Natural convection in power-law fluids from a tilted square in an enclosure

In this study, laminar natural heat transfer from a heated tilted square (two-dimensional) to a quiescent power-law medium filled in a square enclosure has been investigated numerically. In particular, the coupled momentum and energy equations have been solved numerically over the range of kinematic conditions as: Grashof number, 102⩽Gr⩽105; Prandtl number, 0.71⩽Pr⩽100 and power-law index, 0.2⩽n⩽1.5. In addition, the effect of the two commonly employed thermal boundary conditions, namely, that of the constant temperature or constant heat flux on the surface of the tilted bar is also examined. However, the results reported herein are restricted to three relative positions of the heated bar on the vertical mid-plane of the enclosure, namely, β2 = 0.25, 0.5 and 0.75 whereas the side of the enclosure is four times the size of the heated cylinder. Depending upon the placement of the heated cylinder with respect to the bottom of the enclosure, one may observe single- or double-celled flow patterns. Overall, the influence of the power-law fluid behavior is strongly modulated by the values of the Grashof number (Gr), Prandtl number (Pr) and the relative positioning of the cylinder (β2). The detailed flow and temperature fields are visualized in terms of the streamline and isotherm contours. The heat transfer characteristics are interpreted in terms of the local Nusselt number on the surface of the heated cylinder and the overall gross behavior is denoted in terms of the average Nusselt number. Finally, the numerical results obtained in this work have been correlated as functions of the Grashof number, Prandtl number, power-law index and the relative positioning of the heated cylinder.