Analytical analysis of impacts of nanoparticle shapes and uncertainty in thermophysical properties on optimum operating conditions of MHD nanofluid flow in a microchannel filled with porous medium

The effects of different nanoparticle shapes and uncertainty in the nanofluid thermophysical properties on the optimal operating conditions of MHD flow of Al2O3/water nanofluid through a horizontal microchannel with a porous medium considering hydrodynamic slip, suction/injection and thermal radiation were investigated. The momentum and heat transfer equations were solved analytically using the methods of undetermined coefficients and variation of constants, respectively. From the exact solutions of the velocity and temperature fields, the global entropy ⟨S⟩ and Nusselt number Nu were computed. The impacts of hydrodynamic slip α , Biot number Bi , nanoparticle concentration ϕ and Darcy number Da on entropy production and heat transport were investigated. The results revealed that optimum values of Bi and α with minimum global entropy and maximum heat transport were achieved for symmetric slip conditions and asymmetric heat transfer. The platelet shape of nanoparticles was the most effective to achieve the optimum conditions with the lowest minimum value of ⟨S⟩ , while the blade shape was the most effective to reach the optimum conditions with the highest maximum value of heat transport. Thus, optimum values of both Biot number of bottom plate equal to 0.01 and slip equal to 0.045 with the smallest values of ⟨S⟩ were achieved for the platelet shape. Also, optimum slip value of 0.15 with the largest maximum Nu at top plate of 5.13 was achieved for the blade shape. On the other hand, when ϕ increased from 0 to 0.045, ⟨S⟩ always decreased and Nu always increased. The greatest decrease of entropy from 0.133 to 0.088 (33 ϕ was varied from 0 to 0.01, ⟨S⟩ decreased 9.2 α was varied, the minimum value of ⟨S⟩ achieved for Cu was 0.47 and 0.64