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DOI: 10.1615/ICHMT.2008.CHT.180
21 pages

Ridha Ben Mansour
Faculty of Engineering, Université de Sherbrooke, Sherbrooke, Qc., Canada J1R 2R1

Nicolas Galanis
THERMAUS, Département de génie mécanique, Université de Sherbrooke, Sherbrooke J1K 2R1, Quèbec, Canada

Cong Tam Nguyen
Faculty of Engineering, Universite de Moncton, Moncton, New Brunswick, Canada E1A 3E9


The problem of hydro-dynamically and thermally developing laminar mixed convection in a vertical tube with uniform wall heat flux has been studied numerically. The flow was assumed steady and axis-symmetrical and the fluid incompressible with constant thermo-physical properties except for its density in the gravity forces (Boussinesq's assumption). The system of non-linear, elliptic and coupled governing equations, subjected to appropriate boundary conditions, was successfully solved using the finite-control-volume method, a staggered non-uniform 34 (r) x 40 (φ) x 700 (z) grid and the power-law scheme for computing the heat and momentum fluxes. The modified SIMPLE procedure was used to treat the velocity-pressure coupling. Numerical results obtained for the developing velocity and temperature profiles of water were used to compute the rate of entropy production due to heat transfer and viscous effects. Some significant results showing profiles of these variables for various axial positions and different Grashof numbers are presented and discussed. The entropy profiles in the fully developed region are in excellent agreement with the corresponding analytical results. These results clearly show that the entropy production by both mechanisms is more important near the tube wall. In general, the entropy production due to heat transfer is several orders of magnitude larger than that due to viscous effects. It has also been found that the entropy generation increases considerably with an augmentation of the Grashof number.

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