Analysis of radiative mixed convective heat transfer for non-Newtonian fluid with heat generation/absorption phenomena

Abstract

The current work consists of investigating the heat generation/absorption and non-linear thermal radiation effects for two-dimensional mixed convective bi-viscosity fluid flow inside the C-shaped enclosure with uniformly heated left and linearly heated top and bottom walls. The physical flow problem is governed by applying the constitutive laws of bi-viscosity model, conservation of mass, momentum and energy balance equations. The governing non-linear coupled partial differential equations is transformed into the algebraic nonlinear system by using Galerkin's finite-element technique after eradicating the pressure terms via the penalty method, and then the Newton–Raphson technique is used to solve it. It is noted that at a low value of $\beta$ (which gives the high plasticity of the bi-viscosity liquid), only the primary circulations with intensity ${\psi }_{max}=-0.063$ appeared, but at a high value of $\beta$ decreased the plasticity which caused enhanced buoyancy-driven that generate also the secondary bowls with intensity ${\psi }_{max}=0.063$ inside the enclosure. The heat transfer rate increased $91.6667\text{\%}$ by an increase in the Reynolds number from $1$ to ${10}^2$ . The findings of this study will play a role in improving the thermal performance of microelectronic devices, cooling systems, food processing, solar collectors, and high performance boilers by tracing the energy transport trajectories through heatlines.