A Mathematical Model of Local and Average Heat Transfer in Channels with Heat Transfer Intensifiers

Abstract

The expressions derived previously from the three-layer Owen model of a turbulent boundary layer and the Deissler and the van Driest models are demonstrated to be valid for predicting heat transfer coefficients in the entrance region of channels. The basic parameters in these expressions are the dynamic velocity, dimensionless viscous sublayer thickness, and dimensionless turbulent boundary layer thickness. Correlations are presented for predicting these parameters in the entrance region of a plate or circular pipe. The predicted heat transfer coefficients agree with the available data. With consideration of the fact that the friction and the heat transfer laws established by S.S. Kutateladze and A.I. Leont’ev are conservative with respect to disturbances in the turbulent boundary layer, parameters of the expressions for average heat transfer coefficients in channels with heat transfer intensifiers (such as roughness, transverse ring protrusions, and annular groves in pipe walls) were determined. In calculating friction and heat transfer, the main characteristics are the dynamic velocity and the ratio of the friction coefficient on a smooth surface to that on a surface with heat transfer intensifiers. The expression was derived for calculating the Nusselt number as a function of the Reynolds number and the friction factor. The predicted average heat transfer coefficients agree well with the experimental data and the predictions by empirical correlations. Calculations were performed in a wide range of Reynolds number (from 10⁴ to 10⁶) and smooth-to-intensified surface friction factor ratio (from 1.92 to 9.2). The proposed correlations can be used for predicting local heat transfer coefficients in the entrance region on a body in a flow and average heat transfer coefficients in intensified channels.