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\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\left\langle {\text{S}} \right\rangle$$\end{document} and Nusselt number Nu were computed. The impacts of hydrodynamic slip alpha\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha$$\end{document}, Biot number Bi\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$Bi$$\end{document}, nanoparticle concentration phi\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\phi$$\end{document} and Darcy number Da\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$Da$$\end{document} on entropy production and heat transport were investigated. The results revealed that optimum values of Bi\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathrm{\text{Bi}}$$\end{document} and alpha\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha$$\end{document} 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\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\left\langle {\text{S}} \right\rangle$$\end{document} , 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\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\left\langle {\text{S}} \right\rangle$$\end{document} 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 phi\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\phi$$\end{document} increased from 0 to 0.045, S\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\left\langle {\text{S}} \right\rangle$$\end{document} always decreased and Nu always increased. The greatest decrease of entropy from 0.133 to 0.088 (33%) occurred for the platelet shape, while the greatest increase of Nu at top plate from 4.96 to 5.57 (12.3%) occurred for the blade shape. When phi\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\phi$$\end{document} was varied from 0 to 0.01, S\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\left\langle {\text{S}} \right\rangle$$\end{document} decreased 9.2% for the platelet shape compared to spherical shapes, and Nu at top plate increased 2.6% for the blade shape compared to spherical shapes. The results also indicated that the greatest variations of optimum operating conditions occurred when the experimental correlations of viscosity and thermal conductivity were used compared to theoretical correlations. This is because the estimated values of viscosity and conductivity using the different theoretical correlations differ very little from each other. Thus, the maximum value of Nu at top plate increased from 5.067 for SM1 model to 5.092 for SM6 model (0.5%), while it increased from 4.96 for EM3 model to 5.17 for EM6 model (4.2%). Finally, the effects of Al2O3, Cu and TiO2 nanoparticles in water as base fluid on the optimum conditions were investigated. Both the lowest entropy production and the highest heat transfer were reached for Cu nanoparticles. When alpha\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha$$\end{document} was varied, the minimum value of S\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\left\langle {\text{S}} \right\rangle$$\end{document} achieved for Cu was 0.47 and 0.64% lower than the minimum value of TiO2 and Al2O3, respectively. Also, the maximum value of Nu achieved for Cu improved by approximately 0.2 and 0. 4% compared to Al2O3 and TiO2, respectively.
