International Journal of Thermal Sciences 47 (2008) 1701–1711 www.elsevier.com/locate/ijts Entropy analysis for non-linear viscoelastic fluid in concentric rotating cylinders M. Mirzazadeh, A. Shafaei, F. Rashidi ∗ Department of Chemical Engineering, Amirkabir University of Technology, Hafez Ave., No. 424, Tehran, Iran Received 11 June 2006; received in revised form 26 October 2007; accepted 13 November 2007 Available online 20 June 2008 Abstract An analytical solution is presented for the forced convection and entropy generation of a viscoelastic fluid obeying the Phan-Thien–Tanner (PTT) constitutive equation in a concentric annulus with relative rotation of the inner and outer cylinders. Two different types of boundary conditions are considered: at the first case both cylinders are isothermal and kept at different temperatures and in the second case the heat flux is kept constant at the outer cylinder and the inner one is isothermal. Analytical expressions for dimensionless temperature profile (Θ), dimensionless entropy generation number (N S ), and the Bejan number (Be) are obtained. The effect of velocity ratio (β ), the group parameter (Br/Ω), the Brinkman number (Br), and fluid elasticity (ε We 2 ) on the above parameters are investigated. The results show that the total entropy generation number decreases as the fluid elasticity increases. The results also show that entropy generation number increases with increasing Brinkman number.  2007 Elsevier Masson SAS. All rights reserved. Keywords: Entropy generation; Annular flow; Phan-Thien–Tanner constitutive equation; Analytical solution; Heat transfer 1. Introduction Tangential flows of non-Newtonian fluids within annuli have wide range of engineering applications such as in the journal bearings, commercial viscometers, swirl nozzles, chemical and mechanical mixing equipments and electrical motors (see e.g. Maron and Cohen [1]). Forced convective heat transfer of Newtonian fluids in an- nular space has been investigated extensively in the litera- ture. A comprehensive review of paper is given by Childs and Long [2]. An extensive bibliography of papers on the flow of non- Newtonian fluids through annular channels is given in a recent paper by Escudier et al. [3]. Convective heat transfer of non- Newtonian fluids inside the annuli were considered in several works, for example Khellaf and Lauriat [4] analyzed the con- vective heat transfer characteristics for the flow of a Carreau fluid between rotating concentric vertical cylinders. Naimi et * Corresponding author. Tel.: +9821 6499066; fax: +9821 6405847. E-mail addresses: mirzazadeh_m@yahoo.com (M. Mirzazadeh), shafaei_a@cic.aut.ac.ir (A. Shafaei), rashidi@aut.ac.ir (F. Rashidi). al. [5] performed a flow visualization study of the develop- ment and structure of Taylor–Couette vortices for the case of a power-law fluid (Carbopol 940) with and without axial flow in the forced convection regime. From their experimental study, they derived heat transfer correlations for various flow regimes. Laminar forced convection heat transfer of purely viscous, non- Newtonian fluid flow in both concentric and eccentric annuli was numerically investigated by Manglik and Fang [6]. Capo- bianchi and Irvine [7] have considered heat transfer to modified power-law liquids in concentric annuli. Although the forgoing research works have covered a wide range of problems involving the flow and heat transfer in con- centric annuli they have been restricted, from thermodynamic point of view, to only the first law (thermodynamic) analysis. The contemporary trend in the field of heat transfer and thermal design is the second law (of thermodynamics) analysis and its design-related concept of entropy generation minimization (Be- jan [8]). Entropy generation is associated with thermodynamic irreversibility, which is common in all types of heat transfer processes. The ultimate motive behind the infusion of entropy generation analysis in heat transfer and thermal design is eco- nomics, and it is clear that minimizing irreversibility in the thermal systems results in decreasing the operating cost. Since 1290-0729/$ – see front matter  2007 Elsevier Masson SAS. All rights reserved. doi:10.1016/j.ijthermalsci.2007.11.002