In the present study, natural-convective heat transfer along with the effects of radiation of aluminum/water nano-fluid between two blades of a heat sink, which is under the impact of a uniform magnetic-field, is studied numerically. The space between two blades of the heat sink is considered as a two-dimensional square enclosure. In the square cavity, there are four pipes with constant temperature T-h with a circular cross section. The RSM method is used to optimize the geometric parameters of the pipes. The results show that the heat transfer rate from the pipes and the irreversibility generation augment and the Bejan number reduces by augmenting the Rayleigh number. The heat transfer intensified 7% and 16% by doubling of the aspect ratio of the pipes at the Rayleigh number of 10(3) and 10(6), respectively. As the distance between constant-temperature pipes intensified, Nusselt number augments. As the horizontal enclosure rotates 90 degrees, i.e., it becomes a vertical enclosure, the heat transfer decreases by 22% and total irreversibility decreases by 21%. The optimum physical conditions of the pipes are is in the diameter of 0.15 and 0.25 of distance from each other to have maximum heat transfer and the minimum irreversibility generation. (C) 2019 Society of Powder Technology Japan Published by Elsevier B.V. All rights reserved.