14. Calculation Examples on Heat Transfer by Using Conversion Formulae

The predictive and conversion formulae on heat transfer respectively reported in Chaps. 9 and 13 are innovative achievement of the theoretical research of Al₂O₃-water natural convection. Their theoretical and practical value lies in that they are developed by theoretical analysis and numerical calculation based on comprehensive consideration of effects of nanofluid’s variable thermophysical properties, nanoparticle’s shape factor and concentration, and fluid’s boundary temperatures. These calculation examples show that the heat transfer increases with increase of fluid’s average temperature of nanofluid’s natural convection, due to increasing nanofluid’s thermal conductivity level. If the fluid boundary temperatures are interchanged, the heat transfer coefficient will be changed, and the higher the fluid bulk temperature, the larger the heat transfer rate. It demonstrates the theoretical flaws and practical inaccuracies of Boussinesq approximation, and it is important to comprehensively consider the effects of fluid’s variable thermophysical properties in the study of heat transfer of natural convection. All these show the charm of the present formulae on heat transfer application. Of course, these developed formulae on heat transfer prediction need to be verified by the experiment. There are two different groups of the predictive formulae on heat transfer of Al₂O₃-water nanofluid’s natural convection. Group 1 is for predictive formulae and group 2 is for conversion formulae on heat transfer prediction. Since the formulae of group 2 is developed based on those of group 1, the calculation results of group 1 are coincident to those of group 2. However, the conversion formulae in group 2 are more convenient to be used than those in group 1 for heat transfer prediction of Al₂O₃-water nanofluid’s natural convection.