Correlations highlighting effects of the PCB’s Copper ratio on the free convective heat transfer for a tilted QFN32 electronic package

International Journal of Heat and Mass Transfer 92 (2016) 110–119

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International Journal of Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ijhmt

Correlations highlighting effects of the PCB’s Copper ratio on the free convective heat transfer for a tilted QFN32 electronic package A. Baïri University of Paris, LTIE-GTE EA 4415, 50, rue de Sèvres, F-92410 Ville d’Avray, France

a r t i c l e

i n f o

Article history: Received 26 April 2015 Received in revised form 20 August 2015 Accepted 20 August 2015

Keywords: Electronics thermal control Natural convection QFN32 Enclosure Packaging Convective heat transfer coefficient

a b s t r a c t The main objective of this work is to examine the effects of the Copper ratio constituting the upper face of a tilted Printed Circuit Board (PCB) on the natural convective heat transfer concerning an electronic equipment containing a quad flat non-lead type (QFN32) package. Calculations are done by means of the finite volume method for several positions of electronic device on the PCB which is inclined with respect to the horizontal at an angle ranging from 0° (horizontal position) to 90° (vertical position) with a step of 15°. The power generated by the QFN32 varies between 0.1 and 0.8 W, and 10 Copper ratio varying between 0.26% and 39.45% are considered. These ranges correspond to the normal operating of the active electronic device for the intended applications. The study shows that the thermal behavior of the distinct areas of the active package is affected by the Copper ratio. Correlations are proposed, allowing determination of the average convective heat transfer coefficient on the different areas of the QFN32 device, according to the considered values of the Copper ratio, the PCB’s inclination angle and the generated power. They optimize its design while controlling its temperature during operation. The results of this survey provide a better modeling of this conventional arrangement widely used in electronic applications. Ó 2015 Elsevier Ltd. All rights reserved.

1. Introduction Integration of increasingly active components in the electronic assemblies generates substantial thermal problems. This is particularly important given that these components and assemblies are becoming smaller and more powerful, producing volumetric heat fluxes up to several GW m
3. Thermoregulation is then essential for their correct operation. Several studies have been conducted by examining the influence of various parameters on the thermal state of the devices. Among the most important parameters, mention may be made to the geometry, dimensions and physical characteristics of the enclosure in which the equipment is installed, to thermophysical characteristics of the fluid, thermal and dynamical boundary conditions governing the considered case, temperature levels, and to the inclination of the electronic card relative to the gravity field. The thermal characteristics of the components and their position on the PCB play an important role, as well as the interaction between different cards and their position relative to each other. The thermal phenomena that occur in a cavity containing an electronic circuit used in a telecommunication radar system is examined in [1] by means of the finite volume method. The proposed physical configuration avoids exceeding http://dx.doi.org/10.1016/j.ijheatmasstransfer.2015.08.064 0017-9310/Ó 2015 Elsevier Ltd. All rights reserved.

the maximum allowable temperature for Radio Frequency (RF) components. Heat exchanges are partly made through a finned surface installed on an aluminum box containing some cards on which various electronic components, generating different powers, are welded. The study shows that the arrangement of the active elements is essential to avoid exceeding the critical temperature. Thermal phenomena concerning an active personal cell phone are studied in [2]. A centrifugal fan is implemented within the cavity of the mobile phone in order to improve the heat transfer concerning the active electronic components, which ensures the correct operation of the device. Solutions including surfacic heat transfer by forced convection, natural convection and radiation are proposed for temperature control of the device, thus ensuring a longer life associated with good performance. Design of a heat sink modules with an encapsulated chip is proposed in [3]. The survey is done by means of the Levenberg–Marquardt Method (LMM) combined with a CFD code. The thermal performance and cooling capacity of microchannel heat sinks are applied to the electronic devices in the numerical survey [4]. The convectant fluid plays an essential role in thermoregulation of electronic assemblies contained in cavities whose size, shape, and thermal characteristics vary depending on the treated case. Natural convection using air

A. Baïri / International Journal of Heat and Mass Transfer 92 (2016) 110–119

111

Nomenclature AQ B a Cp ~ eg g hi h h L P Pr p p qi Ra T Tc T Ti T max TQB

area corresponding to ðQ B Þ (m2) thermal diffusivity of the air (m2 s
1) specific heat at constant pressure (J kg
1 K
1) dimensionless unit vector opposite to the gravity direction gravity acceleration (m s
2) local convective heat transfer coefficient of the ith element (W m
2 K
1) average convective heat transfer coefficient for a given area (W m
2 K
1) ratio defined by h ¼ hðsCu Þ=hðsCu ¼ 5:26%Þ (–) characteristic length (m) generated power (W) Prandtl number (–) pressure (Pa) dimensionless pressure (–) heat flux for the ith element (W m
2) Rayleigh number (–) temperature (K) temperature of the cavity’s walls and initial temperature of the whole system (K) average surface temperature (K) local temperature of the ith wall element (K) maximal temperature on the considered surface (K) average temperature corresponding to ðQ B Þ (K)

as the working fluid is often preferred, considering its well known advantages as described in [5,6]. Some results concerning the mixed convection in a 2D lid-driven enclosure are presented in [7] for different boundary conditions and in [8] in the case of a rotating cylinder in a vented cavity. This heat transfer mode combined with radiation is applied for electronics in [9,10] by using the finite-difference method. Effects of the main parameters and the location of the discrete heat source and board surface emissivity on the local and maximum temperature distribution are highlighted. Contribution of the convective and radiative heat transfer phenomena are also detailed. Various aspects concerning the conjugate natural convection and conductive heat transfer in a triangular enclosure filled with a porous medium are presented in the numerical study [11], based on the finite difference technique. The main characteristics of the Lattice-Boltzmann Method (LBM) used in natural convection are presented and commented in [12] for some cases. This method is applied in [13] for the case of an air-filled square enclosure. The survey shows the influences of the heat source length, inclination angle, and Rayleigh number on some flow characteristics and heat transfer by means of the Nusselt number. The use of conventional rotary fans is to be avoided as much as possible, because of the failure risks and their power consumption. Moreover, if their noise and electromagnetic nuisance are sometimes allowable, they are prohibitive in some applications such as telephony or radar systems especially in aeronautics. Radiation contributes with more or less intensity in the heat transfer balance applied to the electronic devices, depending on the considered thermal boundary conditions and characteristics of the elements contained in the cavity. In some applications involving high powers in a cavity of reduced volume, it may be necessary to use fluids whose characteristics substantially improve the natural convective heat transfer. This is the case of power electronics concerning several fields of engineering. Phase change material (PCM) can then be used, as is the case in [14]. The study [15] shows that the heat transfer using nanoparticules composed of Copper–Water, TiO2–Water and Alumina–Water is improved in comparison with the heat transfer observed when only water

T dimensionless temperature (–) ~ u velocity vector ~ u dimensionless velocity vector u dimensionless velocity (–) ðx; y; zÞ Cartesian coordinates (m) ðx ; y ; z Þ dimensionless coordinates (–) Greek symbols a inclination angle of the PCB with respect to the horizontal (°) b air volumetric expansion coefficient (K
1) ~ r dimensionless nabla operator (–) 2 r dimensionless Laplacian operator (–) DT difference of average temperatures for sCu ¼ 0:26% and sCu ¼ 39:47% (K) DT max difference of maximal temperatures for sCu ¼ 0:26% and sCu ¼ 39:47% (K) / volumetric heat flux (W m
3) k air thermal conductivity (W m
1 K
1) ke equivalent PCB’s surfacic thermal conductivity (W m
1 K
1) l air dynamic viscosity (Pa s) q air density (kg m
3) sCu PCB’s Copper ratio (–)

is considered. This remains valid in a wide range of the Rayleigh number and various thermal boundary conditions imposed on the hot active wall of a square cavity. The heat transfer enhancement is confirmed in [16,17] considering Al2O3–water nanofluids in differentially heated wavy cavities. The recent review [18] contains interesting elements of comparison between natural convective heat transfer with and without nanofluids. The case of electrostatic fluid accelerators (EFA) is described in [19] which also presents a review of the main passive and active methods for cooling electronics. The works [20,21] show that the thermal boundary conditions and the entropy generation have an important influence on the natural convective phenomena that occur in a porous cavity. This is confirmed in the numerical survey [22] done by means of the finite element method involving large Prandtl and Grashof numbers ranges for a square enclosure. The quad flat non lead (QFN) package is widely used in electronics. It concerns several engineering applications given its electrical and thermal performance. Its reduced size and weight allow its installation in reduced volumes. This is for example the case for portable computers that are becoming smaller, lighter and more efficient as required by the current market. These advantages of the QFN are associated with excellent electrical performance, allowing its integration in the assemblies involving high power and frequency. The QFN is then called to become generalized in various applications, hence numerous research works are done for its development. The resolution of the thermal problems constitutes an important part of the scientific and technological surveys performed today. The QFN packages commercially available are moderately voluminous, varying between (0.8  1.5  2.0) mm3 and (1.0  9.0  9.0) mm3. Some characteristics concerning these devices are available in the technical note [23] which also contains a Standard and Land Pattern Calculator Tool. More information and thermal test methods can be found in [24–26]. The QFN’s ‘‘Achilles’ heel” is its low reliability when it is subjected to several thermal cycles, which is the case in some applications. These solicitations often cause breakdowns or deactivation of the corresponding electronics assembly. The opportunity to implement the QFN therefore

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requires a prior study with actual thermal cycles in order to determine their exact reliability. The knowledge of the QFN’s end-of-life is required for their maintenance programming. A ‘‘health monitoring method” and the end-of-life estimation concerning the QFN solder-joint is proposed in the numerical and experimental study [27]. The presented method that could be applied for any IC type with QFN packages, is based on serial ohmic resistance changes in solder joints as a function of crack propagation. The influence of temperature on solder-joint reliability of the QFN package is presented in [28]. Solder-joint reliability presenting a low building height and a heat sink has been studied in [29]. The numerical approach by means of the finite element method validated by some measurements has been performed for some QFN-packages welded on Printed Circuit Boards. The study shows that the glass transition temperature of the board material affects the solder fatigue life and confirms that the PCB’s thermal expansion coefficient impacts the thermal fatigue of the interconnections. Excessive temperatures at the junctions and contact between the components and the PCB may cause malfunctions in the assembly. This known phenomenon was confirmed in [30] by considering Radio Frequency power amplifiers with high power dissipation. The study shows that exceeding the maximum allowable junctions temperature significantly reduces the reliability of the assembly and leads to premature components’ fatigue. Some problems concerning the QFN devices manufacturing such as deformations and cavitations are discussed in [31]. The thermal conductivity of the electronic assembly’s materials plays a crucial role in the thermal comportment of the QFN package. This essential characteristic is taken into account in several studies such as [32]. The studies [33,34] deal with thermoregulation of QFN32 and QFN16 packages respectively, welded on a PCB contained in a cubic cavity that may be inclined between the horizontal and vertical position. Nusselt–Rayleigh type correlations are proposed, valid for Rayleigh Numbers in the range 1:31  107 to 1:01  108 , allowing calculation of the convective overall heat transfer coefficient. Specific correlations allowing determination of the convective heat transfer coefficient on the different elements of an electronic assembly containing an active QFN32 are proposed in [35]. In these [33–35] studies, the

conductivity of the top layer of the PCB was kept constant, equal to an average value concerning the usual electronic assemblies. This value corresponds to the effective Copper rate representing the network of connections linking the package to other elements of the assembly. However, this network being highly variable from one installation to another, it is necessary to know the thermal behavior of the electronic package when the equivalent thermal conductivity of the top layer of the PCB varies. This is the main objective of this study. The proposed correlations allow determination of the convective heat transfer coefficient on the top, back and sides surfaces of the QFN32 package. They are valid for wide ranges of the Copper ratio (0.26–39.45%), generated power (0.1–0.8 W) and inclination angle of the PCB (0–90°). These ranges correspond to the normal operation of the QFN32 device widely used in electronics for various engineering applications. 2. The treated case The conventional electronic assembly considered in this survey is presented in Fig. 1. It is constituted by a QFN32 device (Fig. 1(a)) welded in several positions of a Printed Circuit Board (PCB) (Fig. 1 (b)) inclined with respect to the horizontal at an angle a ranging from 0° (horizontal position) to 90° (vertical position) with a step of 15° (Fig. 1(c)). This PCB is installed in a large cubical (800 mm side) air-filled enclosure maintained isothermal at T c temperature. The power P generated by the active device QFN32 varies between 0.1 and 0.8 W corresponding to its normal operating range. The assembly consists on five distinct areas:  the top surface ðQ T Þ and lateral (sides) faces ðQ S Þ of the QFN package.  the back face ðBB Þ, lateral faces (sides) ðBS Þ and upper free area ðBT Þ of the PCB. The thermal conductivity of the upper copper layer of the PCB plays an important role in the thermal behavior of the electronic assemblies. This layer of 35 lm thickness deposited on a resinous substrate is used to connect the electronic components of the

(d)

800 QFN32

(a) (b)

5 5

800

g

100 100 0.9 1.6

(c) α

800

g

(e)

Fig. 1. The treated assembly; (a) the QFN32 package; (b) the assembly in horizontal position contained in the air-filled cubic cavity; (c) PCB’s inclination angle; (d–e) QFN32 welded on a PCB with Copper connecting network more or less dense. All dimensions are given in mm.

Table 1 Correspondence between the equivalent thermal conductivity ke and the Copper ratio

sCu of the PCB’s upper layer.

ke

1

2

4

5

20

45

70

100

130

150

sCu

0.26%

0.53%

1.05%

1.32%

5.26%

11.84%

18.42%

26.32%

34.21%

39.45%

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assembly. These connections are often very thin, a few microns wide, and randomly arranged according to the considered assembly. Furthermore, the connecting network is more or less dense as illustrated in Fig. 1(d) and (e). In this survey, 10 Copper ratio are considered. The thermal conductivity of the upper face of the PCB cannot therefore be considered as constant (obvious anisotropy). Depending on the copper network density, the equivalent thermal conductivity ke of the board’s copper layer in both directions of its plane can vary between 1 and 150 W m
1 K
1, being 380 W m
1 K
1 the reference copper conductivity value. The pure conductive heat transfer between the QFN package and the plate can vary in a ratio of 1 to 150 depending on the considered case. It is the same for the conductive heat transfer according to the thickness of the plate. The thermal field of the electronic package and PCB depends on the considered configuration. In some cases, the maximum temperature recommended by the manufacturer QFN is exceeded. The device is then switched off and sometimes destroyed. In the previous works [33–35], the equivalent thermal conductivity of the board is assumed to be equal to 20 W m
1 K
1 in the plate’s plane and 0.35 W m
1 K
1 in its thickness. In the present study, 9 new specific values (1, 2, 4, 5, 45, 70, 100, 130 et 150 W m
1 K
1) are considered for the PCB’s plane, while the thickness one is kept the same (0.35 W m
1 K
1). The design of the track network causes the extraction of part of the copper, so the equivalent value of the resulting parallel resistor network depends of the kept copper quantity. The equivalent thermal conductivity ke can then be replaced by the Copper ratio often used by electronic equipment manufacturers, denoted as sCu according to Table 1.

3. Governing equations, numerical procedure and thermal modeling The problem under consideration is based on the resolution of the governing system whose dimensionless form is

8  ~ u¼0 > :  ~  2  2  ~ u r T ¼ r T ðairÞ; r T þ 1 ¼ 0 ðQFN32 active partÞ

ð1Þ

being ~ u and p the dimensionless velocity vector and pressure defined as

~ u ¼

~ uL ; a

p ¼

L2 p q a2

ð2Þ

The dimensionless Cartesian coordinates x ; y ; z , temperature T  , the Prandtl number Pr and the Rayleigh number Ra based on the side of the QFN32 package L ¼ 5 mm are defined by

x ; y  ; z  ¼

x; y; z T
Tc lC p gbL5 q ; T ¼  ; Pr ¼ ; Ra ¼ / L k lak T
Tc

ð3Þ

being T the average surface temperature. The overall considered domain is assumed initially as isothermal at temperature T c . The air is incompressible, the Boussinesq approximation is applied, no-slip condition is imposed on all the internal walls of the assembly and the Die’s active part generates a constant volumetric heat flux /. Given that as only natural convective phenomena are examined in this survey, radiation is not considered. This condition is realized by imposing a zero global infrared emissivity for all the internal walls. Calculations are realized by means of the commercial software Ansys-Fluent [36] based on the control volume method associated to the SIMPLE algorithm. Several configurations were also calculated with a CFD house code to check the previous calculations for the thermal aspects. The deviation is less than 2% with regard to the convective heat transfer, the main objective of this study. These codes are complemented by a second home software allowing determination of the thermal characteristics. A preliminary work was done to optimize the mesh on which a logarithmic refinement is performed all around the assembly to determine with precision the thermal gradient distribution. This parameter allows calculation of the local heat flux qi ¼
kð@T i =@nÞ at every ith wall

QFN32

(a) (c)

(b) (d)

(e)

(h)

(f)

(g)

Fig. 2. Assembly mesh with centered QFN32 package (a) front face with QFN32 detail; (b) Back face with details; (c–e) mark on the PCB, front face and sides of the QFN32 package; (f) PCB sides; (g) PCB profil vue and detail; (h) the assembly in the cavity.

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A. Baïri / International Journal of Heat and Mass Transfer 92 (2016) 110–119

element, being k the air thermal conductivity. The distribution of the local convective heat transfer coefficient hi ¼ qi =ðT i
T c Þ is subsequently determined. Its integration over the external area of each of the 5 considered areas ðQ T Þ, ðQ S Þ, ðBB Þ, ðBS Þ and ðBT Þ allows determination of the corresponding average convective heat transfer coefficient h. This parameter constituting the main parameter of this survey is used to determine the optimal mesh. The numerical solution is considered as mesh-independent when the variation in successive h values are less than 3% after refining the mesh. The convergence criteria in the numerical process are set to 10
5 for the velocity components and 10
6 for energy. The final mesh configuration consists of 368,955 nodes, 1,187,588 quadrilateral wall faces and 387,849 hexagonal cells. Meshes corresponding to the different elements of the treated assembly and some details are presented in Fig. 2. 4. Results The thermal behavior of the assembly is examined for: the 5 areas ðQ T Þ, ðQ S Þ, ðBT Þ, ðBS Þ and ðBB Þ; 15 P values in the range 0:1 6 P 6 0:8 W step 0.05 W; 7 PCB’s inclination angles a in the range 0 6 a 6 90 step 15°; 9 Copper ratio sCu of Table 1, being the 10th case ðsCu ¼ 5:26%Þ examined in [33,35];  the 9 positions of the QFN device on the board (Fig. 1(b)).

   

4.1. The dimensionless temperature fields The dimensionless temperature fields around the assembly are presented in Fig. 3 for the combinations sCu ¼ 5:26%; 39:45% and

0°

τ Cu = 5.26%

a ¼ 0 ; 90 . When the PCB is horizontal, the isotherms are round shaped and centered around the assembly for the sCu large value, reflecting a good thermal conduction between the QFN package and the board. This is not the case for the low Copper ratio. This phenomenon remains valid for the vertical plate over a large area around the active device and isotherms deformation is more pronounced for sCu ¼ 5:26%. Details in Fig. 4 shows that the shape of the dimensionless temperature and velocity fields around the active package are not significantly impacted by the Copper ratio sCu . These observations remain valid for all the ðP; a; sCu Þ treated combinations. However, the absolute temperature and velocity values depend, of course, on the considered sCu value, for a given ðP; aÞ configuration. This is clearly showed with the absolute temperature fields T in Fig. 5 for ðQ T Þ and around this area: the temperature decreases as sCu increases. Details of the average and maximal temperature are presented in Fig. 6 for P ¼ 0:1; 0:3; 0:5; 0:8 W and 3 representative angles a ¼ 0 ; 45 ; 90 . Since the ðBB Þ’s surface is larger than the ðBS Þ’s one, and considering the important role of the PCB in the convective heat transfer phenomena between the assembly and the environment, these two surfaces are grouped together, which simplifies the presentation of results. 4.2. The average temperature The average temperature T of all the PCB’s areas decreases as the Copper ratio increases in the range 0:26% 6 sCu 6 5:26% and stabilizes for greater values (mean deviation of about 1.1%), as shown in Fig. 6(a). The T decreasing is however moderate, ranging between 0.1 and 0.7 K. On both board’s sides, the T values decrease when the generated power P decrease, and the inclination angle

0°

90°

τ Cu = 39.47%

90°

T*

QFN32 Fig. 3. Dimensionless temperature fields around the assembly for

sCu ¼ 5:26%; 39:47% and a ¼ 0 ; 90 .

QFN32 0°

τ Cu = 5.26%

90°

0°

1

T*

τ Cu = 39.47%

0

Fig. 4. Dimensionless temperature and velocity fields around the QFN32 package for the combinations

90°

1

u*

0

sCu ¼ 5:26%; 39:45% and a ¼ 0 ; 90 .

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A. Baïri / International Journal of Heat and Mass Transfer 92 (2016) 110–119

QFN32 0°

90°

τ Cu = 5.26%

330.5

T 311.8

293.2

τ Cu = 39.47%

Fig. 5. Temperature fields T around the QFN32 package for the combinations

does not affect significantly the average temperature for a given power. The temperature differences corresponding to the T values for sCu ¼ 0:26% and sCu ¼ 39:47% have been calculated for the four areas ðQ T Þ, ðQ S Þ, ðBT Þ and ðBB þ BS Þ. They are very low for the board, for all the treated inclination angles and generated powers. The mean deviation is of about 0.2 K for 0:1 6 P 6 0:5 W and 0.3 K for P ¼ 0:8 W, the maximum of 0.6 K being reached for the horizontal plate. However, the difference is very important on both QFN areas. As shown in Fig. 7(a), the temperature difference DT ¼ TðsCu ¼ 0:26%Þ
TðsCu ¼ 39:47%Þ reaches 97 K for the vertical position and exceeds 112 K on ðQ T Þ for the horizontal position ðP ¼ 0:8 W; a ¼ 0 Þ. This difference DT linearly increases with increasing P in the entire operating power range 0:1 6 P 6 0:8 W. These results show the significant influence of the PCB Copper ratio on the QFN package: the average temperature of the active device drops significantly when the conductive heat transfer with the PCB is enhanced by high sCu values. The PCB’s average temperature remains insensitive to sCu . Being DT very small for ðBT Þ and ðBB þ BS Þ, it is not presented in Fig 7(a).

sCu ¼ 5:26%; 39:47%, a ¼ 0 ; 90 and P ¼ 0:8 W.

4.4. The average convective heat transfer coefficient The average convective heat transfer coefficient h can reach high values close to 33 W m
2 K
1 on the QFN package, as shown in Fig. 8. For ðQ T Þ, it increases systematically when a and P increase. In this area, it decreases with a strong slope when the Copper ratio increases from 0.26% to 5.26% (low copper network density). The coefficient h finally stabilizes (low deviation) when the Copper ratio reaches or exceeds approximately 25%. A similar trend is observed for ðQ S Þ for the range 0:26% 6 sCu 6 5:26%. The

coefficient h increases with a and P but in contrast with ðQ T Þ, it increases significantly and monotonically for sCu > 5:26%. For the

QFN package, the decrease of h is of about 20% for ðQ T Þ, while the increase is of about 12% for ðQ S Þ. The h values obtained in the present study in the range 0:26% 6 sCu 6 39:47% have been compared to those of [33,35] valid for sCu ¼ 5:26% (corresponding to ke ¼ 20 W m
1 K
1). Evolution of the ratio

h ¼ hðsCu Þ=hðsCu ¼ 5:26%Þ 4.3. The maximal temperature The maximal temperature T max is an important data for the thermal design of electronic assemblies. It allows to check that the maximal temperature recommended for the electronic device is not reached or exceeded. Fig. 6(b) shows that T max continuously decreases as sCu increases with a significant variation in the range 0:26% 6 sCu 6 5:26% for the 4 areas of the assembly. The reduction continues when sCu is increasing for sCu > 5:26% but nevertheless very moderately. The maximal temperature differences DT max ¼ T max ðsCu ¼ 0:26%Þ
T max ðsCu ¼ 39:47%Þ have been determined on all the assembly’s surfaces. In contrast with DT, it is not always negligible for the PCB. As represented in Fig. 7(b), the lowest average difference is of about 9 K on ðBT Þ for the vertical plate and P ¼ 0:1 W but exceeds 84 K on ðBB þ BS Þ for ðP ¼ 0:8 W; a ¼ 0 Þ. The maximum difference is greater for DT max than for DT on the both QFN’s areas, exceeding 117 K on ðQ T Þ for the horizontal position ðP ¼ 0:8 W; a ¼ 0 Þ. As for T, the difference T max ðsCu ¼ 0:26%Þ
T max ðsCu ¼ 39:47%Þ increases linearly with increasing P on the 4 areas of the assembly and the considered P range. These values show that in some cases, the maximum temperature T max recommended by the manufacturers of the package and the board could be exceeded.

ð4Þ

is presented in Fig. 9 on both ðQ T Þ and ðQ S Þ for the whole considered P and a ranges. The results of Fig. 9 show that (i) For high values 5:26% 6 sCu 6 39:45%, the Copper ratio has small influence on h for ðQ T Þ. However, it is not the case for the ðQ S Þ area on which the influence of sCu on h is clear with a regular increase as sCu increases. In this area, the inclination angle does not significantly affect h in the overall considered sCu range. The deviation of h around the average value for all the treated angles is moderate, ranging between
0.3% and +0.8%. (ii) For low values 0:26% 6 sCu 6 1:32%, there is a steady decrease of h with a power law when sCu increases, on both ðQ T Þ and ðQ S Þ areas. In contrast with large sCu values, the evolution is different according to the considered P value.

The h evolutions corresponding to the other inclination angles considered in the present survey follow the same trends and are intercalated with those presented in the previous figures. The power exchanged by convection between the assembly and the environment is clearly dependent on the ratio sCu . The values

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A. Baïri / International Journal of Heat and Mass Transfer 92 (2016) 110–119

QS

430

430

T

Tmax

370

370

280 0%

QT

20%

τ Cu

280 40%

0%

430

430

T

Tmax

370

370

τ Cu

20%

40%

QFN32 0.8 W, 0° 0.8 W, 45° 0.8 W, 90°

280 0%

20%

τ Cu

280 0%

40%

0.5 W, 0° 40%

0.5 W, 45° 0.5 W, 90°

430

298

BT

τ Cu

20%

T

Tmax

296

370

0.3 W, 0° 0.3 W, 45° 0.3 W, 90° 0.1 W, 0° 0.1 W, 45° 0.1 W, 90°

293 0%

BB + BS

20%

τ Cu

280 0%

40%

298

430

T

Tmax

296

370

293 0%

20%

τ Cu

20%

τ Cu

40%

20%

τ Cu

40%

280 0%

40%

(a)

(b)

Fig. 6. Influence of the Copper ratio sCu on (a) the average temperature T; (b) the maximal temperature T max on the 4 assembly’s surfaces with QFN32 package for P ¼ 0:1; 0:3; 0:5; 0:8 W and a ¼ 0 ; 45 ; 90 .

QFN32 120

120

ΔT

ΔTmax

60

60

(a) 0

0.1

0.5

P

(b) 0.8

0

0.1

0.5

P

0.8

QT, 0° QS, 0° QT, 45° QS, 45° QT, 90° QS, 90° BT, 0° BB+BS, 0° BT, 45° BB+BS, 45° BT, 90° BB+BS, 90°

Fig. 7. Differences DT ¼ TðsCu ¼ 0:26%Þ
TðsCu ¼ 39:47%Þ and DT max ¼ T max ðsCu ¼ 0:26%Þ
T max ðsCu ¼ 39:47%Þ versus P on the ðQ T Þ, ðQ S Þ, ðBT Þ and ðBB þ BS Þ areas, for a ¼ 0 ; 45 ; 90 .

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A. Baïri / International Journal of Heat and Mass Transfer 92 (2016) 110–119

34

34

QT

h

h

(a)

QFN32

30 0.8 W, 0°

22

0.8 W, 45°

QS 14 0%

20%

τ Cu

40%

26 0%

34

34

h

h

(b)

τ Cu

20%

0.8 W, 90° 0.5 W, 0° 40%

0.5 W, 45° 0.5 W, 90° 0.3 W, 0° 0.3 W, 45° 0.3 W, 90°

30

0.1 W, 0°

22

0.1 W, 45° 0.1 W, 90° 14 0%

τ Cu

0.5%

1.5%

26 0%

τ Cu

0.5%

1.5%

sCu on ðQ T Þ and ðQ S Þ for P ¼ 0:1; 0:3; 0:5; 0:8 W and a ¼ 0 ; 45 ; 90 (a) for 0:26% 6 sCu 6 39:45% (b) details of (a) for 0:26% 6 sCu 6 1:32%.

Fig. 8. Evolution of h versus

1.4

1.4

QT

QS *

*

QFN32

h

h

(a)

0.8 W, 0° 0.8 W, 45° 1.0

1.0

0.9 0%

20%

τ Cu

40%

0.9 0%

1.4

1.10

*

h

20%

τ Cu

0.5 W, 0° 40%

0.5 W, 45° 0.5 W, 90° 0.3 W, 0°

*

h

(b)

0.8 W, 90°

0.3 W, 45° 0.3 W, 90°

1.2

0.1 W, 0° 1.00

0.1 W, 45° 0.1 W, 90°

1.0 0% Fig. 9. Evolution of h versus

0.5%

τ Cu

0.95 1.5%

0%

0.5%

τ Cu

1.5%

sCu on ðQ T Þ and ðQ S Þ for P ¼ 0:1; 0:3; 0:5; 0:8 W and a ¼ 0 ; 45 ; 90 (a) for 0:26% 6 sCu 6 39:45% (b) details of (a) for 0:26% 6 sCu 6 1:32%.

and evolutions of h give an important information on the convective phenomena corresponding to the active device. However, it is necessary to associate h to (i) the surface of the considered area, (ii) the part of the power P exchanged by convection in this area and (iii) the difference between its average surface temperature T and that of the environment. Although the ðQ T Þ’s h coefficient is generally lower than that of ðQ S Þ for sCu > 5:26%, and the temperature differences with the environment corresponding to ðQ S Þ is higher, the power exchanged by the top of the active package is greater than the sides’ one, given that its surface is of about 40% greater than the ðQ S Þ’s one. The thermal sizing of the QFN32 package requires knowledge of the heat exchange in the QFN-PCB interface which can be repre-

sented by the equivalent average convective heat transfer coefficient hQ B corresponding to its back face ðQ B Þ calculated with

hQ B ¼

P
ðP Q T þ PQ S Þ AQ B ðT Q B
T c Þ

ð5Þ

This equation is obtained by means of a heat balance considering the convective powers P Q T and PQ S exchanged by the ðQ T Þ and ðQ S Þ respectively. In Eq. (5), AQ B and T Q B are the ðQ B Þ’s area and average temperature respectively. The ratio h ¼ hðsCu Þ=hðsCu ¼ 5:26%Þ of Eq. (4) was then performed by using the reference values for sCu ¼ 5:26% determined in [35]. These calculations done for all the ðP; a; sCu Þ combinations show that the generated power and

118

A. Baïri / International Journal of Heat and Mass Transfer 92 (2016) 110–119

QFN32 2.5

QB *

h

*

h = 2.664 − 2.267 exp −

1.0

τ Cu 17%

*

0.5013 h = 4.376τ Cu

0.0 0%

20%

τ Cu

40%

Fig. 10. Evolution of h versus sCu on ðQ B Þ for 0:26% 6 sCu 6 39:45%. Details of h correlations for 0:26% 6 sCu 6 5:26% and 5:26% 6 sCu 6 39:45%. Valid for 0:1W 6 P 6 0:8 W and 0 6 a 6 90 .

inclination board have little influence, being the maximum deviations limited to ±2.3% and ±2.1% respectively. The average h value represented in Fig. 10 shows that the evolution is of the power type in the range 0:26% 6 sCu 6 5:26% and of the exponential type for 5:26% 6 sCu 6 39:45%. The same work has been performed for the 9 positions of the QFN32 on the PCB (Fig. 1(b)). The results show that the position does not affect significantly the convective heat transfer coefficients on the active device. Its values increase slightly when the QFN32 approaches the edge of the plate and when it is located downward of the plate, but the deviation between the extreme values is nevertheless limited to ±2%. Finally the average convective heat transfer coefficient on the considered QFN32 package can be determined with the following correlations 3 82
0:083
0:33sCu > > 6 Q T : 0:796sCu > 7 >
0:02 >
0:33sCu 5 for 0:26% 6 sCu 6 5:26% 4 Q S : 0:950sCu > > > > 0:5013 < Q B : 4:376sCu h ¼ 2 3 > > QT : 1 > > > 6 7 > > 4 Q S : 0:981 þ 0:345sCu 5 for 5:26% 6 sCu 6 39:45% > > : Q B : 2:664
2:267exp½
ðsCu =17%Þ being h ¼ hðsCu Þ=hðsCu ¼ 5:26%Þ and 2

Q T : 15:806 þ ð0:0665 þ 0:0317PÞa þ 1:6584P

3

7 6 hðsCu ¼ 5:26%Þ ¼ 4 Q S : 27:072 þ ð0:0295 þ 0:0027PÞa þ 1:1094P 5 Q B : 1297:5 þ 0:9745a
0:0028a2 8 > < QFN32

for

> :

0 6 a 6 90

0:1 6 P 6 0:8 W ð6Þ

according to [35]. 5. Conclusions The natural convective heat transfer is determined on distinct areas of an electronic equipment containing a quad flat non-lead type QFN32 package. This active well-known electronic device

package generating different powers may be welded in several positions of a Printed Circuit Board which is inclined at various angles respect to the horizontal plane. The influence of the Copper ratio constituting the upper face of the PCB on the convective average heat transfer coefficient as well as the average and maximal temperatures of these elements have been determined for all the considered configurations. Evolution of these parameters versus the Copper ratio are detailed and commented for the considered cases. Correlations are proposed, allowing determination of the average convective heat transfer coefficient on any area of the QFN32 package, according to the considered values of the Copper ratio, PCB’s inclination angle and generated power. They complement those proposed in the previous works [33,35], valid for a constant Copper ratio corresponding to the average value taken into account in various engineering applications. The results of the present survey optimize the thermal design and performance of this device widely used in electronics.

Conflict of interest None declared.

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