Effect of different flow regimes on free convection heat transfer from isothermal convex bodies over all range of Rayleigh and Prandtl numbers

Abstract

In the present study, effect of different flow regimes on free convection heat transfer has been examined. In the light of this, a novel analytical method is developed to calculate free convection heat transfer from isothermal convex bodies with arbitrary shape over all range of Rayleigh number in fluids with any Prandtl number. The crux of this method is based on the concept of dynamic behaviors existing in natural convection flow. In the previous models the Body Gravity Function (BGF) and Turbulent Function (TF) have been taken as constant values. In this study, BGF accounts for the effect of body shape and orientation with respect to gravity vector in laminar free convection. Besides, TF accounts for the impact of Prandtl number, body shape and orientation with regard to gravity vector in turbulent free convection. By contrast, it is shown that these two parameters undergo a change through the variation of Rayleigh number and cannot be considered as a constant. These two parameters are modeled based upon the thermal resistance concept. Moreover, two transition criteria happening in free convection heat transfer will be obtained according to this new analytical method (conduction–laminar and laminar–turbulent transitions). Finally, three models (models 1, 2 and 3) are proposed for calculation free convection heat transfer and present results for ten isothermal convex bodies with various aspect ratios ( $$0.298 \le \frac{\sqrt A }{P} \le 2.470$$ ) have been compared with the available experimental and numerical data. Here, the results of model 2 are almost equal to those of model 3. Also, the results of model 1 are more precise than those of model 3 while the parameters computation of model 1 is more intricate in comparison with model 3. On the one hand, the model 1 has an average difference <6 % vis-a-vis numerical data in entire range of Rayleigh number (laminar and turbulent). On the other hand, the average difference of model 1 is not more than 8 % versus experimental data in complete range of Rayleigh number. Outstanding agreement exhibits that the proposed model has a great potential to predict free convection heat transfer from isothermal convex bodies in the whole range of Rayleigh numbers in fluids with any Prandtl number.