Mathematical Correlation Study of Nanofluid Flow Merging Points in Entrance Regions

Here, hydrodynamic features of laminar forced nanofluid flow between two parallel plates are numerically investigated, and the results are mathematically discussed. The conventional understanding of developing flow in the entrance region of internal flows is based on the idea that boundary layers start forming at the inlet and merge at some point just before the fully developed section. However, because of the consideration of mass and flow conservation, the entire conception is required to be detailed with appropriate criteria according to the numerical simulations. Hence, nanofluid flow between two parallel plates is solved by ANSYS Fluent 19.3 for laminar forced in an isothermal condition. Two major criteria are studied to find the location of the boundary layer merging points: vorticity and velocity gradient in a direction perpendicular to the flow. The former presents the influential area of wall shear stress, and the latter is the direct infusion of the boundary layer induced by the solid walls. Vorticity for an irrotational flow is obtained by calculating the curl of the velocity. It is found that the merging points for the hydrodynamic boundary layers are considered before the fully developed region. For the first time, in this study, the results of various Reynolds numbers are collected, and correlations are proposed to predict the length of the boundary layer merging location by using a regression analysis of the data.