Akhilesh K. Sahu

Forced Convection Heat Transfer from a Heated Square Cylinder to Power Law Fluids in the Unsteady Flow Regime

Forced convection heat transfer to incompressible power law type non-Newtonian fluids from a heated square cylinder in the unsteady cross-flow regime has been studied numerically by solving the relevant momentum and thermal energy equations using a finite-volume method for the range of conditions 0.7 ≤ Pr ≤ 50, 60 ≤ Re ≤ 160, and 0.5 ≤ n ≤ 1.8. Over this range of Reynolds numbers, the flow is truly periodic for Newtonian and shear-thickening fluids, while in the case of shear-thinning fluids it becomes pseudo-periodic at high values of Re (≥140) and low values of n(≤ 0.6). This work is concerned only with the truly periodic regime and therefore the range of Reynolds number studied varies with the value of the power law index. The dependence of the local and average Nusselt number on the Reynolds number, Prandtl number, and power law index has been studied in detail. Broadly, shear-thinning (n < 1) fluid behavior promotes heat transfer, whereas shear-thickening (n > 1) impedes it. Further insights into the heat transfer phenomenon are provided in terms of isotherm contours in the vicinity of the cylinder for a range of values of the Reynolds number, Prandtl number, and power law index.

The Effect of a Blockage on Forced Convection Heat Transfer From a Heated Square Cylinder to Power-Law Fluids

Forced convection heat transfer characteristics of a long, heated square cylinder blocking the flow of a power-law fluid in a channel is numerically investigated in this study. In particular, the role of the power-law index n, Reynolds number Re, Prandtl number Pr, and blockage ratio β(=B/H) on the rate of heat transfer from a square cylinder in a channel has been studied over the following ranges of conditions: 0.5 ≤ n ≤ 1.8, 60 ≤ Re ≤ 160, β = 1/4, 1/2, and 0.7 ≤ Pr ≤ 50. A semi-explicit finite-volume method is used on a nonuniform collocated grid arrangement. The third-order QUICK and the second-order central difference schemes are used to discretize the convective and diffusive terms, respectively, in the momentum and energy equations. Irrespective of the type of behavior of fluid (different values of n), the average Nusselt number increases as the blockage ratio increases. Similar to the unconfined flow configuration, the average Nusselt number increases monotonically with Reynolds and Prandtl numbers for both values of the blockage ratio and for all values of power-law index considered here. Further insights into the heat transfer phenomenon are provided by presenting isotherm contours in the vicinity of the cylinder for a range of values of the Reynolds number, Prandtl number, and power-law index for the two values of β considered in this work.

Two Dimensional Unsteady Laminar Flow of Power Law Fluids Past a Square Cylinder: A Numerical Study

The two-dimensional and unsteady flow of power-law fluids past a long square cylinder has been investigated numerically in the range of conditions 60 ≤ Re ≤ 160 and 0.5 ≤ n ≤ 2.0. Over this range of Reynolds numbers, the flow is periodic in time for Newtonian fluids. However, no such information is available for power law fluids. A semi-explicit finite volume method has been used on a non-uniform collocated grid arrangement to solve the governing equations. The macroscopic quantities such as drag coefficients, Strouhal number, lift coefficient as well as the detailed kinematic variables like stream function, vorticity and so on, have been calculated as functions of the pertinent dimension-less groups. In particular, the effects of Reynolds number and of the power-law index have been investigated in the unsteady laminar flow regime. The leading edge separation in shear-thinning fluids produces an increase in drag values with the increasing Reynolds number, while shear-thickening behaviour delays the leading edge separation. So, the drag coefficient in the above-mentioned range of Reynolds number, Re, in shear-thinning fluids (n 1) drag coefficient reduces with Reynolds number, Re. Furthermore, the present results also suggest the transition from steady to unsteady flow conditions to occur at lower Reynolds numbers in shear-thickening fluids than that in Newtonian fluids. Also, the spectra of lift signal for shear-thickening fluids show that the flow is truly periodic in nature with a single dominant frequency in the above range of Reynolds number. In shear-thinning fluids at higher Re, quasi-periodicity sets in with additional frequencies, which indicate the transition from the 2-D to 3-D flows.Copyright