Entropy generation and pumping power to heat transfer ratio (PPR) of a laminar flow, for a circular tube immersed in an isothermal fluid, are studied analytically in this paper. Two different fluids, namely, water and ethylene glycol, are chosen to study the influence of fluid properties on entropy generation and PPR. The expressions for dimensionless entropy generation, Bejan number and PPR are derived in a detailed way and their variations with Reynolds number, external Biot number, and the dimensionless temperature difference are illustrated. The results of the analysis are compared with those for a laminar flow in a circular tube with uniform wall temperature boundary condition. Finally, a criterion is established to determine which type of thermal boundary conditions is more suitable for a particular fluid, with respect to its influence on entropy generation. 1. Introduction Heat transfer is a fundamental source of thermodynamic irreversibility in all real engineering devices. When heat is transferred across a finite temperature difference, some capacity to do work is lost. In convection, apart from heat transfer, fluid friction is the other source of loss of available work. Both heat transfer and fluid friction generate entropy. This entropy generation must be minimized to reduce the loss of available work. Entropy generation minimization is no longer an avant-garde philosophy but a mainstream one in the design of thermal systems. In the past, many researchers have studied the problem of entropy generation minimization in fluid flow with heat transfer. Bejan [1, 2] outlined the method for evaluating the entropy generation in fluid flow with heat transfer. He found out the entropy generated in fluid flow with heat transfer over a flat plate, in a duct, for cylinders in cross flow and in various other geometrical configurations. ？ahin [3] studied the entropy generated in a circular duct with uniform wall temperature for two fluids, namely, water and glycerol. The effect of temperature on viscosity was taken into account in that study. He found out that the total energy loss (due to pumping process and entropy generation) can be minimized with respect to the duct length for viscous fluids with temperature dependent viscosity. ？ahin [4, 5] also considered the effect of duct geometries on the entropy generation, both for uniform wall temperature and for uniform heat flux boundary conditions. The various duct geometries like circular, square, rectangular, equilateral triangle, and sinusoidal were considered. In general, circular geometry was found to be
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