Free convection from a heated circular cylinder in confined power-law fluids

In this work, free convection heat transfer from a horizontal cylinder (isothermal or dissipating heat at a constant rate) placed on the horizontal axis of a square duct filled with an incompressible power-law fluid has been investigated. On the other hand, along the vertical centre line, three relative positions of the heated cylinder are considered, namely, at the centre, close to the upper wall and close to the bottom wall to elucidate the effect of the symmetric and asymmetric confinement. The governing differential equations, namely, continuity, momentum and energy have been solved numerically to elucidate the effect of the pertinent kinematic (Rayleigh number, Ra; Prandtl number, Pr; power-law index, n) and geometric parameters, especially the relative positioning of the heated cylinder with reference to the bottom wall. Overall, the present results span the wide range of conditions as 102 ≤ Ra ≤ 106; 0.71 ≤ Pr ≤ 100; 0.2 ≤ n ≤ 1.8 and 0.25 ≤ β1 ≤ 0.75, and the flow is believed to be laminar and steady over this range of Rayleigh numbers. Overall, the average Nusselt number shows positive dependence on Grashof number and Prandtl number. The overall heat transfer also decreases as the cylinder gradually approaches the upper adiabatic wall. The streamline and isotherm contours reveal interesting flow patterns which show a rather strong dependence on the value of β1.