A Simple Method of Determining Entropy Generation Rate in Viscous Fluid Flow Through Ducts

Entropy generation rate in a flow channel is associated with a number of parameters including the geometry of the channel, the thermal boundary conditions, and the thermo-physical properties of the fluid. Accurate determination of the overall rate of entropy generation in a duct may take considerable computational time, especially when two- or three-dimensional modeling is required as a result of geometry and complex relationship between the convection heat transfer and fluid flow parameters involved. In this paper, a simple yet accurate method of estimation for the total rate of entropy generation in a duct is presented. Consequently, a representative temperature, the "Log Mean Temperature", at which the convection heat transfer and fluid flow properties are evaluated for the determination of total rate of entropy generation, is introduced. It is shown that the approximate Log Mean Temperature method provides considerably accurate values of total rate of entropy generation in a duct for both uniform wall heat flux and uniform wall temperature boundary conditions. Water and glycerol (highly viscous fluid at around room temperature) are used to assess the accuracy of the approximate Log Mean Temperature method. The assessment is done within the coverage of laminar flow (Re < 3,000) and single phase fluid (i.e., no phase change). It is shown that the error in using the approximate Log Mean Temperature method in evaluating the total rate of entropy generation in a duct stays within less than 1 % for the entire practical range of Re numbers and temperature changes considered.