A similarity transformation of velocity field and its application for an in-depth study on laminar free convection heat transfer of gases

Abstract

An innovative similarity transformation of velocity field is reported for equivalent transformation of governing partial differential equations of laminar free convection. To demonstrate its rationality theoretically, its rigorous theoretical derivation is presented firstly in this work. On this basis, an example is presented with successful application for demonstration of its advantages in in-depth study on free convection heat transfer. The governing ordinary differential equations of laminar free convection equivalently transformed by the innovative similarity transformation are presented. It is seen that by the innovative similarity transformation the variable physical properties are transformed into the forms of the related physical property factors, which are organically coupled in the transformed governing ordinary differential equations. It proves that the innovative similarity transformation is very well suitable for consideration of variable physical properties. Then, a new algorithm is presented to calculate fluids flow and heat transfer of laminar free convection. It contains the theoretical and numerical models on laminar free convection, to consider the variable physical properties, to obtain the system of numerical solutions, and then, to create formalization equations for the convection heat transfer coefficient by means of an optimal curve-fitting approach based on the system of numerical solutions. A system of numerical calculations of the governing ordinary differential equations is presented for the gaseous laminar free convection. A temperature parameter model is induced for convenient and reliable treatment of variable physical properties of gases. The delivered formalization equations of heat transfer coefficient on gaseous free convection have strong theoretical and practical value for heat transfer applications because they are created based on the theoretically reasonable similarity transformation model combined with a better model of consideration of fluid's variable physical properties, accurate numerical solutions, and rigorous formalization equations combined with rigorous theoretical derivation. All these prove that the reported innovative similarity transformation is a better alternative applied for in-depth study on free convection heat transfer.