### Abstract:

Laminar natural convection heat transfer in a power-law fluid from an isothermal rotating cylinder placed coaxially in a square duct has been studied numerically over the following ranges of conditions: Grashof number ; Prandtl number ; power-law index and non-dimensional rotational velocity . The spatial variation of the velocity and temperature fields are visualised in terms of the streamline and isotherm patterns, and temperature and vertical velocity at a few locations, respectively. Indeed, a range of flow patterns including twin-celled and single-celled recirculating regions can be observed depending upon the relative strengths of the buoyancy-induced and forced flow. The rate of heat transfer is described in terms of the distribution of the local Nusselt number over the surface of the cylinder together with its surface averaged value. As expected, the mean Nusselt number shows a positive dependence on the both Grashof and Prandtl numbers irrespective of the values of the power-law index and rotational velocity. For a non-rotating cylinder (S = 0), shear-thinning fluid behaviour promotes heat transfer, whereas shear-thickening viscosity impedes it with reference to that in Newtonian fluids otherwise under identical conditions. For the case of a rotating cylinder (), the rotation has positive influence on the rate of heat transfer at low values of the Grashof or Rayleigh number () irrespective of the type of fluid behaviour, i.e., shear-thinning or shear-thickening or Newtonian. However, at high values of the Grashof or Rayleigh numbers, the gradual increase of rotation of the cylinder first lowers the rate of heat transfer, and then increases it for shear-thickening (n > 1) and Newtonian fluids (n = 1). On the other hand, a reverse trend is seen for shear-thinning fluids. These non-monotonous trends in the overall heat transfer stem from the interactions between the rate of variation of the fluid viscosity and the temperature gradient on the surface of the cylinder. Therefore, a prudent choice of the operating conditions and the fluid behaviour can be used to regulate the rate of heating or cooling from a rotating cylinder. Finally, the present values of the average Nusselt number are correlated in order to facilitate the interpolation of the present results for the intermediate values of Gr, Pr, S and n and/or the estimation of heat transfer duty in a new application.