Heat transfer enhancement in suddenly expanding annular pipe flows of Newtonian and shear-thinning non-Newtonian fluids is studied within the steady laminar flow regime. Conservation of mass, momentum, and energy equations, along with the power-law constitutive model are numerically solved. The impact of inflow inertia, annular-diameter-ratio, k, power-law index, n, and Prandtl numbers, is reported over the following range of parameters: Re = {50, 100, 150), k = {0, 0.5, 0.7); n = {1, 0.8, 0.6); and Pr = {1, 10, 100). Heat transfer enhancement downstream of the expansion plane, i.e., Nusselt numbers greater than the downstream fully developed value, Nu/Nu(fd) > 1, is only observed for Pr = 10 and 100. In general, higher Prandtl numbers, power-law index values, and annular-diameter-ratios, result in more significant heat transfer enhancement downstream of the expansion plane. Heat transfer augmentation, for Pr = 10 and 100, increases with the annular-diameter-ratio. For a given annular-diameter-ratio and Reynolds numbers, increasing the Prandtl number from Pr = 10 to Pr =100, always results in higher peak Nu values, Nu., for both Newtonian and shear-thinning flows. All Nu(max) values are located downstream of the flow reattachment point, in the case of suddenly expanding round pipe flows, i.e., kappa = 0. However, for suddenly expanding annular pipe flows, i.e., kappa = 0.5 and 0.7, Nu(max) values appear upstream the flow reattachment point. For Pr =10 and 100, shear-thinning flows display two local peak Nu/Nu(fd) values, in comparison with one peak value in the case of Newtonian flows. The highest heat transfer enhancement, Numax/ Nu(fd) approximate to 5, is observed at kappa = 0.7, n = 0.6, and Pr = 100. (C) 2017 Elsevier Ltd. All rights reserved.