This work is about studying the natural convection of two-dimensional steady state non-Newtonian power law fluid numerically. The inner cylinder was put eccentrically into the outer one. The cylinders are held at constant temperatures with the inner one heated isothermally at temperature Th and the outer one cooled isothermally at temperature Tc (Th>Tc). The simulations have been taken for the parameters 10 3 ≤Ra≤10 5 , 10≤Pr≤10 3 , 0.6≤n≤1.4, 0≤ɛ≤0.9 and an inclination angle ϕ from 0° up to 90°. The average Nusselt numbers for the previous parameters are obtained and discussed numerically. The results revealed that the average Nusselt number has the highest values when n=0.6, Ra=10 5 at ϕ=0 which is a signal for the large transfer herein and has the lowest values for n=1.4, Ra=10 3 at ϕ=90° which is a signal that the transfer is by conduction more than convection. Furthermore, the increasing of eccentricity causes an increase in the Nusselt number for all the cases. Finally, the best case where we can get the best heat transfer is at ϕ = 0, ɛ=0.9 among them all. The results have compared with some precedent works and showed good agreement.

This work examines the two-dimensional steady laminar natural convection of non-Newtonian fluid obeys the Ostwald-de Waele model in a gap between two concentric cylinders (the internal cylinder is grooved). The presence of grooves is of importance owing to their effectiveness in ameliorating the heat transfer of devices like micro-system, ICE (Internal Combustion Engine)….; Thus, we have conducted a numerical study for ranges of values Prandtl number 10≤Pr≤10 3 , Rayleigh number 10 3 ≤Ra≤10 5 , power law index 0.4≤n≤1 and number of grooves 4, 8, 12 and 16 in this order, with the help of ANSYS-CFX 16.2. The finite volume method was used to discretize the governing equations and they solved by the SIMPLE algorithm. It is to be said that the Nusselt number is proportional with Ra while it is disproportional with n. Increasing the number of grooves drastically affects the heat transfer characteristics in the gap, by minimizing the surface that loses the heat between one groove and another, and therefore, the heat transfer is too small especially at the case of 16 grooves.