Computational Behavior of Second Law Poiseuille Flow of Micropolar Fluids in a Channel: Analytical Treatment

The present analysis explores an analytical treatment for the computation of Poiseuille flow of a micropolar fluid in a channel placed in between two horizontal parallel plates. Both the plates are placed at constant wall temperatures. Therefore, the flow region is portioned into two different zones named zone I and zone II. Eringen’s micropolar fluid flow phenomena are taking place assuming no-slip conditions at the interface. Suitable nondimensional variables are imposed for the transformation of governing equations. Analytical treatment is carried out employing the in-house symbolic command using the MAPLE software. The behavior of several contributing parameters such as material parameters, the couple stresses for both the zones on the velocity, and microrotation profiles are investigated and presented via graphs. The volume flow rate is also calculated and presented via the tabular form. The major outcomes of the results are presented as the higher the Reynolds number, the rate increases significantly. The profile is tiled near the central region with a pick starting from the lower plate region to the central region in zone I and retards from the central region to the upper plate in the zone II, and the profiles of angular momentum seem to be symmetric in nature about the central region that is shown in both the zones.