This paper presents a numerical study of two dimensional incompressible flow of non-Newtonian power-law fluid over a pair of elliptical tandem cylinders confined in a channel. The studied range of condition is 0.2 <= n <= 1.8, (power-law index), 1 <= Pr <= 100 (Prandtl number), 0.25 <= E <= 2 (aspect ratio) and 1.25 <= L <= 20 (cylinders' distance) for 1 <= Re <= 40. The effect of those parameters on the drag coefficient and heat transfer characteristic of both cylinders are examined in detail. This research addresses the combined characteristics of the flow and the heat transfer for power-law fluids and completes the previous research in the field by taking the generalized form of the cylinder geometry in the confined region. The results demonstrate by employing the highly shear-thinning fluid, the heat transfer is maximized while minimizing the momentum loss. The Nusselt number over drag coefficient ratio, NDR, is proposed as a design parameter in initial sizing of small scale heat exchangers. The NOR shows an elliptical cylinder with aspect ratio E = 0.5 can be more efficient than circular cylinders for a range of moderate Re numbers. (C) 2012 Elsevier B.V. All rights reserved.