In current paper, a finned micro-channel is designed for the cooling application in Light Emitting Diode (LED), numerically using Galerkin weighted residual Finite Element Method (GFEM). Selected materials for LED-chip is GaN, Die from Si, Die-attach is made by Au-20Sn, substrate is copper and heat sink material is considered to be Al. To make a convection heat transfer for cooling process, Al2O3-water nanofluid is used as the cooling fluid flow through the micro-channel and tried to maximize the heat transfer efficiency by optimized geometry. For this aim, there geometry variables from the microchannel were selected and minimum possible geometry cases (11 cases) were proposed by Central composite design (CCD) and variables were optimized by the Response Surface Method (RSM). As a main result, parameter B, i.e. fin length had the most effect on the Nusselt number and Al2O3 nanoparticles with φ = 0.05 stated greatest heat transfer value. Also, different designs of fins arrangements, caused up to 6.5% increase in the nanofluid temperature which enhanced the LED cooling process.

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