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This paper presents a numerical study concerning an improved heat sink for a light emitting diodes (LED) lamp operating under natural convection conditions. Basic geometry of the heat sink is of cylindrical nature, to be obtained from cutting an aluminum extruded bar comprising a cylindrical central core and a number of uniformly distributed radial fins. Minimum diameter of the central core is fixed and the parameters to be explored are the number of fins, their thickness, length (radial dimension) and height. Although not included in the numerical simulations, the thermal resistance due to the use of a thin thermal interface material (TIM) layer between the LED lamp back and the heat sink is taken into account in the analysis. The main objective of the heat sink is to cool the LED lamp so that the lamp maximum temperature at the contact region with the heat sink is maintained below the critical temperature given by the manufacturer. This is a crucial aspect in what concerns the expected lifetime of the LED lamp and should be achieved at the expenses of as low as possible aluminum mass. Taking these criteria in mind, a design procedure is proposed and followed in the search for the improved heat sink to cool a particular LED lamp. Results obtained with the commercial code ANSYS-CFX clearly show the relative importance of the different governing parameters on the heat sink performance and allow the choice of the better solution within the frame of dimensional constrains. Although the present results concern a particular LED lamp, the proposed methodology can be extended to other types of heat sinks for general light and/or electronic components.