Mathematical Problems in Engineering

Volume 2015, Article ID 765969, 8 pages

http://dx.doi.org/10.1155/2015/765969

## A Novel Heat Sink Design and Prototyping for LED Desk Lamps

^{1}Department of Mechanical Engineering, Southern Taiwan University of Science and Technology, Tainan City 71005, Taiwan^{2}Department of Mechanical and Automation Engineering, I-Shou University, Kaohsiung City 84001, Taiwan

Received 28 September 2014; Accepted 16 January 2015

Academic Editor: Mo Li

Copyright © 2015 Li-Ming Chu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

Light-emitting diode (LED) is a modern lighting device. If the heat dissipating mechanism of LED desk lamp is not well designed, the induced high temperature will cause the reduction of illumination and life time of lamp. Therefore, the heat sink design becomes a key technology for LED lighting device. This study developed a methodology to design and analyze a heat sink for LED cooling. Four different types of heat sinks with fins in longitudinal or transverse directions and with or without vents on the base plate were compared. By using the CFD software FLUENT, heat flux and temperature around the heat sink were analyzed, and the surface temperature distribution was also investigated. The simulation outcomes were compared with experiments results to verify analysis accuracy. The comparisons show only slight differences, and the deviations were less than 4.0%. For cooling LED desk lamp, the design of using 12 vents on both sides of heat sink through natural convection to create the chimney effect was adopted; consequently, the temperature dropped 5°C in average. This design can also reduce the material of heat sink, LED lamp weight, and production cost.

#### 1. Introduction

Traditional incandescent lambs are energy consuming devices with high heat emitting rate. For a 100 W incandescent lamb, 12% consumed energy is converted into heat, 83% energy becomes infrared radiation, and only 5% turns to visible light. In contrast, for a light-emitting diode, so called LED, 15% to 30% consumed energy is converted into visible light, and the rest becomes heat. In recent years, due to the rising awareness of environmental issue, the high luminous efficiency LED, contributed by low power consumption and long life time, has great potential for lighting application.

A higher power LED produces relatively more heat, which makes heat dissipation become very important. There are many popular heat dissipating devices, such as heat pipe, heat sink, and fan. To most LED devices, heat sink is favored. The cooling fins design of heat sink will affect the LED luminous efficiency. This study developed a technology to design high efficiency heat sink for LED desk lamp.

The use of LED lighting is a trend of the future; there are many research works focusing on heat releasing problems of LED. Most input energy of high power LED turns to heat; if it fails to effectively discharge the waste heat generated by the current (Joule’s law), it will make the temperature at the junction of LED chip become too high and consequently decrease the luminous efficiency and life-time of LED [1, 2].

Shaukatullah et al. [3] studied the optimal design of pin fin at low flow rates; the results showed that, with 6 × 6 cylindrical aluminum fins on a 25 mm × 25 mm base plate, a better cooling effect can be achieved by using 15 mm high pins with 1.5 × 1.5 mm cross section at 1 m/s flow rate of air.

De Lieto Vollaro et al. [4] studied a finned plate in natural convection circumstance; they used a simplified relation of fins efficiency to present a process to optimize the fin spacing. The results showed that, with such simple model to calculate the heat transfer of fins, the temperature variation and end effects in the vertical direction can be neglected, and the finite fin conductivity reduced the optimal fin spacing. Chuang et al. [5] analyzed the cooling fins of high power LED, in order to apply LED to the liquid crystal display. The experiments were done in constant temperature environment, and the temperatures of cooling fins were measured. CFD simulation was then conducted with four concerned parameters, which were the thickness of the fin base, fin height, fin thickness, and the interval of fin. The simulation results were verified with the experiments data. Finally, with the Taguchi method, the optimal shape of the fin was decided.

NICHIA Corp. [6] pointed out that the maximum temperature of LED configuration normally happens at the PN junction, so the junction temperature is an important parameter for LED design, and it can be obtained by the introduction of the concept of “thermal resistance.” Theatrically, under constant power consumption and the same ambient temperature condition, the greater the thermal resistance, the larger the value of junction temperature, which implied poor cooling effect. In spite of using practical measurements or theoretical analysis to obtain the thermal resistance of the heat sink components, it is important for designing electronic products. Tian et al. [7] investigated the heat dissipating condition of high power LED with different kinds of heat sinks. A simplified model of LED was introduced with two resistances; one is the resistance between the die junction and the top, and the other is the resistance between the die junction and the printed circuit board (PCB). In addition to the PCB and lamp body models, the thermal model of LED lamp was built.

Harahap and Setio [8] investigated five different types of cooling fins through experiments by changing the fin spacing, length, and thickness. With nondimensional parameters formulated by similarity analysis, the results showed that the fin spacing and length were the main parameters to affect the cooling effect. Narasimhan and Majdalani [9] explored the performance of the plate-fin and cylindrical fin in natural convection through a CFD software. They successfully used a compact heat sink model to reduce the number of grids and computing time but still accurately presented the entrance temperature and velocity distribution.

This work developed an analysis technology for designing the heat sink of LED lamp, which is suitable for LED lamp manufacturers to design cooling fins for heat dissipation. In the early design stage, CAD was used to design the heat sink of LED lamp and then to using computer graphics software to construct the grid pattern inside the fins. Natural convection was adopted as the movement of surrounding air without considering the influence of radiation [10, 11]. Measured heat flux data from experiments were applied as boundary conditions in the simulation model, a commercial software FLUENT was used to analyze flow field and temperature field around the cooling fins, and temperatures from different positions of fin were acquired to confirm the relevance of design concept.

#### 2. Theoretical Analysis

##### 2.1. Governing Equation

The heat convection condition in this study was considered as a three-dimensional incompressible flow; the process was assumed to be in steady state. For momentum equations, the working fluid is air, and density changes with temperature. The solving equations can be expressed as follows.

Continuity equation is as follows:

The momentum equation in direction is as follows:

The momentum equation in direction is as follows:

The momentum equation in direction is as follows:

Energy conservation equation is as follows.

Object in 3-dimensional space is as follows:

Working fluid is as follows:wherein , , and represent , , and direction of velocity vector, is the fluid density, and are the fluid pressure and temperature, respectively, is the dynamic viscosity coefficient, is the gravitational acceleration, is the thermal expansion coefficient of the fluid, is the ambient temperature, is the specific heat of the object, is the thermal conductivity of object, is the power output of the heat source, and is the thermal diffusivity.

In natural convection, Rayleigh number is used to classify the laminar flow and turbulent flow. is expressed aswherein is the gravitational acceleration, is the length of the heat sink, is the thermal expansion coefficient of the fluid, is average temperature of the LED chip connectors, is the ambient temperature, is the coefficient of dynamic viscosity, is the thermal diffusivity, and is the ratio of buoyancy force to viscous force. means laminar flow, and is turbulent flow.

##### 2.2. Boundary Conditions

In this study, the output boundary of CFD analysis was assumed to be a pressure outlet. The heat sources are nine 1 W LEDs, and the radiant heat was ignored. Cooling fins and base plate were made of aluminum. The ambient temperature was 20°C; the air properties at 20°C are shown in Table 1.