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The falling ball method (FBM) is one of the well‐established techniques for measuring the viscosity of Newtonian liquids at the room as well as at elevated temperatures and pressures. Owing to its simplicity and low cost, the possibility of extending its range of application to non‐Newtonian systems including virgin and filled polymer melts, composites, polymer‐solutions, and so forth, is explored here, In this work, theoretical results for the flow of power‐law fluids past a sphere have been used to extract the values of the zero‐shear viscosity and shear‐dependent viscosity in the low‐shear rate limit. The theoretical scheme outlined here has been validated by presenting comparisons with experimental results for scores of polymer solutions for which both falling sphere and rheological data are available in the literature. Indeed, the good correspondence obtained between these two independent data is encouraging and it is thus possible to use the FBM for shear‐thinning systems when the resulting Reynolds numbers are such that the flow is viscosity‐dominated, and the inertial effects are negligible. This implies that the Reynolds number should be ≤ ~1 for shear‐thinning fluids and ≤ ~10−5 for shear‐thickening fluids. [ABSTRACT FROM AUTHOR]

Extensive results are reported on the flow and heat transfer for Bingham plastic fluids for the same configuration as in Part I over the ranges: Reynolds number (5 − 200) , Prandtl number (1 − 100) , and Bingham number (0. 01 − 100) and the gap ratio (0. 3 − 0. 7). At small Bingham numbers, the results deviate a little from that in Newtonian fluids except for the pockets of unyielded material. With the increasing fluid yield stress, the flow field consists of preferred flow channels between the inlet and outlet ports with high shear zones which directly influence the drag and Nusselt number. Depending upon the extent of fluid yielding, the drag on the middle cylinder can be higher by up to ∼100% or lower by up to ∼90% than that on the upstream cylinder. Similarly, the strong back flow observed at low Bingham numbers and high Reynolds numbers in the rear of the downstream cylinder leads to negative drag. In sparse arrays, the drag of upstream and downstream cylinders is comparable but that on the middle cylinder is always smaller. Similarly, the average heat transfer coefficient for each successive cylinder decreases with respect to the upstream cylinder. For the upper and downstream cylinder, this ratio is about 28-65% depending upon the kinematic conditions. In most cases, the first cylinder offers the maximum heat transfer. [ABSTRACT FROM AUTHOR]

Forced convection heat transfer in power-law fluids has been investigated numerically around four identical circular cylinders in a diamond array in a square enclosure. For the laminar flow, the governing equations have been solved numerically over the following ranges of parameters: Reynolds number (5 − 200), Prandtl number (0.7 − 100), power-law index (0.2 − 2) and center-to center gap between cylinders (0.3 − 0.7) to elucidate their influence. The detailed kinematics and engineering parameters are influenced by the gap between the cylinders via the development of multiple secondary flow regions and/or the splitting of incoming fluid stream. The drag on the trailing cylinders with reference to the lead cylinder can be up to ± ∼ 80% higher or lower depending upon the gap between the cylinders, power-law index and Reynolds numbers. In compact arrays, the drag becomes slightly negative due to the reverse flow for certain combinations of power-law index (< 1) and high Reynolds numbers (100 and 200). Similarly, the heat transfer affected by the subsequent cylinders ranges from 50-60% for the second cylinder which drops to ∼10% for the last cylinder. Finally, the functional dependence of the Nusselt number has been consolidated in terms of Reynolds number, Prandtl number, power-law index and the gap ratio. [ABSTRACT FROM AUTHOR]

This work numerically studies the momentum and thermal characteristics of the power-law fluids flowing through a rectangular-shaped orifice fitted in a two-dimensional channel, over wide ranges of conditions: fluid behavior index, n (0.3–1.0), Reynolds number, Re (1–50), Prandtl number, Pr (10−100), aspect ratio, β (0.3–0.7) and three different locations of the orifice, C o (0.5–0.75). Extensive results have been analyzed in terms of streamlines, separation zones, discharge coefficient, isotherm contours, temperature profiles and local Nusselt number. Multiple separation zones are formed in downstream section depending upon the combinations of parameters, which, in turn, influence the discharge coefficient and the local Nusselt number. Separated flow regions formed on the bottom wall expand with increasing Reynolds number (Re), while it decreases with n and β and shows a complex dependence on C o. The local Nusselt number, Nu L , observed herein which is found to be more pronounced at high C o and low n and β for the upper wall. Further, it bears an inverse relation with n , on both walls while a strong effect of orifice location, C o and aspect ratio, β is seen over the range of conditions spanned here. • Influence of orifice location on the flow and thermal characteristics of power-law fluids. • Effect of orifice aspect ratio on the momentum and heat transfer characteristics. • Discussion on the flow visualization and isotherm contours. • Demonstration of the orifice discharge coefficient. • Effect of orifice location and aspect ratio on the local Nusselt number. [ABSTRACT FROM AUTHOR]

This work reports results on the drag and heat transfer from an in-line array of three isothermal spheres falling in a cylindrical confinement filled with Bingham plastic fluids. The effects of dimensionless parameters, such as the Reynolds number (1 ≤ Re ≤ 100), Prandtl number (1 ≤ Pr ≤ 100), Bingham number (0 ≤ Bn ≤ 100), blockage ratio (2 ≤ β ≤ 4) and sphere-to-sphere distance (1.5 ≤ t ≤ 6) have been elucidated. The flow and heat transfer characteristics were analysed in terms of yielded/unyielded regions, streamline and isotherm contours, drag coefficient, pressure coefficient, and local and average Nusselt number. Broadly, the drag coefficient shows a positive dependence on Bn and sphere-to-sphere distance (t) while it exhibits an inverse dependence on Re and β. On the other hand, the Nusselt number shows a positive dependence on Re, Pr, Bn and β; and a complex dependence on t for each sphere. Simple predictive expressions for the average Nusselt number for each sphere are formulated, thereby enabling its prediction in a new application. [ABSTRACT FROM AUTHOR]