Computational Irreversibility Analysis in Transient Flow of a Non-Newtonian Fluid through a Channel with Porous Walls

A second law analysis is explored to investigate the irreversibility properties in a transient, porous channel flow of a viscous, incompressible, and non-Newtonian fluid. The non-Newtonian fluid model is of a Generalized Newtonian Fluid type with no elastic properties but with shear-thinning viscosity. Additionally, given that the flow is non-isothermal, the viscosity is therefore expectedly also assumed to be temperature dependent. The porous channel is subjected to constant suction and injection of fluid through the walls. Computational solutions for the underlying fluid dynamical equations, based on robust finite difference numerical techniques, are developed and implemented in time and space. We demonstrate the effects of the embedded fluid flow and heat transfer parameters on the fluid velocity and temperature profiles. We also explore the competing effects of heat transfer irreversibility versus fluid friction irreversibility. The major observations are that, in the flow regions where the maximum velocity obtains, heat transfer irreversibility significantly dominates over the otherwise insignificant fluid friction irreversibility. It is also observed that, in those flow regions away from the region of maximum velocity, the opposite scenario obtains, and hence fluid friction irreversibility significantly dominates over heat transfer irreversibility. Along the channel walls, fluid friction irreversibility notably dominates over heat transfer irreversibility. The possibility that certain parameter choices may lead to reverse scenario is not discounted.