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Laminar flow of non-Newtonian fluid (shear-thinning) through a 1:3 planar gradual expansion is numerically investigated, for various Power-Law index (0.6, 0.8 and 1.0) and expansion angles (15, 30, 45, 60 and 90°) at different generalized Reynolds number (1 ≤ Reg ≤ 400). The study of these parameters effect on the flow pattern allowed the determination of the two critical generalized Reynolds numbers (Regcr1 and Regcr2), which correspond to the transition from the symmetric to the asymmetric flow and the appearance of the third recirculation zone respectively. The results showed that decreasing the Power-Law index or the expansion angle stabilizes the flow by increasing significantly the two critical generalized Reynolds numbers. In order to predict the two critical generalized Reynolds numbers, two correlations have been proposed.

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The present investigation set out to assess the influence of the surface roughness on the flow and thermal mean quantities, around the heated corrugated cylinder in the laminar steady flow. The current investigation has been devoted to a numerical analysis of a two-dimensional steady flow and forced convection heat transfer characteristics over a heated longitudinal sinusoidal shape grooved cylinder, immersed in an unconfined Newtonian fluid. The number of the grooved cavities was chosen to be 10, 20 and 30 grooves, equally distributed around the cylinder circumference with wavelength and wave amplitude of 1/50 and 1, respectively. Moreover, the thermal boundary condition effect has been analyzed by imposing a uniform heat flux and constant temperature on the cylinder periphery as a thermal boundary condition, over a Reynolds number range of ([Formula: see text]) and a fixed Prandtl number of 0.715. The numerical procedure is based on the finite volume method. The findings indicate that with increasing groove number, the total drag coefficient of the grooved cylinder reduces markedly compared to the smooth one. This trend is more pronounced as the Reynolds number increases. The effect of the groove number on the pressure coefficients is limited, where the profiles of the grooved cylinder coincide with that of the smooth one over the Reynolds number range. When the Reynolds number varies from 0.1 to 40, the average Nusselt number enhances noticeably by about 86% for the smooth and grooved cylinders. Moreover, the groove number affects significantly the average Nusselt number, where the increased groove number results in a gradual reduction in the average Nusselt number. This attenuation is more pronounced as the Reynolds number increases. To predict the average Nusselt number, a correlation has been proposed.