Guide Vane for Thermal Enhancement of a LED Heat Sink

Abstract

A guide vane was installed on a heat sink to enhance the cooling effect of light-emitting diode (LED) lights. The validity of the numerical analysis was verified against the experimental results and the result of the previous studies. The effect of the guide vane on the heat dissipation performance of the heat sink was identified. The effect of the guide vane on the heat sink was qualitatively studied using the streamline and temperature contour. The cooling effect of the heat sink was enhanced by increased air supplement to the center-bottom part. A parametric study was conducted to determine the thermal resistance according to the guide vane angle, installation height, and vane length. Optimization was performed to minimize the thermal resistance using the Kriging model and micro-genetic algorithm (MGA). The cooling performance of the heat sink was enhanced by a maximum of 17.2% when the guide vane was installed.

1. Introduction

As the lifespan and luminous efficiency of light-emitting diode (LED) lights increase [1,2], research is being conducted to solve the overheating problem [3]. Since the temperature increase due to the heat generation of LED lights is directly related to the life of the LED, research to solve this problem is essential [4,5,6]. Figure 1 shows a typical heat sink installed for heat dissipation of LED lights. Increasing the size of the heat sink not only increases the cost but also increases the weight, requiring a systematic heat sink design. Although studies on various heat sink designs such as geometry modification have been carried out [7,8,9], these studies are structurally complex and increase cost burden due to the complicated manufacturing process. In consideration of these points, there is a limitation in improving the cooling effect by only modifying the shape of a heat sink.

Figure 1. Conventional LED heat sink.

Experimental studies have been performed to improve the cooling effect of a heat sink. Bai et al. [10] conducted an experimental study on the heat sink with heat pipe for automotive LED lights. Mo et al. [11] studied the cooling effect of LED by a thermoelectric cooler with a microchannel heat sink. Wang et al. [12] investigated the cooling effect of LED heat sinks with the oscillating heat pipes. Lu et al. [13] analyzed a efficiency of LED package consisting of heat pipe heat sinks. Alvin et al. [14] experimentally investigated the extruded aluminum fin heat sink for LED cooling. Khatamifar et al. [15] studied the geometry effect on additive manufactured aluminum LED heat sinks.

Studies have been conducted numerically to enhance the cooling effect of a heat sink. Lin et al. [11] conducted a Taguchi analysis on the cooling of the LED heat sink by a thermoelectric cooler. Mey et al. [16] conducted research on the chimney effect on the cooling of a transistor mounted on a cooling fin under natural convection. Silva et al. [17] presented optimal geometry of L and C-shaped channels for maximum heat transfer. Shimoyama et al. [18] estimated the thermal characteristics of an upward-facing heated surface with a cylindrical pipe. Park et al. [19] have suggested installing a hollow cylinder for downlights heat sinks. Souayeh et al. [20] investigated the magnetic dipole flow over a stretching sheet in the presence of a non-uniform heat source/sink. Li et al. [21] proposed an enhanced design of a heatsink with a chimney operating under natural convections. However, most of these studies are difficult to directly apply to radial heat sinks due to the increase in the size and mass of a heat sink or the complicity of the manufacturing process.

In this study, a guide vane was installed on a heat sink to improve the thermal performance of the cooling system. Numerical analysis was conducted to identify the thermal and flow characteristics of the system. The numerical results were validated against the experimental results and the results of the previous studies. A parametric study was conducted to quantitatively investigate the effect of the guide vane on the cooling efficiency. Optimization was performed to minimize thermal resistance using the kriging model and micro-genetic algorithm (MGA).

2. Numerical Modeling

2.1. Mathematical Model

The schematic of the heat sink and guide vane is shown in Figure 2. The heat sink consists of two different length fins regularly arranged on the base. The computational domain is composed of a heat sink, guide vane, and surrounding air as shown in Figure 3a. The heat flux $\dot{q}$ is uniformly supplied from the bottom of the heat sink. The periodic condition was applied since the fins on the radial heat sink repeat rotationally, as shown in Figure 3b. The computational burden was reduced by analyzing only the single-period domain (1/20 model). The boundary conditions of the numerical analysis are shown in Table 1.

Figure 2. Schematic of a heatsink with a guide vane. (a) Isometric view 1; (b) isometric view 2.

Figure 3. Computational domain. (a) Side view; (b) top view.

Table 1. Boundary conditions for the numerical analysis [24].

Domain	Wall	Momentum	Energy
Fluid	Periodic wall	$u_i(\overrightarrow{r_i})=u_i(\overrightarrow{r_i}+\overrightarrow{L})$$,\nabla p({\chi }_i)=\eta \frac{\overrightarrow{L}}{\left|\overrightarrow{L}\right|}+\nabla p^{*}({\chi }_i)$	$T(\overrightarrow{r_i})=T(\overrightarrow{r_i}+\overrightarrow{L})$
	Outer face	Pressure inlet/outlet condition	$T_{inlet}=T_{outlet, backflow }=T_{\infty }$
Solid	Base of heat sink	$u_i=0$	$-k_s{\frac{\partial T_s}{\partial n}|}_{\mathrm{heat} \sin \mathrm{k} \mathrm{base}}= \dot{q}$
	Symmetric face	$u_i=0$	${\frac{\partial T_s}{\partial n}|}_{\mathrm{sectional} \mathrm{wall}}= 0$

The heat sink operates under natural convection conditions, and the assumptions of the numerical analysis are as follows:

(1)

The air is incompressible ideal gas.

(2)

The air properties are constant except for the density.

(3)

The flow is steady state.

The results of various numerical models were compared with the experimental results to find an appropriate turbulence model (Table 2). As compared in the table, it was the renormalization group (RNG) k-ε model that had the least error [22,23]. Accordingly, the numerical analysis was conducted using the (RNG) k-ε model.

Table 2. Numerical model selection (T_s = 293 K, $\dot{q}$ = 800 W/m²).

Model	Rth (K/W)	Error (%)
Experiment	2.45	-
SST k-ω	1.99	11.7
Standard k-ω	2.26	7.9
Standard k-ε	2.29	14.9
Realizable k-ε	2.57	12.1
RNG k-ε	2.60	1.5

The governing equations for the continuity, energy, and momentum are as follows [19]:

$$\frac{\partial }{\partial x_j}(\rho u_j\varphi )=\frac{\partial }{\partial x_j}({\mathsf{\Gamma }}_{\varphi }\frac{\partial \varphi }{\partial x_j})+S_{\varphi }$$

(1)

In the Equation (1), ${\mathsf{\Gamma }}_{\varphi }$ is a coefficient of diffusion, $S_{\varphi }$ is a source term, and $\varphi$ is an arbitrary scalar, and they are summarized in Table 3. The definition of G_k, S_k, ${({\tau }_{ij})}_{eff}$, ${\mu }_t$, ${\mu }_{eff}$ are as follows [19]:

$$G_k={\mu }_t{S}^2$$

(2)

$$S_k=-{\rho }_{op}g (\mathrm{for} z \mathrm{direction})$$

(3)

$${({\tau }_{ij})}_{eff}={\mu }_{eff}(\frac{\partial u_j}{\partial x_i}+\frac{\partial u_i}{\partial x_j})-\frac{2}{3}{\mu }_{eff}\frac{\partial u_k}{\partial x_k}{\delta }_{ij}$$

(4)

$${\mu }_t=\rho C_{\mu }\frac{k^2}{\epsilon }$$

(5)

$${\mu }_{eff}={\mu }_{mol}{\left(1+\sqrt{\frac{{\mu }_t}{{\mu }_{mol}}}\right)}^2$$

(6)

Table 3. Conservation laws components [24].

	Mass	Momentum	Turbulent Kinetic Energy	Turbulent Dissipation Rate	Energy
$\mathrm{Scalar} \left(\varphi \right)$	1	$u_i$	$k$	$\epsilon$	cpT
$\mathrm{Diffusion} \mathrm{coefficient} \left({\mathsf{\Gamma }}_{\varphi }\right)$	0	$\mu +{\mu }_t$	${\alpha }_k{\mu }_{eff}$	${\alpha }_{\epsilon }{\mu }_{eff}$	$\alpha c_p{\mu }_{eff}$
$\mathrm{Source} \left(S_{\varphi }\right)$	0	$-\frac{\partial p}{\partial x_i}+ S_k$	$G_k-\rho \epsilon$	$C_{1\epsilon }{G}_k(\epsilon /k)-C_{2\epsilon }({\epsilon }^2/k)$	$\frac{\partial }{\partial x_j}(u_i{({\tau }_{ij})}_{eff})$

2.2. Numerical Procedure

ANSYS Fluent 20202 R2 was used as a tool to carry out the numerical analysis. The SIMPLE algorithm was utilized to link the pressure and velocity, and the relative errors of all variables were set to less than 10⁻⁶ for convergence of the numerical results. Figure 3 shows the geometry of the cooling system. The dimensions of the parameters for the heat sink are $H_f=20 \mathrm{mm}$, $L_m=20 \mathrm{mm}$, $L_l=40 \mathrm{mm}$, $r_i=5 \mathrm{mm}$, $r_o=75 \mathrm{mm}$, $t_f=2 \mathrm{mm}$. In order to estimate the effect of the computational domain size on the flow and temperature, it was evaluated by changing the height H_d, and the radius $r_d$ of the domain (Figure 3). When the height H_d of the domain is five times the height of the heat sink H_f and the radius r_d is twice the radius r_o of the heat sink, it was confirmed that the numerical results changed by 0.4%, and this value was set as the domain size. To check the grid dependency, the numerical analysis was performed while modifying the grid number from 200,000 to 2,000,000 (Figure 4) [25]. As a result, when the number of grids was 1,823,490, the change of thermal characteristics was lower than 0.4%, and this was set as the reference [26].

Figure 4. Thermal resistance in different number of meshes [27].

3. Experiments and Validation

Figure 5 shows the experimental setup consisting of a heat sink, guide vane, aluminum plates, heater, heat resistance glass, and insulator. The heat sink consists of aluminum 6061 ($k=170$ W/m°C), and the emissivity is $\epsilon =0.2$. The dimensions of the parameters for the heat sink are $H_f=20 \mathrm{mm}$, $L_m=20 \mathrm{mm}$,$L_l=40 \mathrm{mm}$, $r_i=5 \mathrm{mm}$, $r_o=75 \mathrm{mm}$, $t_f=2 \mathrm{mm}$. The guide vane is manufactured of acrylic with thermal conductivity of $k=0.2$ W/m°C. The range of the parameters for the guide vane are $0°\le {\theta }_v\le 90°$, $0 \mathrm{mm}\le H_v\le 20 \mathrm{mm}$, $0 \mathrm{mm}\le L_v\le 20 \mathrm{mm}$. A radial plate heater was installed to supply a heat flux to the heat sink uniformly, and the power was controlled using a transformer. An aluminum plate of 2 mm thickness was inserted between the heat sink and the heater so that the heat flux is uniformly transferred.

Figure 5. Experimental setup.

A heat resistance glass with a thermal conductivity of $k=1.005$ W/m°C was used to measure the heat flux transferred to the bottom of the heater, and the temperature above and below the glass was measured and calculated as follows.

$${\dot{Q}}_g=k_{g}A\frac{T_{g, top}- T_{g, bottom}}{t_g}$$

(7)

The heat flux delivered to the heat sink base was calculated by the difference between the input heat flux ${\dot{Q}}_{in}$ and the heat resistance glass ${\dot{Q}}_g$ as follows.

$${\dot{q}}_h=\frac{{\dot{Q}}_{in}- {\dot{Q}}_g}{A}$$

(8)

Heat loss was minimized by installing an insulator, and thermal grease was applied to all interfaces to minimize thermal resistance between solids. To measure the temperature of the heat sink, thermocouples were installed evenly on the heat sink base, long fin, and middle fin each. When the experiment was in a steady state, the temperature was recorded, and the temperature variation was less than 0.1 °C. Each experiment was conducted five times to secure a liability of 95% [28]. Thermal resistance was used as an index to determine the cooling effect, and the equation is as follows.

$$R_{th}=\frac{T_{h, ave}- T_s}{q_{h, b}A}$$

(9)

The thermal resistance according to the heat flux was shown in Figure 6. It was confirmed that the numerical results obtained using the RNG k-ε model were in good agreement with the experimental results within 2% of the maximum error (Table 2). In addition, the model was validated against the previous experimental results as shown in Table 4. The results show that the maximum error of the thermal resistance was 5.4%.

Figure 6. Comparison of the thermal resistance with and without a guide vane.

Table 4. Comparison with the previous studies.

Previous Study				Errors Using Present Model
Author	Tair [°C]	$\dot{\mathit{q}}$ (W/m2)	Rth (°C/W)	Error [%]
Park et al. [19]	17.5	615	1.75	5.4
		875	1.61	3.9
Jang et al. [24]	30	437	1.89	4.8
		919	1.52	5.3

4. Results and Discussion

In this section, the effect of the guide vane on the cooling effect of the heat sink was quantitatively studied. The heat resistance was used to determine the performance of the heat sink, and the influence of the guide vane on the cooling performance was identified through flow analysis. Optimization was performed to minimize thermal resistance using the Kriging model and micro-genetic algorithm (MGA).

4.1. Effect of Guide Vane

In order to determine the temperature distribution of the heat sink, the temperature contour was shown in Figure 7. As shown in the figure, the temperature is relatively high at the center-bottom of the heat sink. The air does not flow deep into the center of the heat sink causing heat concentration. Therefore, it is important to cool the center part of the heat sink, and the guide vane can facilitate the centripetal flow.

Figure 7. Temperature contours of a heat sink (T_s = 20 °C, $\dot{q}$ = 800 W/m²).

The streamline around the heat sink was shown in Figure 8. The streamline helps to identify the cooling effect due to the installation of the guide vane. Figure 8a is a streamline without a guide vane, and Figure 8b is a streamline with a guide vane installed.

Figure 8. Streamlines around heat sinks. (a) Without guide vane; (b) with guide vane.

Without the guide vane, the flow does not move deep inside the heat sink center and rises as if passing around the surroundings. However, when a guide vane is installed, a flow is formed in which the flow moved into the center of the heat sink. When comparing the thermal resistance according to the heat flux, the cooling efficiency improved by 9.2% on average when the guide vane was installed (see Figure 6). Therefore, by installing a guide vane, the central portion of the heat sink with the highest temperature is cooled, and the cooling efficiency is significantly improved.

A parametric study was performed to investigate the effects of the guide vane angle (${\theta }_v$), installation height ($H_v$), and length ($L_v$) on the thermal resistance ($R_{th}$). In order to grasp only the effect of a single factor, the other factors were set constant as a reference (middle value of the range) and were made dimensionless using the following equation.

$$X_i=\frac{x_i-x_{i,\min }}{x_{i,\max }-x_{i,\min }}, x_1= {\theta }_v, x_2= H_v,x_3= L_v$$

(10)

where

$$\begin{array}{l} 0°\le {\theta }_v\le 90°\\ 0 \mathrm{mm}\le H_v\le 20 \mathrm{mm}\\ 0 \mathrm{mm}\le L_v\le 20 \mathrm{mm}\end{array}$$

(11)

The ranges of the parameters were determined considering the geometrical limitation. The thermal resistance was nondimensionalized as $R_{th}/R_{th, ref}$, and the reference value ($R_{th, ref}$) is the thermal resistance at the reference parameters ${\theta }_v=45°$, $H_v=10 \mathrm{mm}$, $L_v=10 \mathrm{mm}$.

To determine whether each factor has a positive or negative effect on thermal resistance, dimensionless thermal resistance according to $X_i$ was shown in Figure 9.

Figure 9. Thermal resistance of a heat sink with a guide vane with variation of X_i.

Thermal resistance tended to decrease as X₁ (vane angle) increased, and then increased when X₁ was greater than 0.82. When the X₁ was small, the guide vane did not play a role in changing the flow direction, and the flow moved to the heat sink center when X₁ was around 0.82. However, a streamlined flow was not created when the angle was greater than 0.82, and the thermal resistance tended to increase. This means that there is a specific angle that supplies flow into the heat sink and creates an optimal streamline.

The thermal resistance decreased sharply as X₂ (installation height) increased, and then increased gradually when X₂ was greater than 0.19. The air flowing into the heat sink is small when X₂ is less than 0.19, and sufficient flow was supplied at a specific height to the center of the heat sink. However, the thermal resistance tended to increase gradually when X₂ was increased above a certain value, since the amount of air supplied to the center-bottom of the heat sink decreased. The streamline was similar to that without the guide vane when X₂ was close to 1.

The thermal resistance decreased as X₃ (vane length) increased, and then increased when X₃ was greater than 0.67. The air flowing into the center of the heat sink increased as the vane length increased, decreasing the thermal resistance, and when it exceeded a certain value, the flow was obstructed, increasing the thermal resistance. In other words, there is an optimal point where the vane moves the flow into the center, not disturbing the flow.

4.2. Optimization

The dimensionless thermal resistance ($R_{th}/R_{th, ref}$) was set as an objective function, and the design variable was set as X_i for optimization, and it is expressed as an equation as follows.

$$\begin{array}{l}\mathrm{Minimize} f(X_1, X_2, X_3)=\frac{R_{th}(X_1, X_2, X_3)}{R_{th, ref}(X_1, X_2, X_3)}\\ \mathrm{Subject} \mathrm{to} 0\le X_i\le 1 (i=1, 2, 3) \end{array}$$

(12)

In total, 25 experimental points were adopted using the orthogonal array (OA) method L₂₅ (5³). The object function f (X₁, X₂, X₃) was derived using the Kriging model, and the optimization was conducted using the micro-genetic algorithm (MGA) [29]. The specific parameters of MGA are listed in Table 5. The optimization results were summarized in Table 6 and Table 7. As discussed in Section 4.2 parametric study, there were certain points for X_i that minimized the thermal resistance for all of the parameters, and they were not on the boundaries of the range. When the optimized guide vane was set on the heat sink, the thermal resistance ($R_{th}$) was improved by a maximum of 17.2% compared to that without guide vane.

Table 5. Details of micro-genetic algorithm (MGA).

Parameters	Values
Size of population	50
Initial seed value of the generation	100
Maximum number of generations	200
Crossover probability	1.0
Violated constraint limit	0.003
Selection probability	0.15

Table 6. Optimal parameters of a guide vane.

Guide Vane Parameters	Range	Reference	Optimum
Angle, θv	0° ≤ θv ≤ 90°	45°	79.2°
Height, Hv	0 mm ≤ Hv ≤ 20 mm	10 mm	2.12 mm
Length, Lv	0 mm ≤ Lv ≤ 20 mm	10 mm	13.84 mm

Table 7. Optimization results (T_s = 20 °C, $\dot{q}$ = 800 W/m²).

Installation of Guide Vane	Thermal Resistance, Rth [°C/W] (Improvement, %)
Without guide vane	2.451
Reference guide vane	2.225 (−9.2%)
Optimum guide vane	2.028 (−17.2%)

Figure 10 shows the temperature contour of the heat sink with the guide vane installed. As can be seen from the figure, the average heat sink temperature with the guide vane is considerably reduced when compared to that without the guide vane shown in Figure 7. For the validity of the numerical analysis in the optimized shape, an experiment was performed, and the numerical and the experimental results were compared and shown in Figure 11. The results of the numerical analysis were in good agreement with the experimental results showing a maximum error of 1.5%. In addition, the cooling efficiency of the heat sink with the guide vane installed was improved by 16.3% on average compared to the heat sink without the guide vane. Therefore, the guide vane helps to cool the center of the heat sink, and the cooling efficiency can be significantly improved.

Figure 10. Temperature contours of a heat sink with a guide vane (T_s = 20 °C, $\dot{q}$ = 800 W/m²).

Figure 11. Validation of the optimal results.

5. Conclusions

A guide vane was installed to enhance the cooling effect of a heat sink, and experiments and numerical analysis were conducted. The numerical analysis was conducted to identify the flow and thermal characteristics of the system, and it was verified by comparison with the experimental results. The effect of the guide vane on the cooling performance of the heat sink was investigated. The streamline and temperature contour were analyzed to identify the influence of the guide vane. It was found that the cooling performance was significantly improved by supplying the air to the center bottom of the heat sink. Optimization was conducted to minimize thermal resistance using the Kriging model and micro-genetic algorithm (MGA). As a result of quantitatively grasping the cooling effect of the heat sink, the performance was enhanced by up to 17.2% when the guide vane was installed. It is expected that this study may help solve the overheating problems in heat sink for LED lights operating under natural convection conditions.