Optimization of MHD nanofluid flow in a vertical microchannel with a porous medium, nonlinear radiation heat flux, slip flow and convective-radiative boundary conditions

The optimization of a magnetohydrodynamic flow of Al2O3-water nanofluid was carried out numerically considering the combined effects of various parameters such as porous medium permeability, Forchheimer drag, slip length, conduction-radiation parameter and nanoparticle volume fraction on heat transfer and entropy generation. The numerical computations were made by using the shooting technique together with Runge-Kutta-Fehlberg method, and the results were compared with already published studies obtaining a very good agreement. Here, optimal operating conditions with minimum entropy and maximum or minimum heat transfer not yet reported in previous similar configurations were reached and the effects of porous medium in the presence of combined convective-radiative boundary conditions and nonlinear radiation heat flux were analyzed. Results showed that the global entropy increased with the porous medium permeability, while it decreased with the inertia parameter. In addition, optimum values of slip length and nanoparticle volume fraction that minimize the global entropy, were found. These optimum values of both quantities moved to higher values as the porous medium permeability increased. The Nusselt number was also explored for different conditions. Optimum values of Grashof number and conduction-radiation parameter with maximum heat transfer, as well as slip length with minimum heat transfer were found. These optimum values of Grashof moved to lower values as the permeability increased, while their optimum values shifted toward higher values with the inertia parameter. The obtained optimum values of slip length with minimum heat transfer moved to higher values when the permeability increased. Finally, four different models were defined to show the effects of uncertainties in thermophysical properties of nanofluid on heat transfer and entropy generation. These models were obtained from the combination of two relations used for both the dynamic viscosity and the thermal conductivity of nanofluid. It was seen that, independent of the model, optimal operating conditions were achieved for the explored values.