The annular geometry with inner cylinder eccentricity and rotation is significant in many thermal and engineering fields, particularly with non-Newtonian fluid flows. A numerical analysis examines the effects of rotation and eccentricity of the inner cylinder on the fluid flow and heat transfer characteristics of shear-thinning non-Newtonian fluids within annular geometry under developing steady laminar flow. The computational model simulates non-Newtonian annular flow using a power-law viscosity model for generalized Reynolds numbers ($100\le Re_{g}\le1000$), flow behavior index ($0.2\le n\le0.8$) and Taylor number $Ta=10^{4}$ with radius ratio $r^{*}=0.5$. The simulation employs hydraulic and thermal boundary conditions, including an adiabatic outer cylinder and a constant temperature at the inner rotating cylinder, while the outer cylinder remains stationary. Results show that axial flow at $n=0.2$ exhibits lower flow resistance and enhances convective transport compared to higher $n=0.8,$ especially for the concentric case $(\epsilon=0)$. However, increasing eccentricity from $\epsilon=0.2$ to $\epsilon=0.6$ alters the heat transfer behavior, with $n=0.8$ yielding the highest Nusselt numbers at $\epsilon=0.6$, due to the strong secondary flows and intensified local acceleration in the narrow gap. These outcomes reveal that heat transfer enhancement is not solely governed by flow resistance but is also influenced by secondary flows, boundary layer stability, and localized acceleration effects.
The present research studies experimentally the effect of the ratio of the centurial hollow on the average of laminar convective heat transfer and the thermal gradation of the thermal boundary layer of three square flat plates. An experimental set-up was made for this purpose containing basically three uniformly Aluminum flat plates of a centurial hollow representing (0.25,0.5,0.75) of the entire surface area of each plate. Each of the three plates were heated by a constant heat flux for a rang of Rayleigh number of (5.62x105≤Ra≤1.67x106).The study showed that increasing the hollow ratio causes to increase the average of convective heat transfer by increasing the average Nusselt number, and the increasing average from a ratio to another decreases by the increases of the hollow ratio. The increasing between the two surfaces at (m=0.25&m=0.5) reached (39.6%) and for (m=0.5&m=0.75) was less than that and reached (29.2%).The increase average between the biggest and smallest hollow ratio was (78%).The study also showed that the maximum thermal gradation was on the out side edge of the plates and increases with the increase of Rayleigh number and the hollow ratio.