In this paper, we tried to find a solution for the quick transfer of atomic dump (nuclear wastes) from pools of cool water to dry stores in order to reduce the environmental and financial expenses of burying atomic waste considerably. So the velocity of heat transfer should be increased from the atomic waste materials to the area outside the container. Therefore, in Bottom of the pool, we can embed space with conical fins (vertically) applied within it, and inside the space, such fins are in a porous medium, and natural convection flow of Newtonian nanofluid passes upon it. In this research, we study the velocity of heat transfer by using such a special space. In this research, free convection boundary layer flow on a vertical cone in a porous medium for Newtonian nanofluid with Analytical solutions has been studied. Similarity solution for a cone subjected to Consideration boundary conditions is a nonlinear ordinary differential equation, which has been solved through the Homotopy Analysis Method (HAM). The obtained analytical solution, in comparison with the numerical ones, represents remarkable accuracy. The results also indicate that HAM can provide us with a convenient way to control and adjust the convergence region. By the way, we also calculate the Nusselt number, which is an important parameter in heat transfer, by obtaining an analytical solution using HAM.