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This paper examines the effects of thermal buoyancy on momentum and heat transfer characteristics of symmetrically and asymmetrically confined cylinder submerged in incompressible Poiseuille liquid. The detailed flow and temperature fields are visualized in term of streamlines and isotherm contours. The numerical results have been presented and discussed for the range of conditions as 10 ≤ Re ≤ ≤ 40, Richardson number 0 ≤ Ri ≤ 4, and eccentricity factor 0 ≤ ε ≤ 0.7 at Prandtl number Pr = 1, and blockage ratio B = 20%. The representative streamlines and isotherm patterns are presented to interpret the flow and thermal transport visualization. When the buoyancy is added, it is observed that the flow separation diminishes gradually and at some critical value of the thermal buoyancy parameter it completely disappears resulting a creeping flow. Additionally, it is observed that the down vortex requires more heating in comparison to upper vortex in order to be suppressed. In the range 1.5 ≤ Ri ≤ 4, two counter rotating regions appear above the cylinder and on the down channel wall behind the cylinder. The total drag coefficient, C D , increases with increasing Richardson number at (ε = 0). Moreover, an increase in eccentricity factor from 0 to 0.3 increases C D by 37% at Re = 10, and 30% at Re = 20 for Ri = 4. An increase in eccentricity factor form 0 to 0.4 increases local Nusselt number by 20.4% at Re = 10, and 18.6% at Re = 30 for Ri = 4.

In this paper, three-dimensional numerical simulations are carried out to investigate and analyze the gradual effects of thermal buoyancy strength on laminar flow of an incompressible viscous fluid and heat transfer rate inside a 180° curved channel of square cross-section. The governing equations of continuity, momentum and energy balance are obtained and solved numerically using finite volume method. The effect of Dean number, De, and Richardson number, Ri, on dimensionless velocity profiles and Nusselt number are examined for the conditions: De = 125 to 150, Ri = 0 to 2 at Pr = 1. The mean results are illustrated in terms of streamline and isotherm contours to interpret the flow behaviors and its effect on heat transfer rate. Dimensionless velocity profiles and the local Nusselt number at the angle 0° and 90° are presented and discussed. Also, the average Nusselt number on surfaces of curved duct is computed. The obtained results showed that by adding thermal buoyancy to computed domain, some early Dean vortices are observed at the angle 0° and new sort are observed at 90°. Furthermore, increase in Dean number increases the heat transfer rate. In other hand, increase in Richardson number decreases the average Nusselt number of 180° curved duct.

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Nomenclature B -volume expansion coefficient,1/K; Cf -skin friction coefficient; CD -drag coefficient; d -cylinder size, m; g -gravitational acceleration, m/s 2 ; Gr -Grashof number; H -Channel width, m; h -Local convective heat transfer coefficient, W/(m 2 K); I2 -second invariant of the rate of deformation tensor, s 2 ; k -fluid thermal conductivity, W / (m 2 K); Lr -dimensionless recirculation length; L * r -recirculation length, m; Ld -downstream distance, m; Lu -upstream distance, m; m -power-law consistency index, Pa s n ; n -power-law flow behavior index; ns -direction normal to the cylinder surface; Nu -average total Nusselt number; p -pressure, Pa; P -dimensionless pressure; Pr -Prandtl number; Pe -Peclet number; Re -Reynolds number; Ri -Richardson number; T -temperature, K; U -dimensionless cross-stream velocity; u -cross-stream velocity, m/s; Vdimensionless stream-wise velocity; v -velocity stream-wise velocity, m/s; X -dimensionless cross-stream coordinate; Y -dimensionless stream-wise coordinate; y -stream-wise coordinate, m;greek lettersεrate of deformation, s -1 ; η -viscosity, Pa s; -fluid density kg/m 3 ; β -blockage ratio; τ -shear stress rate tensor, Pa; θ -dimensionless temperature;