Non-isothermal flow of a power law fluid past a rectangular obstacle (of aspect ratio 1 × 2) in a channel: Drag and heat transfer

A two-dimensional numerical study has been carried out to investigate the drag and Nusselt number characteristics under forced convection conditions between a streaming power law liquid and a rectangle (with its longer side aligned with the direction of flow) placed symmetrically between two solid walls. In particular, the values of the individual and total drag coefficients, and of the Nusselt number are obtained as functions of the flow behaviour index (1.4 ⩾ n ⩾ 0.5), of Reynolds number (5 ⩽ Re ⩽ 40) and of the Peclet number (5 ⩽ Pe ⩽ 400) for a fixed value of the blockage ratio (1/8). Within these ranges of kinematic and rheological conditions, the drag and Nusselt number show only fair to moderate deviation from the corresponding Newtonian values at the same values of the Reynolds and Peclet numbers. Qualitatively speaking, the shear-thinning behaviour (n < 1) augments the drag and heat transfer while the shear-thickening behaviour (n > 1) causes both the drag and heat transfer to drop below the corresponding Newtonian values. The power-law fluid behaviour does not seem to alter the streamline, isovorticity and isotherm plots in a significant manner, except for the fact that the shear-thinning behaviour not only delays the formation of a visible wake but the resulting wake is also somewhat shorter than that in a Newtonian fluid. The shear thickening, on the other hand, has exactly the opposite influence on wake formation.