In this paper, hydro-thermally performance of a circular concentric heat pipe is evaluated using the analytical least square method (LSM) and the accuracy of results is examined by fourth order Runge-kutta numerical method. In described problem, the pipe walls are permitted to carry different and opposite slip velocities of nanouids and they are either preserved at constant heat flux of outer wall with the inner wall insulated or vice versa. For this study, five distinct types of nanoparticles: Ag, Cu, Cuo, Al 2 O 3 and T iO 2 are considered in the water base fluid and the results of velocity profiles and Nusselt numbers in different slip conditions were presented and discussed. As a main result, by decreasing the distance between the pipes, more heat will transfer to nanofluids from the wall under the heat flux, so it makes larger Nusselt number.