9. Predictive Formulae on Heat Transfer of Al₂O₃-Water Nanofluid’s Natural Convection

In view of a lack of study on heat transfer coefficient of nanofluid’s convection, the correlations on heat transfer coefficient of Al₂O₃-water nanofluid’s natural convection are reported in this chapter. Such correlations are based on the theoretical equations with heat transfer analysis of nanofluid’s natural convection, and contain the wall temperature gradient, the only unknown variable for prediction of heat transfer of nanofluid’s natural convection. The correlation of wall temperature gradient is obtained according to systems of the related rigorous numerical solutions on Al₂O₃-water nanofluid’s natural convection. These systems of the numerical solutions on wall temperature gradient are based on comprehensive consideration of nanofluid’s variable thermophysical properties, nanopartical shape factor and concentration, and fluid’s boundary temperatures. Thus, the reported correlations on heat transfer rate and coefficient of Al₂O₃-water nanofluid’s natural convection have theoretical and practical value for heat transfer application. Furthermore, correlations on heat transfer coefficient of water natural convection are obtained with the nanoparticle’s volume fraction \(f_{p} = 0\).