- Email: [email protected]
Heat spreading and heat transfer coefficient with fin heat sink
Accepted Manuscript Research Paper Heat spreading and heat transfer coefficient with fin heat sink. K.S. Ong, C.F. Tan, K.C. Lai, K.H. Tan PII: DOI: Reference:
S1359-4311(16)31983-4 http://dx.doi.org/10.1016/j.applthermaleng.2016.09.161 ATE 9186
To appear in:
Applied Thermal Engineering
Received Date: Revised Date: Accepted Date:
2 August 2016 26 September 2016 27 September 2016
Please cite this article as: K.S. Ong, C.F. Tan, K.C. Lai, K.H. Tan, Heat spreading and heat transfer coefficient with fin heat sink., Applied Thermal Engineering (2016), doi: http://dx.doi.org/10.1016/j.applthermaleng.2016.09.161
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Paper FHS (ATE format) - Revised Update: 23.9.16
Heat spreading and heat transfer coefficient with fin heat sink. K. S. Ong1, C. F. Tan1, K. C. Lai1, K. H. Tan1. 1
Universiti Tunku Abdul Rahman,Malaysia. Email: [email protected]
Highlights.
Heat transfer coefficients were obtained under natural and force convection.
Two different aspect ratios showed the effects of thermal heat spreading.
A CFD simulation was performed.
Heat transfer coefficients depended upon thermal heat spreading effect.
Abstract.
Compact high powered semiconductor chips require greater heat dissipation and more effective thermal cooling systems have to be devised such as incorporating vapor chambers and thermoelectric. As a first step, the performance of two conventional fin heat sinks with flat metal base and an array of cooling fins on top are determined under force and natural convection air cooling and with various heating power input. Fin temperatures and heat transfer coefficients were determined for different size heating elements producing different area aspect ratios. This paper reports on the effect of thermal heat spreading effect and determination of the thermal heat spreading resistance. Heat spreading and contact resistances are small compared to the thermal resistance of the FHS itself.
Keywords: Fin heat sink, thermal heat spreading, natural convection, force convection, CFD simulation.
1.
Introduction.
A heat sink is a thermal heat transfer device that is employed to dissipate heat from a high temperature heat source to a lower temperature surrounding. A problem normally encountered in thermal management of electronic packages is thermal heat spreading resistance which occurs as heat flows by conduction from a high temperature heat source to a low temperature heat sink with different cross-sectional areas. A typical flat plate heat sink is shown in Fig. 1. Heat from a smaller heat source at a high temperature (Ts) is dissipated to
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the lower temperature surroundings (Ta) via the heat sink. Heat transfer occurs upwards as well as outwards from the base of the heat sink via two-dimensional heat conduction. This thermal heat spreading phenomena causes a non-uniform temperature distribution along the base of the heat sink resulting in inefficient cooling. The temperature at the bottom of the heat sink (Tf) would display a maximum value (Tfmax) at the center and a mean value (T fm) along the base, where Tfmax > Tfm. In the case of perfect heat spreading, Tfmax = Tfm with onedimensional heat flow. The effects of heat spreading increases with greater heat emissions and smaller heat source/heat sink surface areas.
Fig. 1. Heat spreading effect in a flat plate heat sink.
As high powered semiconductor chips are made more compact and requiring greater heat dissipation, more effective thermal cooling systems have to be devised. A typical fin heat sink (FHS) consists of a flat metal base with an array of cooling fins on top. Aluminum or copper are the most common metals used. Conventional air-cooled and water-cooled FHSs are shown in Figs. 2(a) and 2(b), respectively. Thermal heat spreading resistance occurs at the bottom of the FHS if the heat source is smaller than the base of the heat sink. Heat spreading effect increases with larger differences in sizes between source and sink. Various methods could be employed to minimize this heat spreading resistance. These include increasing the thickness of the base of the FHS or height of the fins. Another method is to use more
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expensive highly conductive materials like aluminum, copper and diamond which would increase FHS cost.
Fig. 2. Thermal cooling with air-cooled fin heat sink and water-cooled jacket heat sink.
Lee et al. [1] investigated analytically the constriction and spreading resistances of various flat rectangular plates with uniform heat flux on one surface and cooling over the other with various heat transfer coefficients. They obtained closed form expressions and compared their simulations with other known existing theories and found that for relatively thick plates, the constriction resistance is insensitive to changes in both plate thickness and Biot number and that it became solely dependent upon relative contact size between heat sink and heat source. Simons [2] obtained simulated thermal heat spreading resistance results using analytical solutions to the exact partial differential heat transfer equations for thermal heat spreading provided by the Thermal Analyzer for Multilayer Structures (TAMS) program and compared them with a simplified closed form solution provided by Lee et al. [1]. The heat sinks considered were based on aluminum and copper flat plate heat spreaders and under forced convection air cooling. He found very little difference between the two sets of results. Ellison [3] derived an exact three-dimensional solution to determine the maximum heat spreading resistance for rectangular heat sources centered on larger size plane heat sinks. Their work provided expressions for computing the thermal resistance for any combination of source and plate aspect ratios. Muzychka et al. [4] presented a general solution based on the separation
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of variables method for the thermal spreading resistances of eccentric heat sources on a rectangular flux channel. General expressions of isoflux rectangular source on the surface of finite isotropic and compound rectangular flux channels were presented as well as the solution for the temperature at the surface of a rectangular flux channel.
Chingulpitak and Wongwises [5] reviewed the effect of flow on the thermal performance of conventional flat and pin heat sinks. Numerous papers have been writen on the thermal performance of various types of FHSs under different air flow condtions and orientations [6, 7, 8, 9].
Other devices employed to improve or enhance the cooling performance of FHSs are HPs and VCs [10, 11, 12] and thermoelectric (TE) which are reported in [13, 14]. Sauciuc et al. [15] showed theoretically that there is a threshold envelope where a solid metal heat sink base as shown in Fig. 1(a) may have lower thermal spreading resistance than a VC. They adopted a simplified model where the spreading resistance is assumed equal to the boiling heat transfer coefficient in the evaporator section of the VC. Their
model showed that thrmal heat
spreading resistance increased with diminishing heat source area and that there will be a maximum base thickness depending upon heat source and heat sink sizes. They concluded that consideration should be given to base thickness before deciding whether to use a VC or not and that the heat pipe system can only be efficiently used when they conduct heat to a remote heat exchanger away from the actual heat transfer surfaces. Choi and Jeong [16] investigated the heat pipe incorporated with a circular FHS for high end PCs. TE devices can be applied for power production (TEG), thermal heating (TEH) or cooling (TEC). They are small, compact, light weight, passive in operation, noiseless and no vibration during operation, environmentally friendly to use and reliable. However as pointed out by the researchers, they are expensive to use and have low cooling performance. Astrain and Martinez [17] described some heat exchanger used with TE devices. Ionic wind cooling may be expensive to use [18, 19, 20] but may have future potential because they are inherently silent and consume very little power. Avenas et al. [22] performed thermal analysis of thermal heat spreaders used in power electronics cooling.
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2.
Objective.
The objective of this research is to investigate the thermal cooling of a heating element with a FHS under NC and FC air cooling modes for 1- and 2-D heat flows.
3.
Theoretical model of FHS.
3.1
Thermal resistance model of FHS for 1-D heat flow.
An isometric view of a conventional rectangular profile straight fin and wall heat sink combination is shown in Fig. 3(a). The temperature distribution along the fin is shown in Fig. 3(b). Heat transfer is assumed to be one-dimensional. For a straight fin of uniform cross section and a corrected fin length with an adiabatic tip, the fin efficiency is given by [2]
fin
tanh (m fin L fin,c ) (m fin L fin,c )
(1)
where
m fin
2 (W fin t fin ) ha W fin t fin k fin
(2)
and the corrected fin length
L fin,c L fin
t fin 2
(3)
In an array consisting of a Nfin number of fins, the total heat transfer surface area of the heat sink is At N fin A fin A fin,b
(4)
where the heat transfer surface area of each fin is
A fin (2L fin t fin ) W fin
(5)
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and the total heat transfer surface area of the non-finned or bare portion of the heat sink array is
A fin,b (S fin t fin ) W fin ( N fin 1) (6)
The overall surface fin efficiency of a multi fin array and the base surface to which they are attached to is given by
o 1
N fin A fin (1 fin ) At
(7)
The total heat transfer rate from the heat sink is given by .
q h o ha At (Tb Ta )
(8)
The thermal resistance of the entire surface of the FHS is calculated from
R fin
1 o ha At
(9)
For a plane wall with a base of thickness xbase, wall thickness resistance is given by
Rbase
xbase (10) k fin W fin [ S fin ( N fin 1) t fin ]
The total thermal resistance of the FHS under 1-D heat flow from Fig. 3(c) is equal to
R f 1D R fin Rbase
(11)
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Fig. 3. Thermal resistance model of rectangular FHS for 1-D heat flow.
3.2
Thermal resistance model of FHS for 2-D heat flow.
Thermal heat spreading occurs when the heat source is smaller than the heat sink. The aspect ratio is defined by the ratio of heat source/fin heat sink contact surface areas, viz.,
Aheat source Aheat sin k
(12)
The exact analytical solution for 2-D heat flow in the FHS is quite complicated. It is beyond the scope of the present investigation to present this. A simple model is presented here for estimating the thermal heat spreading resistance of the FHS. Fig. 4(a) shows a thermal resistance model for a FHS placed over a heat source together with an aluminum block. The aluminum block is to ensure uniform heat transfer from the heat source the FHS. The heat source and the aluminum block are assumed to be perfectly insulated around the bottom and sides. Heat is assumed lost to the ambient via both the finned and un-finned portions of the FHS by either NC or FC air cooling. The thermal resistance network is shown in Fig. 4(b). As
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a result of thermal heat spreading, the temperature distribution along the base of the FHS would not be uniform. There would be a maximum temperature (Tfmax) at the center and a mean surface temperature (Tfm) here. As a result of thermal contact resistance at the interface between the aluminum block and the FHS, the mean temperature (Talm) of the upper surface of the aluminum block would be higher than T fm. The effect of heat spreading on the temperature profile is shown by the dashed line. In the absence of heat spreading, ( 1.0), the temperature profile shown in Fig. 4(b) would move towards the left.
Fig. 4. Thermal resistance model of fin heat sink under 2-D heat flow.
The thermal resistance of the aluminum block may be calculated from Ral
(Ts Talm )
(13)
PEH
The contact thermal resistance at the interface between the aluminum block and the base of the FHS may be determined from
Rcr1
(Talm T f max ) PEH
(14)
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The thermal heat spreading resistance is estimated from
Rsrf
(T f max T fm )
(15)
PEH
and the 1-D thermal resistance of the FHS from
R f 1D
(T fm Ta )
(16)
PEH
The total 2-D thermal heat resistance of the FHS is equal to R f 2 D Rcr1 Rsrf R f 1D
(17)
It may be determined from
R f 2 D
(Talm Ta ) PEH
(18)
The contact resistance could be estimated from data supplied by the manufacturer of the thermal interface material (TIM)
Rcr1
4.
xtim ktim Atim
(19)
Computational fluid dynamics (CFD) simulation.
4.1 CFD simulation software.
Computational fluid dynamics (CFD) is a software employed to simulate the flow of fluid and its effect on a targeted object in the flow field. CFD software makes use of applied mathematics, physics and computational software to solve the Navier-Stokes equations used to model the fluid flow together with the associated boundary conditions. It involves the relationship between fluid velocity and pressure together with fluid properties like density and viscosity. The Star-CCM+® CFD simulation software used in this study was developed by cd-adapco. The software provides a user-friendly interface device to model a cooling
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system. The general sequence of operations is shown in Figure 5. The following steps are followed: 1. Star-CCM+® requires a geometry to represent the actual object or scenario. The geometry of the object is first set up according to the actual dimensions and sizes. 2. Parts from the geometrical model are then assigned to regions, boundaries and interfaces of the computational model to construct a simulation topology. These parts represent the discretized portions of the geometry to be analysed while physical models are applied. 3. A mesh for the geometry is then generated. Meshing is a process to discretize the geometry into smaller subdomains commonly in the shape of hexahedra in 3D and quadrilaterals in 2D. Physics solvers or governing equations provide numerical solution and solve for each of these subdomains. 4. Next, the physics on every surface and volume of the object/s are defined. The physics consist of fluid flow, heat transfer, dynamic fluid body interaction, material properties and other related phenomena. Total heat generated from the heating element/s and material properties such as thermal conductivity of the heat sink are prescribed. 5. Subsequent reports, monitors and plots for analysis are then prepared. Reports are computed numerical data extracted from simulation. Monitors use reports to record the reported data while the simulation is in progress. Plots use the monitored data to show the trends of solution. 6. The simulation process is started after all the preliminary preparations are made. The solution is then initialized and the solver is launched. 7. The simulated results can be visualized through 3D CAD models or plots.
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Fig. 5. General sequence of operations for CFD simulation.
4.2 Typical simulation of FHS with CFD.
A results of a typical simulation was performed to obtain the temperature distribution in a FHS heated by an electrical heater. The model set up is shown in Fig. 6. Input parameters that could affect the performance of the FHS are power input to the heating element (PEH), thermal contact resistance at the interface between the FHS and the heating element (R cr), thermal conductivity (k FHS), dimensions and fin arrangement and whether cooling is performed under NC or FC air flow. A very important parameter is the aspect ratio () that causes thermal heat spreading effect. The FHS was assumed to measure 137 mm wide × 125 mm long with a base thickness of 10 mm. There are fourteen fins each 5 mm thick and 30 mm long. Ambient temperature was assumed constant at 20C. A typical simulated temperature distribution output in the FHS was obtained with PEH = 100 W, ha = 10 W/m2K, = 0.09, kFHS = 220 W/m K and Rcr = 0.5 K/W and shown in Fig. 7. Thermal heat spreading with maximum temperature at the center of the FHS could be observed.
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Fig. 6. Cross-sectional view of model set up for simulation.
Fig. 7. Typical simulated temperature distribution in FHS.
5.
Experimental Investigation.
5.1 FHS under 1-D NC and FC heat flow.
Experiments (Runs A1 to A6) were first conducted to determine the heat transfer coefficients under 1-D NC and FC air cooling on a small conventional aluminum FHS, identified here as FHS#1. Further experiments (Runs B1 to B3) were then conducted to investigate the performance of a larger aluminum FHS, identified as FHS#2 under 2-D and NC heat flow with thermal heat spreading.
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The experimental lay-out for Runs A1 to A6 is shown in Fig. 8. A small FHS#1 measuring 45 x 45 mm with a 10 mm thick base and with 5 fins was heated with a heating element measuring 40 x 40 mm x 4 mm thick. As the aspect ratio ( = 0.79) is nearly equal to 1.0, 1-D heat transfer with no heat spreading effect ( ≈ 1.0) is assumed in this case. Type T copperconstantan thermocouples (accuracy + 0.5oC) were employed to measure temperatures. Four holes were drilled from the top of the FHS and thermocouples inserted through these holes to measure the surface temperature of the aluminum block. Locations of these holes are shown in Fig. 9. The mean surface temperature of the aluminum block (Talmfm) was calculated based on the arithmetic average of the four thermocouples (T f1 - Tf4). Ambient (Ta) and two insulation surface temperatures (Tins) were measured with three other thermocouples. An electric element was employed to provide heat input (PHE) at the bottom of the heat sink. Experiments were conducted under FC and NC air cooling conditions with various power inputs. The power input was adjusted before the start of each experimental run and switched on. Initial power input was at 10 W. The cooling fan was then switched on or kept off, depending upon whether FC or NC conditions were required. Temperatures were then logged using the data logger. Power input was increased after 30 minutes. Experiments were performed at 10 W, 15 W and 20 W power input for NC condition and at 10 W, 20 W and 30 W for FC condition. The experimental runs were conducted three times at each setting to determine the repeatability. The duration between each power input setting was 30 minutes for FC and 120 minutes for NC. Results for Runs A1 to A6 are tabulated in Table 1. Ambient temperature was not kept constant and varied from about 19.7 – 21.1oC. In general, results were repeatable to within 2 oC. From the insulation temperature results, heat loss from the sides accounted for < 1% of the power input.
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Fig. 8. Experimental set-up to determine heat loss coefficient for FHS#1 with = 0.79.
Fig. 9. Location of thermocouples in FHS#1.
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Table 1. Experimental results for FHS#1 under NC and FC ( = 0.79). Heat sink NC Run PEH Ta dimensions /FC # (W) (C) (mm x mm)
45 x 45
45 x 45
FC
10.0 A1 20.0 30.0 9.9 A2 20.0 30.0 9.9 A3 20.0 30.0
21.0 21.1 20.9 20.7 20.7 21.0 20.6 20.9 21.0
NC
10.0 A4 15.0 20.1 9.9 A5 15.2 20.0 9.9 A6 15.1 20.1
20.2 20.3 20.3 20.3 20.4 20.2 20.7 19.7 20.1
Talm (C) 31.5±0.1 41.2±0.1 50.5±0.1 30.4±0.1 40.2±0.1 50.1±0.1 30.5±0.1 40.2±0.1 49.7±0.1 Average 63.8±0.0 82.1±0.0 98.9±0.1 63.1±0.1 82.7±0.1 98.4±0.1 63.6±0.1 81.6±0.1 98.5±0.0 Average
Rf1D = Rf2D - Rcr1 ha Rf2D (K/W) (W/m2K) (K/W) (Rcr1= 0.05 K/W) Eqns. (1-11) Eqn. (18) Eqn. (17) 1.05 1.00 0.98 0.98 0.97 0.97 1.00 0.95 0.95 0.98 4.36 4.11 3.92 4.32 4.09 3.91 4.33 4.11 3.90 4.12
1.00 0.95 0.93 0.93 0.92 0.92 0.95 0.90 0.90 0.93 4.31 4.06 3.87 4.27 4.04 3.86 4.28 4.06 3.85 4.07
69.0 73.0 74.1 74.1 74.9 74.9 73.0 75.8 75.8 73.8 15.2 16.1 16.9 15.3 16.2 17.0 15.3 16.1 17.0 16.1
Typical transient temperatures showing the mean temperature of the base of the FHS (T alm) are plotted in Fig 10 for FC and in Fig. 11 for NC. The time taken to reach steady state for FC was about 30 minutes and for NC, about 120 minutes. Temperatures increase with power input as expected.
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Fig. 10. Transient temperatures for FHS#1 (FC, = 0.79 - Runs A1 – A3).
Fig. 11. Transient temperatures for FHS#1 (NC, = 0.79 - Runs A4 – A6). The temperature distribution at the base of the FHS#1 measured by thermocouples (T f1 – Tf4) along the centerline under FC and NC are shown in Figs. 12 and 13, respectively. It could be seen that the temperature distributions are quite uniform, varying by about only 0.1C for all
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three different power inputs. Hence it can be concluded that 1-D heat transfer is occurring and there is no heat spreading.
Fig 12. Temperature distribution along centerline of FHS#1 (FC, = 0.79 - Runs A1 – A3).
Fig 13. Temperature distribution along centerline of FHS#1 (NC, = 0.79 - Runs A4 – A6).
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The thermal heat spreading resistance (Rsrf) is assumed equal to 0 for 1-D heat flow. With xtim = 100 m, ktim = 1.22 W/m K and contact surface area Atim = 0.04 m x 0.04 m, Rcr1 is calculated to be equal to 0.05 K/W from Eqn. (19). Experimental values of ∑R f2D are calculated from Eqn. (18) and tabulated in Table 1. Also shown are corresponding values of fin resistance (Rf1D) from Eqn. (17) and heat loss coefficients (ha). The heat loss coefficient values (ha) are calculated from the 1-D heat transfer analysis [2]. A trail-and-error procedure was followed in order to make the calculated Rf1D value to be equal to the experimental value. Heat loss coefficient is plotted against Talm in Fig. 14. The results show that it increases slightly with temperature as a result of higher power input. High power input increases the operating temperature of the FHS resulting in higher convection heat loss. Also, the convection heat transfer coefficient values obtained under FC are higher than those under NC as expected. The following correlations are obtained: FC: ha 0.137 Talm 68.2
(20)
NC: ha 0.048 Talm 12.2
(21)
with average values of 74 W/m2 and 16 W/m2 K, respectively.
The total thermal heat spreading resistance of the FHS#1 varied from 0.90 to 1.00 K/W under NC compared to about 3.85 to 4.31 K/W under FC. Contact resistance is very small, about 0.05 K/W compared to the total thermal resistance of the FHS.
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Fig. 14. Heat loss coefficient ha for FHS#1 (Runs A1-A6). 5.2 FHS under 2-D NC heat flow.
For this series, only NC air flow was considered. The experimental lay-out for Runs B1 to B3 is shown in Fig. 15. The larger FHS#2 measured 135 mm × 123 mm with 10 mm thick base and with fourteen fins each 30 mm long. The heating element measured 30 mm x 30 mm x 5 mm. The small aspect ratio = 0.053 is expected to produce some heat spreading effect here. A 22 mm thick aluminum block with similar dimensions as the heating element was located between the FHS#2 and the heating element. Twenty one holes were drilled from the top of FHS#2 through to its base to allow thermocouples (Tf1-f21) to be inserted. The locations of these thermocouples are shown in Figure 16. The mean temperature (Tfm) at the bottom surface of FHS#2 is estimated from the arithmetic average of the twenty one thermocouples (Tf1-f21). The mean surface temperature (T alm) at the top of the aluminum block is estimated from the arithmetic average of the five thermocouples (T f7, Tf10, Tf11, Tf12 and Tf15). The maximum temperature at the bottom of the FHS (T fmax) is assumed equal to the mean surface temperature of Al block (Talm). Other thermocouples measured the insulation surface temperature (Tins1, Tins2) and the ambient temperature (T a). An ac power supply provided electrical power (PEH) to the heating element. Power input was controlled using a variable ac voltage regulator. Three separate runs were conducted over a period of 2 hours each to
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determine experimental repeatability. The results are tabulated (Run B1 – B3) in Table 2. Again, results were generally repeatable to within 2oC.
Fig. 15. Experimental set-up to determine thermal resistance for FHS#2 with = 0.053.
Fig. 16. Location of thermocouples in FHS#2.
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Table 2. Experimental results for FHS#2 under NC ( = 0.053). Heat sink Run PEH Ta dimensions # (W) (C) (mm x mm)
135 x 123
10.1 B1 29.3 50.4 10.1 B2 29.9 50.1 10.0 B3 29.8 50.1
20.8 20.7 20.9 20.0 20.4 21.3 19.8 20.4 20.4
Tfmax Talm (C) 37.8±0.3 62.5±0.6 84.3±1.2 36.6±0.2 62.0±0.7 85.3±1.2 35.1±0.3 61.2±0.6 84.1±1.2
Tfm (C) 36.9±1.0 60.1±2.6 80.1±4.3 35.7±1.0 59.5±2.6 80.9±4.6 34.3±1.0 58.7±2.6 79.8±4.6 Average
Rcr1 + Rsrf Rf1D ha Rf2D (K/W) (K/W) (K/W) (W/m2K) Eqns. Eqn. (16) Eqn. (18) Eqn. (21) (14&15) 0.09 1.59 1.68 14.0 0.08 1.34 1.42 15.1 0.08 1.17 1.25 16.0 0.09 1.55 1.64 13.9 0.08 1.31 1.39 15.1 0.09 1.19 1.28 16.1 0.08 1.45 1.53 13.8 0.08 1.29 1.37 15.0 0.09 1.19 1.28 16.0 0.08 1.34 1.43 14.9
The transient temperatures (Tfm, T fmax) for FHS#2 under NC condition is shown in Fig. 17. Steady state could be achieved after about 120 minutes of operation. The center-line temperature distribution is shown in Fig. 18. The results show that high power input (PEH) results in higher temperatures as expected. The temperature (Talm) along the base of the FHS was non-uniform, varying up to 4.6oC at high power input due to thermal heat spreading.The total thermal resistance of the FHS#2 (Rf2D) varied from 1.25 to 1.68 K/W under NC and 2D heat flow. Spreading (Rsrf) and contact resistances (Rcr1) are small and amounted to about 0.10 K/W.
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Fig. 17. Transient temperatures for FHS#2 (NC, = 0.053 - Runs B1 – B3).
Fig. 18. Temperature distribution along centerline of FHS#2 (NC, = 0.053 - Runs B1 – B3).
5.3
Comparison between experimental and CFD simulated temperature results for
FHS#2.
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A CFD simulation was performed to obtain simulated results for the mean temperature of the base of the FHS (Tfm) and the maximum temperature (Tfmax) and to compare them against the experimental results obtained from Runs B1 to B3 for FHS#2 under NC. Since the experimental heat loss was found to be less than 1%, it was assumed negligible in the CFD simulation. The CFD simulated and experimental temperatures are tabulated and compared in Table 3. Three sets of results are shown in Table 3. The first set shows the experimental temperatures (Tfmax and T fm) and heat loss coefficient (ha) from Runs B1 to B3. The second set shows the simulated values obtained with heat loss coefficient from Eqn. (21) with T fm assumed equal to Talm and input into the CFD software package. The third set shows simulated temperatures obtained by using modified heat loss coefficients which are about a third lower than experimental values. The reason is because the experimental heat loss coefficients obtained from the FHS could be different under 1-D or 2-D heat flow because of non-uniform temperature distribution within the FHS due to heat spreading. In general, temperatures increase with input heat power. A comparison of the temperatures between sets #1 and 2 shows poor agreement. Simulated temperatures are about half that obtained experimentally. A comparison between sets #1 and #3 obtained with lower heat loss coefficient values show that by reducing the values of ha as input into the CFD program very good agreement is obtained between experimental and simulated results. Hence this brings us to the conclusion that the heat loss coefficient for FHS#2 under NC air cooling with 2dimensional heat spreading effect could be much smaller than the 1-dimensional heat loss coefficients obtained without heat spreading effect. Further investigations would need to be conducted to verify this.
Table 3. Comparison of experimental and CFD simulated results for FHS#2 with modified heat transfer coefficients. Experimental (Table 2) Run PEH # (W)
10.1 B1 29.3 50.4 B2 10.1
ha (W/ m2 K) Eqn. (21) 14.0 15.1 16.0 13.9
Tfmax Talm (C)
Tfm (C)
37.8±0.3 62.5±0.6 84.3±1.2 36.6±0.2
36.9±1.0 60.1±2.6 80.1±4.3 35.7±1.0
Simulated with ha from Simulated with Eqn. (21). modified ha ha (W/ ha T Tfmax,CFD Tfm,CFD T m2 K) fmax,CFD fm,CFD (W/ (oC) (oC) (C) (C) 2 Eqn. m K) (21) 14.0 27.6 26.7 5.3 37.2 36.4 15.1 39.2 36.7 6.3 61.2 58.6 16.0 51.2 46.8 7.3 81.6 77.2 13.9 26.8 26.0 5.4 36.1 35.2
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29.9 50.1 10.0 B3 29.8 50.1 6.
15.1 16.1 13.8 15.0 16.0
62.0±0.7 85.3±1.2 35.1±0.3 61.2±0.6 84.1±1.2
59.5±2.6 80.9±4.6 34.3±1.0 58.7±2.6 79.8±4.6
15.1 16.1 13.8 15.0 16.0
39.3 51.3 26.6 39.3 50.5
36.7 46.9 25.8 36.7 46.2
6.4 7.1 5.8 6.5 7.1
61.1 83.2 34.8 60.4 82.3
58.5 78.9 33.9 57.8 78.0
Conclusions.
The performances of two FHSs were determined. FC cooling resulted in lower temperature compared to NC. Heat loss coefficient was found to be higher under FC compared to NC air cooling condition. Thermal heat spreading occurred when the heat source was smaller than the FHS. Thermal heat spreading and contact resistances are small compared to the thermal resistance of the FHS itself. Further investigations are recommended to determine the heat loss coefficients under 2-D heat flow with thermal heat spreading effect.
Referances.
1. S. Lee, S. Song, V. Au V, K. P. Moran, Constriction/spreading resistance model for electeronic padkaging, Proc. ASME/JSME Engineering Conference (1995). 2. R. E. Simons, Simple formulas for estimating thermal spreading resistance, Electronics Cooling Magazine (2004). 3. G. N. Ellison, Maximum thermal spreading resistance for rectangular sources and plates with nonunity aspect ratios, IEEE Trans, Components and Packaging Technologies (2003) 439-454. 4. Y. S. Muzychka, J. R. Culham, M. M. Yovanovich, Thermal spreading resistance of eccentric heat sources on rectangular flux channels, Trans. ASME 125 (2003) 178-185. 5. S. Chingulpitak, S. Wongwises, A review of the effect of flow direcions and behaviors on the thermal prformance of conventional heat sinks, Int. Journal of Heat and Mass Transfer, 81 (2015) 10-18. 6. Y. Joo, S. J. Kim, Comparison of thermal performance between plate-fin and pin-fin heat sinks in natural convection, Int. Journal of Heat and Mass Transfer, 83 (2015) 345-356. 7. H. Y. Li, S. M. Choa, Measurement of performance of plate-fin heat sinks with cross flow cooling, Int. Journal of Heat and Mass Transfer, 52 (2009) 2949-2955. 8. T. Y. Kim, S. J. Kim, Fluid flow and heat transfer charecteristics of cross-cut heat sinks, Int. Journal of Heat and Mass Transfer, 52 (2009) 5358-5370.
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9. K. S. Young, S. L. Li, I. Y. Chen, K. H. Chien, R. Huc, C. C. Wang, An experimental investigation of air cooling thermal module using various enhancements at low Reynolds number region, Int. Journal of Heat and Mass Transfer, 53 (2010) 5675-5681. 10. D. A. Reay, P. A. Kew, Heat Pipes, Elsevier (2007), ISBN: 978-0-7506-6754-8. 11. G. P. Peterson, An Introduection to Heat Pipes - Modeling, Testing and Applications, Wiley (1994). 12. B. Zohuri, Heat Pipe Design and Technology - A Practical Approach, CRC Press (2011). 13. D.M. Rowe, Thermoelectrics Handbook – Macro to Nano, Taylor & Francis, (2006). 14. H. S. Lee, Thermal Design Heat Sinks, Thermoelectrics, Heat Pipes, Compact Heat Exchangers, and Solar Cells, Wiley (2010), ISBN: 978-0-470-49662-6. 15. I. Sauciuc, G. Chrysler, R. Mahajan, R. Prasher, Spreading in the heat sink base: Phase change systems or solid m. etals? Thermal Challenges in Next Generation Electronic Systems. Joshi & Garimella (eds). ISBN 90-77017-03-8:2002. 16. J. Choi, M. Jeong, Compact, lightweight and highly efficient circular heat sink design for high-end PCs, Applied Thermal Engineering, 92 (2016) 162-171. 17. D. Astrain, Á. Martínez, Heat exchangers for thermoelectric devices, in: J. Mitrovic (Ed.), Heat Exchangers - Basics Design Applications, InTech, 2012, pp. 289-308 18. Owsenek, B. L., Seyed-Yagoobi, J., Page, R. H., Experimental investigation of corona wind heat ransfer enhancenent with a heated horizontal flat plate. ASME Journal of Heat transfer, 117, 309-315, 1995. 19. Go, D. B., Garimella, S. V., Fisher, T. S., Mongia, R. K. Ionic winds for locally enhanced cooling. Journal of Applied Physics, 102,2007. 20. Go, D. B., Maturana, R. A., Fisher, T. S., Garimella, S. V. Enhancement of external forced convection by ionic wind. Int. Journal of Heat and Mass Transfer, 51, 6047-6053, 2008. 21. Avenas, Y., Ivanova, M., Popova, N., Schaeffer, C. Thermal analysis of thermal spreaders used in power elecronics cooling, 0-7803-7420-7/02, IEEE, 216-220, 2002. 22. Incropera, D. P. DeWitt, 2007. Introduction to Heat Transfer, 5Ed. Wiley. Experimental Heat Transfer 22 (2009) 26-38. Doi:10.1080/08916150802530187.
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Highlights.
Heat transfer coefficients were obtained under natural and force convection.
Two different aspect ratios showed the effects of thermal heat spreading.
A CFD simulation was performed.
Heat transfer coefficients depended upon thermal heat spreading effect.
S1359-4311(16)31983-4 http://dx.doi.org/10.1016/j.applthermaleng.2016.09.161 ATE 9186
To appear in:
Applied Thermal Engineering
Received Date: Revised Date: Accepted Date:
2 August 2016 26 September 2016 27 September 2016
Please cite this article as: K.S. Ong, C.F. Tan, K.C. Lai, K.H. Tan, Heat spreading and heat transfer coefficient with fin heat sink., Applied Thermal Engineering (2016), doi: http://dx.doi.org/10.1016/j.applthermaleng.2016.09.161
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Paper FHS (ATE format) - Revised Update: 23.9.16
Heat spreading and heat transfer coefficient with fin heat sink. K. S. Ong1, C. F. Tan1, K. C. Lai1, K. H. Tan1. 1
Universiti Tunku Abdul Rahman,Malaysia. Email: [email protected]
Highlights.
Heat transfer coefficients were obtained under natural and force convection.
Two different aspect ratios showed the effects of thermal heat spreading.
A CFD simulation was performed.
Heat transfer coefficients depended upon thermal heat spreading effect.
Abstract.
Compact high powered semiconductor chips require greater heat dissipation and more effective thermal cooling systems have to be devised such as incorporating vapor chambers and thermoelectric. As a first step, the performance of two conventional fin heat sinks with flat metal base and an array of cooling fins on top are determined under force and natural convection air cooling and with various heating power input. Fin temperatures and heat transfer coefficients were determined for different size heating elements producing different area aspect ratios. This paper reports on the effect of thermal heat spreading effect and determination of the thermal heat spreading resistance. Heat spreading and contact resistances are small compared to the thermal resistance of the FHS itself.
Keywords: Fin heat sink, thermal heat spreading, natural convection, force convection, CFD simulation.
1.
Introduction.
A heat sink is a thermal heat transfer device that is employed to dissipate heat from a high temperature heat source to a lower temperature surrounding. A problem normally encountered in thermal management of electronic packages is thermal heat spreading resistance which occurs as heat flows by conduction from a high temperature heat source to a low temperature heat sink with different cross-sectional areas. A typical flat plate heat sink is shown in Fig. 1. Heat from a smaller heat source at a high temperature (Ts) is dissipated to
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the lower temperature surroundings (Ta) via the heat sink. Heat transfer occurs upwards as well as outwards from the base of the heat sink via two-dimensional heat conduction. This thermal heat spreading phenomena causes a non-uniform temperature distribution along the base of the heat sink resulting in inefficient cooling. The temperature at the bottom of the heat sink (Tf) would display a maximum value (Tfmax) at the center and a mean value (T fm) along the base, where Tfmax > Tfm. In the case of perfect heat spreading, Tfmax = Tfm with onedimensional heat flow. The effects of heat spreading increases with greater heat emissions and smaller heat source/heat sink surface areas.
Fig. 1. Heat spreading effect in a flat plate heat sink.
As high powered semiconductor chips are made more compact and requiring greater heat dissipation, more effective thermal cooling systems have to be devised. A typical fin heat sink (FHS) consists of a flat metal base with an array of cooling fins on top. Aluminum or copper are the most common metals used. Conventional air-cooled and water-cooled FHSs are shown in Figs. 2(a) and 2(b), respectively. Thermal heat spreading resistance occurs at the bottom of the FHS if the heat source is smaller than the base of the heat sink. Heat spreading effect increases with larger differences in sizes between source and sink. Various methods could be employed to minimize this heat spreading resistance. These include increasing the thickness of the base of the FHS or height of the fins. Another method is to use more
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expensive highly conductive materials like aluminum, copper and diamond which would increase FHS cost.
Fig. 2. Thermal cooling with air-cooled fin heat sink and water-cooled jacket heat sink.
Lee et al. [1] investigated analytically the constriction and spreading resistances of various flat rectangular plates with uniform heat flux on one surface and cooling over the other with various heat transfer coefficients. They obtained closed form expressions and compared their simulations with other known existing theories and found that for relatively thick plates, the constriction resistance is insensitive to changes in both plate thickness and Biot number and that it became solely dependent upon relative contact size between heat sink and heat source. Simons [2] obtained simulated thermal heat spreading resistance results using analytical solutions to the exact partial differential heat transfer equations for thermal heat spreading provided by the Thermal Analyzer for Multilayer Structures (TAMS) program and compared them with a simplified closed form solution provided by Lee et al. [1]. The heat sinks considered were based on aluminum and copper flat plate heat spreaders and under forced convection air cooling. He found very little difference between the two sets of results. Ellison [3] derived an exact three-dimensional solution to determine the maximum heat spreading resistance for rectangular heat sources centered on larger size plane heat sinks. Their work provided expressions for computing the thermal resistance for any combination of source and plate aspect ratios. Muzychka et al. [4] presented a general solution based on the separation
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of variables method for the thermal spreading resistances of eccentric heat sources on a rectangular flux channel. General expressions of isoflux rectangular source on the surface of finite isotropic and compound rectangular flux channels were presented as well as the solution for the temperature at the surface of a rectangular flux channel.
Chingulpitak and Wongwises [5] reviewed the effect of flow on the thermal performance of conventional flat and pin heat sinks. Numerous papers have been writen on the thermal performance of various types of FHSs under different air flow condtions and orientations [6, 7, 8, 9].
Other devices employed to improve or enhance the cooling performance of FHSs are HPs and VCs [10, 11, 12] and thermoelectric (TE) which are reported in [13, 14]. Sauciuc et al. [15] showed theoretically that there is a threshold envelope where a solid metal heat sink base as shown in Fig. 1(a) may have lower thermal spreading resistance than a VC. They adopted a simplified model where the spreading resistance is assumed equal to the boiling heat transfer coefficient in the evaporator section of the VC. Their
model showed that thrmal heat
spreading resistance increased with diminishing heat source area and that there will be a maximum base thickness depending upon heat source and heat sink sizes. They concluded that consideration should be given to base thickness before deciding whether to use a VC or not and that the heat pipe system can only be efficiently used when they conduct heat to a remote heat exchanger away from the actual heat transfer surfaces. Choi and Jeong [16] investigated the heat pipe incorporated with a circular FHS for high end PCs. TE devices can be applied for power production (TEG), thermal heating (TEH) or cooling (TEC). They are small, compact, light weight, passive in operation, noiseless and no vibration during operation, environmentally friendly to use and reliable. However as pointed out by the researchers, they are expensive to use and have low cooling performance. Astrain and Martinez [17] described some heat exchanger used with TE devices. Ionic wind cooling may be expensive to use [18, 19, 20] but may have future potential because they are inherently silent and consume very little power. Avenas et al. [22] performed thermal analysis of thermal heat spreaders used in power electronics cooling.
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2.
Objective.
The objective of this research is to investigate the thermal cooling of a heating element with a FHS under NC and FC air cooling modes for 1- and 2-D heat flows.
3.
Theoretical model of FHS.
3.1
Thermal resistance model of FHS for 1-D heat flow.
An isometric view of a conventional rectangular profile straight fin and wall heat sink combination is shown in Fig. 3(a). The temperature distribution along the fin is shown in Fig. 3(b). Heat transfer is assumed to be one-dimensional. For a straight fin of uniform cross section and a corrected fin length with an adiabatic tip, the fin efficiency is given by [2]
fin
tanh (m fin L fin,c ) (m fin L fin,c )
(1)
where
m fin
2 (W fin t fin ) ha W fin t fin k fin
(2)
and the corrected fin length
L fin,c L fin
t fin 2
(3)
In an array consisting of a Nfin number of fins, the total heat transfer surface area of the heat sink is At N fin A fin A fin,b
(4)
where the heat transfer surface area of each fin is
A fin (2L fin t fin ) W fin
(5)
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and the total heat transfer surface area of the non-finned or bare portion of the heat sink array is
A fin,b (S fin t fin ) W fin ( N fin 1) (6)
The overall surface fin efficiency of a multi fin array and the base surface to which they are attached to is given by
o 1
N fin A fin (1 fin ) At
(7)
The total heat transfer rate from the heat sink is given by .
q h o ha At (Tb Ta )
(8)
The thermal resistance of the entire surface of the FHS is calculated from
R fin
1 o ha At
(9)
For a plane wall with a base of thickness xbase, wall thickness resistance is given by
Rbase
xbase (10) k fin W fin [ S fin ( N fin 1) t fin ]
The total thermal resistance of the FHS under 1-D heat flow from Fig. 3(c) is equal to
R f 1D R fin Rbase
(11)
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Fig. 3. Thermal resistance model of rectangular FHS for 1-D heat flow.
3.2
Thermal resistance model of FHS for 2-D heat flow.
Thermal heat spreading occurs when the heat source is smaller than the heat sink. The aspect ratio is defined by the ratio of heat source/fin heat sink contact surface areas, viz.,
Aheat source Aheat sin k
(12)
The exact analytical solution for 2-D heat flow in the FHS is quite complicated. It is beyond the scope of the present investigation to present this. A simple model is presented here for estimating the thermal heat spreading resistance of the FHS. Fig. 4(a) shows a thermal resistance model for a FHS placed over a heat source together with an aluminum block. The aluminum block is to ensure uniform heat transfer from the heat source the FHS. The heat source and the aluminum block are assumed to be perfectly insulated around the bottom and sides. Heat is assumed lost to the ambient via both the finned and un-finned portions of the FHS by either NC or FC air cooling. The thermal resistance network is shown in Fig. 4(b). As
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a result of thermal heat spreading, the temperature distribution along the base of the FHS would not be uniform. There would be a maximum temperature (Tfmax) at the center and a mean surface temperature (Tfm) here. As a result of thermal contact resistance at the interface between the aluminum block and the FHS, the mean temperature (Talm) of the upper surface of the aluminum block would be higher than T fm. The effect of heat spreading on the temperature profile is shown by the dashed line. In the absence of heat spreading, ( 1.0), the temperature profile shown in Fig. 4(b) would move towards the left.
Fig. 4. Thermal resistance model of fin heat sink under 2-D heat flow.
The thermal resistance of the aluminum block may be calculated from Ral
(Ts Talm )
(13)
PEH
The contact thermal resistance at the interface between the aluminum block and the base of the FHS may be determined from
Rcr1
(Talm T f max ) PEH
(14)
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The thermal heat spreading resistance is estimated from
Rsrf
(T f max T fm )
(15)
PEH
and the 1-D thermal resistance of the FHS from
R f 1D
(T fm Ta )
(16)
PEH
The total 2-D thermal heat resistance of the FHS is equal to R f 2 D Rcr1 Rsrf R f 1D
(17)
It may be determined from
R f 2 D
(Talm Ta ) PEH
(18)
The contact resistance could be estimated from data supplied by the manufacturer of the thermal interface material (TIM)
Rcr1
4.
xtim ktim Atim
(19)
Computational fluid dynamics (CFD) simulation.
4.1 CFD simulation software.
Computational fluid dynamics (CFD) is a software employed to simulate the flow of fluid and its effect on a targeted object in the flow field. CFD software makes use of applied mathematics, physics and computational software to solve the Navier-Stokes equations used to model the fluid flow together with the associated boundary conditions. It involves the relationship between fluid velocity and pressure together with fluid properties like density and viscosity. The Star-CCM+® CFD simulation software used in this study was developed by cd-adapco. The software provides a user-friendly interface device to model a cooling
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system. The general sequence of operations is shown in Figure 5. The following steps are followed: 1. Star-CCM+® requires a geometry to represent the actual object or scenario. The geometry of the object is first set up according to the actual dimensions and sizes. 2. Parts from the geometrical model are then assigned to regions, boundaries and interfaces of the computational model to construct a simulation topology. These parts represent the discretized portions of the geometry to be analysed while physical models are applied. 3. A mesh for the geometry is then generated. Meshing is a process to discretize the geometry into smaller subdomains commonly in the shape of hexahedra in 3D and quadrilaterals in 2D. Physics solvers or governing equations provide numerical solution and solve for each of these subdomains. 4. Next, the physics on every surface and volume of the object/s are defined. The physics consist of fluid flow, heat transfer, dynamic fluid body interaction, material properties and other related phenomena. Total heat generated from the heating element/s and material properties such as thermal conductivity of the heat sink are prescribed. 5. Subsequent reports, monitors and plots for analysis are then prepared. Reports are computed numerical data extracted from simulation. Monitors use reports to record the reported data while the simulation is in progress. Plots use the monitored data to show the trends of solution. 6. The simulation process is started after all the preliminary preparations are made. The solution is then initialized and the solver is launched. 7. The simulated results can be visualized through 3D CAD models or plots.
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Fig. 5. General sequence of operations for CFD simulation.
4.2 Typical simulation of FHS with CFD.
A results of a typical simulation was performed to obtain the temperature distribution in a FHS heated by an electrical heater. The model set up is shown in Fig. 6. Input parameters that could affect the performance of the FHS are power input to the heating element (PEH), thermal contact resistance at the interface between the FHS and the heating element (R cr), thermal conductivity (k FHS), dimensions and fin arrangement and whether cooling is performed under NC or FC air flow. A very important parameter is the aspect ratio () that causes thermal heat spreading effect. The FHS was assumed to measure 137 mm wide × 125 mm long with a base thickness of 10 mm. There are fourteen fins each 5 mm thick and 30 mm long. Ambient temperature was assumed constant at 20C. A typical simulated temperature distribution output in the FHS was obtained with PEH = 100 W, ha = 10 W/m2K, = 0.09, kFHS = 220 W/m K and Rcr = 0.5 K/W and shown in Fig. 7. Thermal heat spreading with maximum temperature at the center of the FHS could be observed.
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Fig. 6. Cross-sectional view of model set up for simulation.
Fig. 7. Typical simulated temperature distribution in FHS.
5.
Experimental Investigation.
5.1 FHS under 1-D NC and FC heat flow.
Experiments (Runs A1 to A6) were first conducted to determine the heat transfer coefficients under 1-D NC and FC air cooling on a small conventional aluminum FHS, identified here as FHS#1. Further experiments (Runs B1 to B3) were then conducted to investigate the performance of a larger aluminum FHS, identified as FHS#2 under 2-D and NC heat flow with thermal heat spreading.
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The experimental lay-out for Runs A1 to A6 is shown in Fig. 8. A small FHS#1 measuring 45 x 45 mm with a 10 mm thick base and with 5 fins was heated with a heating element measuring 40 x 40 mm x 4 mm thick. As the aspect ratio ( = 0.79) is nearly equal to 1.0, 1-D heat transfer with no heat spreading effect ( ≈ 1.0) is assumed in this case. Type T copperconstantan thermocouples (accuracy + 0.5oC) were employed to measure temperatures. Four holes were drilled from the top of the FHS and thermocouples inserted through these holes to measure the surface temperature of the aluminum block. Locations of these holes are shown in Fig. 9. The mean surface temperature of the aluminum block (Talmfm) was calculated based on the arithmetic average of the four thermocouples (T f1 - Tf4). Ambient (Ta) and two insulation surface temperatures (Tins) were measured with three other thermocouples. An electric element was employed to provide heat input (PHE) at the bottom of the heat sink. Experiments were conducted under FC and NC air cooling conditions with various power inputs. The power input was adjusted before the start of each experimental run and switched on. Initial power input was at 10 W. The cooling fan was then switched on or kept off, depending upon whether FC or NC conditions were required. Temperatures were then logged using the data logger. Power input was increased after 30 minutes. Experiments were performed at 10 W, 15 W and 20 W power input for NC condition and at 10 W, 20 W and 30 W for FC condition. The experimental runs were conducted three times at each setting to determine the repeatability. The duration between each power input setting was 30 minutes for FC and 120 minutes for NC. Results for Runs A1 to A6 are tabulated in Table 1. Ambient temperature was not kept constant and varied from about 19.7 – 21.1oC. In general, results were repeatable to within 2 oC. From the insulation temperature results, heat loss from the sides accounted for < 1% of the power input.
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Fig. 8. Experimental set-up to determine heat loss coefficient for FHS#1 with = 0.79.
Fig. 9. Location of thermocouples in FHS#1.
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Table 1. Experimental results for FHS#1 under NC and FC ( = 0.79). Heat sink NC Run PEH Ta dimensions /FC # (W) (C) (mm x mm)
45 x 45
45 x 45
FC
10.0 A1 20.0 30.0 9.9 A2 20.0 30.0 9.9 A3 20.0 30.0
21.0 21.1 20.9 20.7 20.7 21.0 20.6 20.9 21.0
NC
10.0 A4 15.0 20.1 9.9 A5 15.2 20.0 9.9 A6 15.1 20.1
20.2 20.3 20.3 20.3 20.4 20.2 20.7 19.7 20.1
Talm (C) 31.5±0.1 41.2±0.1 50.5±0.1 30.4±0.1 40.2±0.1 50.1±0.1 30.5±0.1 40.2±0.1 49.7±0.1 Average 63.8±0.0 82.1±0.0 98.9±0.1 63.1±0.1 82.7±0.1 98.4±0.1 63.6±0.1 81.6±0.1 98.5±0.0 Average
Rf1D = Rf2D - Rcr1 ha Rf2D (K/W) (W/m2K) (K/W) (Rcr1= 0.05 K/W) Eqns. (1-11) Eqn. (18) Eqn. (17) 1.05 1.00 0.98 0.98 0.97 0.97 1.00 0.95 0.95 0.98 4.36 4.11 3.92 4.32 4.09 3.91 4.33 4.11 3.90 4.12
1.00 0.95 0.93 0.93 0.92 0.92 0.95 0.90 0.90 0.93 4.31 4.06 3.87 4.27 4.04 3.86 4.28 4.06 3.85 4.07
69.0 73.0 74.1 74.1 74.9 74.9 73.0 75.8 75.8 73.8 15.2 16.1 16.9 15.3 16.2 17.0 15.3 16.1 17.0 16.1
Typical transient temperatures showing the mean temperature of the base of the FHS (T alm) are plotted in Fig 10 for FC and in Fig. 11 for NC. The time taken to reach steady state for FC was about 30 minutes and for NC, about 120 minutes. Temperatures increase with power input as expected.
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Fig. 10. Transient temperatures for FHS#1 (FC, = 0.79 - Runs A1 – A3).
Fig. 11. Transient temperatures for FHS#1 (NC, = 0.79 - Runs A4 – A6). The temperature distribution at the base of the FHS#1 measured by thermocouples (T f1 – Tf4) along the centerline under FC and NC are shown in Figs. 12 and 13, respectively. It could be seen that the temperature distributions are quite uniform, varying by about only 0.1C for all
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three different power inputs. Hence it can be concluded that 1-D heat transfer is occurring and there is no heat spreading.
Fig 12. Temperature distribution along centerline of FHS#1 (FC, = 0.79 - Runs A1 – A3).
Fig 13. Temperature distribution along centerline of FHS#1 (NC, = 0.79 - Runs A4 – A6).
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The thermal heat spreading resistance (Rsrf) is assumed equal to 0 for 1-D heat flow. With xtim = 100 m, ktim = 1.22 W/m K and contact surface area Atim = 0.04 m x 0.04 m, Rcr1 is calculated to be equal to 0.05 K/W from Eqn. (19). Experimental values of ∑R f2D are calculated from Eqn. (18) and tabulated in Table 1. Also shown are corresponding values of fin resistance (Rf1D) from Eqn. (17) and heat loss coefficients (ha). The heat loss coefficient values (ha) are calculated from the 1-D heat transfer analysis [2]. A trail-and-error procedure was followed in order to make the calculated Rf1D value to be equal to the experimental value. Heat loss coefficient is plotted against Talm in Fig. 14. The results show that it increases slightly with temperature as a result of higher power input. High power input increases the operating temperature of the FHS resulting in higher convection heat loss. Also, the convection heat transfer coefficient values obtained under FC are higher than those under NC as expected. The following correlations are obtained: FC: ha 0.137 Talm 68.2
(20)
NC: ha 0.048 Talm 12.2
(21)
with average values of 74 W/m2 and 16 W/m2 K, respectively.
The total thermal heat spreading resistance of the FHS#1 varied from 0.90 to 1.00 K/W under NC compared to about 3.85 to 4.31 K/W under FC. Contact resistance is very small, about 0.05 K/W compared to the total thermal resistance of the FHS.
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Fig. 14. Heat loss coefficient ha for FHS#1 (Runs A1-A6). 5.2 FHS under 2-D NC heat flow.
For this series, only NC air flow was considered. The experimental lay-out for Runs B1 to B3 is shown in Fig. 15. The larger FHS#2 measured 135 mm × 123 mm with 10 mm thick base and with fourteen fins each 30 mm long. The heating element measured 30 mm x 30 mm x 5 mm. The small aspect ratio = 0.053 is expected to produce some heat spreading effect here. A 22 mm thick aluminum block with similar dimensions as the heating element was located between the FHS#2 and the heating element. Twenty one holes were drilled from the top of FHS#2 through to its base to allow thermocouples (Tf1-f21) to be inserted. The locations of these thermocouples are shown in Figure 16. The mean temperature (Tfm) at the bottom surface of FHS#2 is estimated from the arithmetic average of the twenty one thermocouples (Tf1-f21). The mean surface temperature (T alm) at the top of the aluminum block is estimated from the arithmetic average of the five thermocouples (T f7, Tf10, Tf11, Tf12 and Tf15). The maximum temperature at the bottom of the FHS (T fmax) is assumed equal to the mean surface temperature of Al block (Talm). Other thermocouples measured the insulation surface temperature (Tins1, Tins2) and the ambient temperature (T a). An ac power supply provided electrical power (PEH) to the heating element. Power input was controlled using a variable ac voltage regulator. Three separate runs were conducted over a period of 2 hours each to
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determine experimental repeatability. The results are tabulated (Run B1 – B3) in Table 2. Again, results were generally repeatable to within 2oC.
Fig. 15. Experimental set-up to determine thermal resistance for FHS#2 with = 0.053.
Fig. 16. Location of thermocouples in FHS#2.
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Table 2. Experimental results for FHS#2 under NC ( = 0.053). Heat sink Run PEH Ta dimensions # (W) (C) (mm x mm)
135 x 123
10.1 B1 29.3 50.4 10.1 B2 29.9 50.1 10.0 B3 29.8 50.1
20.8 20.7 20.9 20.0 20.4 21.3 19.8 20.4 20.4
Tfmax Talm (C) 37.8±0.3 62.5±0.6 84.3±1.2 36.6±0.2 62.0±0.7 85.3±1.2 35.1±0.3 61.2±0.6 84.1±1.2
Tfm (C) 36.9±1.0 60.1±2.6 80.1±4.3 35.7±1.0 59.5±2.6 80.9±4.6 34.3±1.0 58.7±2.6 79.8±4.6 Average
Rcr1 + Rsrf Rf1D ha Rf2D (K/W) (K/W) (K/W) (W/m2K) Eqns. Eqn. (16) Eqn. (18) Eqn. (21) (14&15) 0.09 1.59 1.68 14.0 0.08 1.34 1.42 15.1 0.08 1.17 1.25 16.0 0.09 1.55 1.64 13.9 0.08 1.31 1.39 15.1 0.09 1.19 1.28 16.1 0.08 1.45 1.53 13.8 0.08 1.29 1.37 15.0 0.09 1.19 1.28 16.0 0.08 1.34 1.43 14.9
The transient temperatures (Tfm, T fmax) for FHS#2 under NC condition is shown in Fig. 17. Steady state could be achieved after about 120 minutes of operation. The center-line temperature distribution is shown in Fig. 18. The results show that high power input (PEH) results in higher temperatures as expected. The temperature (Talm) along the base of the FHS was non-uniform, varying up to 4.6oC at high power input due to thermal heat spreading.The total thermal resistance of the FHS#2 (Rf2D) varied from 1.25 to 1.68 K/W under NC and 2D heat flow. Spreading (Rsrf) and contact resistances (Rcr1) are small and amounted to about 0.10 K/W.
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Fig. 17. Transient temperatures for FHS#2 (NC, = 0.053 - Runs B1 – B3).
Fig. 18. Temperature distribution along centerline of FHS#2 (NC, = 0.053 - Runs B1 – B3).
5.3
Comparison between experimental and CFD simulated temperature results for
FHS#2.
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A CFD simulation was performed to obtain simulated results for the mean temperature of the base of the FHS (Tfm) and the maximum temperature (Tfmax) and to compare them against the experimental results obtained from Runs B1 to B3 for FHS#2 under NC. Since the experimental heat loss was found to be less than 1%, it was assumed negligible in the CFD simulation. The CFD simulated and experimental temperatures are tabulated and compared in Table 3. Three sets of results are shown in Table 3. The first set shows the experimental temperatures (Tfmax and T fm) and heat loss coefficient (ha) from Runs B1 to B3. The second set shows the simulated values obtained with heat loss coefficient from Eqn. (21) with T fm assumed equal to Talm and input into the CFD software package. The third set shows simulated temperatures obtained by using modified heat loss coefficients which are about a third lower than experimental values. The reason is because the experimental heat loss coefficients obtained from the FHS could be different under 1-D or 2-D heat flow because of non-uniform temperature distribution within the FHS due to heat spreading. In general, temperatures increase with input heat power. A comparison of the temperatures between sets #1 and 2 shows poor agreement. Simulated temperatures are about half that obtained experimentally. A comparison between sets #1 and #3 obtained with lower heat loss coefficient values show that by reducing the values of ha as input into the CFD program very good agreement is obtained between experimental and simulated results. Hence this brings us to the conclusion that the heat loss coefficient for FHS#2 under NC air cooling with 2dimensional heat spreading effect could be much smaller than the 1-dimensional heat loss coefficients obtained without heat spreading effect. Further investigations would need to be conducted to verify this.
Table 3. Comparison of experimental and CFD simulated results for FHS#2 with modified heat transfer coefficients. Experimental (Table 2) Run PEH # (W)
10.1 B1 29.3 50.4 B2 10.1
ha (W/ m2 K) Eqn. (21) 14.0 15.1 16.0 13.9
Tfmax Talm (C)
Tfm (C)
37.8±0.3 62.5±0.6 84.3±1.2 36.6±0.2
36.9±1.0 60.1±2.6 80.1±4.3 35.7±1.0
Simulated with ha from Simulated with Eqn. (21). modified ha ha (W/ ha T Tfmax,CFD Tfm,CFD T m2 K) fmax,CFD fm,CFD (W/ (oC) (oC) (C) (C) 2 Eqn. m K) (21) 14.0 27.6 26.7 5.3 37.2 36.4 15.1 39.2 36.7 6.3 61.2 58.6 16.0 51.2 46.8 7.3 81.6 77.2 13.9 26.8 26.0 5.4 36.1 35.2
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29.9 50.1 10.0 B3 29.8 50.1 6.
15.1 16.1 13.8 15.0 16.0
62.0±0.7 85.3±1.2 35.1±0.3 61.2±0.6 84.1±1.2
59.5±2.6 80.9±4.6 34.3±1.0 58.7±2.6 79.8±4.6
15.1 16.1 13.8 15.0 16.0
39.3 51.3 26.6 39.3 50.5
36.7 46.9 25.8 36.7 46.2
6.4 7.1 5.8 6.5 7.1
61.1 83.2 34.8 60.4 82.3
58.5 78.9 33.9 57.8 78.0
Conclusions.
The performances of two FHSs were determined. FC cooling resulted in lower temperature compared to NC. Heat loss coefficient was found to be higher under FC compared to NC air cooling condition. Thermal heat spreading occurred when the heat source was smaller than the FHS. Thermal heat spreading and contact resistances are small compared to the thermal resistance of the FHS itself. Further investigations are recommended to determine the heat loss coefficients under 2-D heat flow with thermal heat spreading effect.
Referances.
1. S. Lee, S. Song, V. Au V, K. P. Moran, Constriction/spreading resistance model for electeronic padkaging, Proc. ASME/JSME Engineering Conference (1995). 2. R. E. Simons, Simple formulas for estimating thermal spreading resistance, Electronics Cooling Magazine (2004). 3. G. N. Ellison, Maximum thermal spreading resistance for rectangular sources and plates with nonunity aspect ratios, IEEE Trans, Components and Packaging Technologies (2003) 439-454. 4. Y. S. Muzychka, J. R. Culham, M. M. Yovanovich, Thermal spreading resistance of eccentric heat sources on rectangular flux channels, Trans. ASME 125 (2003) 178-185. 5. S. Chingulpitak, S. Wongwises, A review of the effect of flow direcions and behaviors on the thermal prformance of conventional heat sinks, Int. Journal of Heat and Mass Transfer, 81 (2015) 10-18. 6. Y. Joo, S. J. Kim, Comparison of thermal performance between plate-fin and pin-fin heat sinks in natural convection, Int. Journal of Heat and Mass Transfer, 83 (2015) 345-356. 7. H. Y. Li, S. M. Choa, Measurement of performance of plate-fin heat sinks with cross flow cooling, Int. Journal of Heat and Mass Transfer, 52 (2009) 2949-2955. 8. T. Y. Kim, S. J. Kim, Fluid flow and heat transfer charecteristics of cross-cut heat sinks, Int. Journal of Heat and Mass Transfer, 52 (2009) 5358-5370.
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9. K. S. Young, S. L. Li, I. Y. Chen, K. H. Chien, R. Huc, C. C. Wang, An experimental investigation of air cooling thermal module using various enhancements at low Reynolds number region, Int. Journal of Heat and Mass Transfer, 53 (2010) 5675-5681. 10. D. A. Reay, P. A. Kew, Heat Pipes, Elsevier (2007), ISBN: 978-0-7506-6754-8. 11. G. P. Peterson, An Introduection to Heat Pipes - Modeling, Testing and Applications, Wiley (1994). 12. B. Zohuri, Heat Pipe Design and Technology - A Practical Approach, CRC Press (2011). 13. D.M. Rowe, Thermoelectrics Handbook – Macro to Nano, Taylor & Francis, (2006). 14. H. S. Lee, Thermal Design Heat Sinks, Thermoelectrics, Heat Pipes, Compact Heat Exchangers, and Solar Cells, Wiley (2010), ISBN: 978-0-470-49662-6. 15. I. Sauciuc, G. Chrysler, R. Mahajan, R. Prasher, Spreading in the heat sink base: Phase change systems or solid m. etals? Thermal Challenges in Next Generation Electronic Systems. Joshi & Garimella (eds). ISBN 90-77017-03-8:2002. 16. J. Choi, M. Jeong, Compact, lightweight and highly efficient circular heat sink design for high-end PCs, Applied Thermal Engineering, 92 (2016) 162-171. 17. D. Astrain, Á. Martínez, Heat exchangers for thermoelectric devices, in: J. Mitrovic (Ed.), Heat Exchangers - Basics Design Applications, InTech, 2012, pp. 289-308 18. Owsenek, B. L., Seyed-Yagoobi, J., Page, R. H., Experimental investigation of corona wind heat ransfer enhancenent with a heated horizontal flat plate. ASME Journal of Heat transfer, 117, 309-315, 1995. 19. Go, D. B., Garimella, S. V., Fisher, T. S., Mongia, R. K. Ionic winds for locally enhanced cooling. Journal of Applied Physics, 102,2007. 20. Go, D. B., Maturana, R. A., Fisher, T. S., Garimella, S. V. Enhancement of external forced convection by ionic wind. Int. Journal of Heat and Mass Transfer, 51, 6047-6053, 2008. 21. Avenas, Y., Ivanova, M., Popova, N., Schaeffer, C. Thermal analysis of thermal spreaders used in power elecronics cooling, 0-7803-7420-7/02, IEEE, 216-220, 2002. 22. Incropera, D. P. DeWitt, 2007. Introduction to Heat Transfer, 5Ed. Wiley. Experimental Heat Transfer 22 (2009) 26-38. Doi:10.1080/08916150802530187.
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Highlights.
Heat transfer coefficients were obtained under natural and force convection.
Two different aspect ratios showed the effects of thermal heat spreading.
A CFD simulation was performed.
Heat transfer coefficients depended upon thermal heat spreading effect.