation is utilized for formulation discretization. Second-degree polynomials are employed as the interpolation function, providing information about velocity and temperature distributions at boundary and intermediate nodes. The system of finalized non-linear equations is resolved by using the Paradiso software. The results for velocity and temperature distributions are attained comparatively for uniformly and non-uniformly heated profiles. The kinetic energy and average Nusselt number are also computed against flow concerning variables. From the attained graphical and tabular data, it is deduced that by increasing the Reynolds number, inertial forces dominate over buoyancy forces and the effect of lid movement is prominent on flow characteristics. It is also inferred that for the shear thickening case and for all values of the Reynolds number, the average Nusselt number shows a constant behavior.