The steady and incompressible flow of power-law type non-Newtonian fluids across an unconfined, heated circular cylinder is investigated numerically to determine the dependence of the individual drag components and of the heat transfer characteristics on power-law index (0.5 e n e 1.4), Prandtl number (1 e Pr e 100), and Reynolds number (5 e Re e 40). The momentum and energy equations are expressed in the stream function/vorticity formulation and are solved using a second-order accurate finite difference method to determine the pressure drag and frictional drag as well as the local and surface-averaged Nusselt numbers and to map the temperature field near the cylinder. The accuracy of the numerical procedure is established using previously available numerical and analytical results for momentum and heat transfer in Newtonian and power-law fluids. The results reported herein provide fundamental knowledge of the flow and heat transfer behavior for the flow of non-Newtonian fluids over a circular cylinder; these results further show that the effect of the power-law index on such behavior is strongly conditioned by the kinematic conditions and less so by the type of thermal boundary condition prescribed at the cylinder surface.

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The heat transfer characteristics from a circular cylinder immersed in power law fluids have been studied in the mixed convection regime when the imposed flow is oriented normal to the direction of gravity. The continuity, momentum, and thermal energy equations have been solved numerically using a second-order finite difference method to obtain the streamline, surface viscosity, and vorticity patterns, to map the temperature field near the cylinder and to determine the local and surface-averaged values of the Nusselt number. Overall, mixed convection distorts streamline and isotherm patterns and increases the drag coefficient as well as the rate of heat transfer from the circular cylinder. New results showing the complex dependence of all these parameters on power law index (n ) 0.6, 0.8, 1, 1.6), Prandtl number () 1,100), Reynolds number (1-30), and the Richardson number (0, 1, and 3) are presented herein. Over this range of conditions, the flow is assumed to be steady, as is the case for Newtonian fluids.

This paper aims to contribute to a better understanding of the concepts of a reversible process and entropy. For this purpose, an adiabatic irreversible expansion or compression is analysed, by considering that an ideal gas is expanded (compressed), from an initial pressure P i to a final pressure P f , by being placed in contact with a set of N work reservoirs with pressures decreasing (increasing) in a geometric or arithmetic progression. The gas entropy change S is evaluated and it is clearly shown that S > 0 for any finite N, but as the number of work reservoirs goes to infinity the entropy change goes to zero, i.e. the process becomes reversible. Additionally, this work draws attention to the work reservoir concept, which is virtually ignored in the literature, and to its analogy with the commonly used heat reservoir concept. Finally, it complements and reinforces an earlier study dealing with irreversible cooling or heating so that the synergy created by the two studies is important from both theoretical and educational standpoints.

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Les modèles de cellules à surface libre et vorticité nulle ont été combinés aux équations de mouvement afi n d'étudier numériquement l'écoulement stationnaire de fl uides (rhéofl uidifi ants et rhéoépaississants) de loi de puissance incompressibles dans des groupes de longs cylindres. Les équations de mouvement exprimées sous forme de fonction de courant/vorticité ont été résolues numériquement à l'aide d'une méthode de différences fi nies précise au second ordre pour obtenir des données complètes sur le comportement du coeffi cient de traînée, de la distribution de vorticité de surface, de lignes de courants et des iso-vorticités, pour des nombres de Reynolds élevés (Re = 50 et 500) et une large gamme de valeurs d'indice de loi de puissance (0,3 ≤ n ≤ 2,0) et de porosité (0,4 ≤ e ≤ 0,9). Le comportement de ces paramètres à de faibles nombres de Reynolds a également été étudié et validé à l'aide du travail théorique et numérique de la littérature scientifi que. Les résultats présentés ici permettent l'extension des limites de comportement d'écoulement rampant jusqu'à Re = 50 pour des fl uides très rhéoépaississants dans des conditions de faible porosité.