Momentum and heat transfer characteristics of a long parallelepiped submerged in power-law fluids in the laminar vortex shedding regime

The governing partial differential equations describing the flow and forced convection heat transfer characteristics of power-law fluids past a long parallelepiped at α = 45° incidence have been solved numerically in the two-dimensional laminar flow regime. In particular, the major thrust of this work is to elucidate the influence of Reynolds number (Re), Prandtl number (Pr) and power-law index (n) on the detailed and macroscopic momentum and heat transfer characteristics in the laminar vortex shedding regime. The detailed features of the flow and heat transfer phenomena are visualized and analyzed in terms of the instantaneous streamlines, iso-vorticity and isotherm contours whereas the surface pressure and local Nusselt number distributions over the surface of the parallelepiped provide the next level of description of these phenomena. The gross features of the flow are captured in terms of the time-averaged drag coefficient, rms value of the lift coefficient, Strouhal number and Nusselt number. The trends seen here are qualitatively similar to that reported in the literature for a circular cylinder and a bar of square cross-section (with zero angle of incidence). Broadly, shear-thinning viscosity promotes heat transfer due to the lower effective viscosity of the fluid in the close proximity of the parallelepiped bar. As expected, shear-thickening behaviour shows the opposite effect. The ranges of the pertinent dimensionless groups spanned in this study are as follows: 0.3⩽n⩽1.8; 45⩽Re⩽120 and 0.7⩽Pr⩽80. Over this range of Reynolds number, the flow was found to be truly periodic. Finally, the numerical heat transfer results are correlated using a simple analytical form which facilitates the interpolation of the present results for the intermediate values of the parameters.