Faculty of Engineering, Cairo University, Egypt, Vol ...

Journal of Engineering and Applied Science (JEAS), Faculty of Engineering, Cairo University, Egypt, Vol. 52, No. 5, pp. 981-1000, October, 2005

Numerical and Neural Study of Flow and Heat Transfer Across an Array of Integrated Circuit Components

Ahmed F. Abdel Gawad, Mofreh M. Nassief, and Nabil M. Gurguis

NUMERICAL AND NEURAL STUDY OF FLOW AND HEAT TRANSFER ACROSS AN ARRAY OF INTEGRATED CIRCUIT COMPONENTS

A. F. ABDEL GAWAD1, M. M. NASSIEF2, AND N. M. GUIRGUIS3

ABSTRACT The present study is concerned with the flow and heat transfer for laminar flow over an array of rectangular blocks. These blocks represent finite heat sources on parallel plates (e.g. the components of integrated circuits). The study is based on simulations of three and six aligned hot small blocks. The investigation aims to determine the effect of different parameters (e.g. Reynolds number and blocks arrangement) on the magnitude and location of the maximum temperature at the surfaces of the hot blocks. The numerical investigation was carried out using the commercial code ANSYS 5.4 based on the finite element technique. Also, experimental investigation was carried out for verification and more understanding of the problem. Neural networks were utilized to predict the values of the mean Nusselt number of the integrated circuit components. Useful discussions and fruitful comments are presented. KEYWORDS: Laminar Flow – Forced Convection – Rectangular Blocks – Integrated Circuits – Neural Networks 1. INTRODUCTION The present problem simulates the components of an integrated circuit (IC) that are placed on a horizontal circuit board. Large amounts of heat are usually generated in the integrated circuits due to flow of current through gates and connections of the smaller areas within the silicon chips. As computing and gate switching speed increases in a chip, heat generation increases. The basic consideration in thermal design is to minimize the maximum temperature at the chip for a given set of design criteria [1]. ________________________________________________________________________________________ 1

Associate Prof., Mech. Power Eng. Dept., Faculty of Eng., Zagazig Univ., Egypt, Member ASME & AIAA. Assistant Prof., Mech. Power Eng. Dept., Faculty of Eng., Zagazig Univ., Egypt. 3 Associate Prof., Building Research Center, Cairo, Egypt. 2

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Temperature distributions must be calculated within the package to ensure reliability of solder joints and devices accurately under thermal stresses. The components (heat sources) are finite, and unevenly distributed on the printed circuit (PC) board. A number of investigators studied this problem. Davalath and Bayazitoglu [1] carried out a numerical investigation on the conjugate heat transfer for two-dimensional, developing flow over an array of rectangular blocks, representing finite heat sources on parallel plates. They stated that although each block generates a constant rate of heat, the heat flux varies as a function of position on all the surfaces exposed to the fluid stream. Nakajima et al. [2] extended the numerical analysis to three-dimensional separated and reattached flow as well as heat transfer around an array of surface-mounted rectangular blocks in a channel with two parallel walls. Majumdar and Amon [3] used direct numerical simulations (DNS) of transitional flows in communicating channels. They reported that the pressure fluctuation and the production terms are mainly responsible for the exchange of energy between the mean and fluctuating flows. Liou and Chen [4] carried out computations and measurements of time mean velocities, total fluctuation intensities, and Reynolds stresses for spatially periodic turbulent flows past an array of bluff bodies aligned along the channel axis. They manifested that the interference between ribs is less significant in the rib-nearwake region and more influential on the rib-far-wake region. Other investigations, concerning the flow and heat transfer of electronic components, were carried out by many researchers, numerically [5-8] and experimentally [9-13]. In each of the above researches, the investigation was focused on a limited number (e.g. three) of heat sources. In the present study, a numerical and experimental investigation was carried out to study the flow and thermal fields of the integrated circuit components. The numerical investigation was carried out using the commercial code ANSYS 5.4 based on the finite element technique. Both the flow and thermal fields were calculated for two arrangements of three and six aligned components. A suction wind tunnel was used to carry out the experiments on scaled-up models of six aligned components. The temperature distributions on the components were recorded for different values of Reynolds number. Neural networks were used to

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predict the values of the mean Nusselt number on the surfaces of the different IC components. Useful remarks and conclusions are drawn from the study. 2. MATHEMATICAL MODEL AND NUMERICAL APPROACH 2.1 Governing Equations Generally, components of integrated circuits (IC) are arranged in rows in such a way that the spacing between components in each row is small compared to the spacing between the rows. For a printed circuit (PC) board, the length of each row (length or width of the PC board) is at least one order of magnitude higher than the width of each component. Therefore, the two-dimensional model for the flow and thermal fields provides a good approximation [1]. The problem consists of flow between parallel plates with multiple blocks containing heat sources, Fig. 1. The flow enters with a parabolic profile from one end and leaves at the other end of the plates carrying the heat dissipated from the blocks. The two-dimensional governing equations for incompressible flow in non-dimensional form are as follows: - Continuity equation:

∂u ∂v + = 0 ∂x ∂y

- Momentum equation: u

- Energy equation: u

(1)

∂ u ∂u ∂ 2u ∂p 1 ∂ 2u + v = ( 2 + ) 2 ∂x ∂y ∂y ∂x Re ∂ x

∂θ ∂θ 1 ∂ 2θ ∂ 2θ + v = ( 2 + ) ∂x ∂y Re Pr ∂ x ∂ y2

Where x = X/h, u = U/Uo, p =

(2)

(3)

P , and θ = [(T – To) λ]/(qw h), qw is the heat flux, ρ U o2

To and Uo are the temperature and velocity of the upstream flow, respectively. 2.2 Boundary Conditions and Computational Aspects

The flow enters the domain with a fully developed parabolic profile. Axial diffusion is set to zero at the exit. Also, at the channel exit the x-component velocity (u) is calculated to satisfy conservation of mass with the pressure set to zero. No-slip and no-penetration conditions are applied to the two parallel plates of the channel as

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well as the IC components (blocks), Fig. 1. For the thermal field, the upper and lower plates are insulated such that

∂θ ∂y

= 0 . The non-dimensional flow inlet y = 0 & y =1

temperature is zero. Constant heat flux (qw = c) is applied along the upper and side surfaces of each component (block). Axial diffusion is set to zero at the exit. The computations were carried out using the finite element technique. Quadratic elements were used, Fig. 2. Careful clustering of the elements was applied near the IC components. The downstream length (Lout) behind the last component (block) was suitably chosen by trial and error to ensure that the recirculation zone was inside the computational domain. The plate length should be long enough so that there is no axial conduction at the exit. 3. EXPERIMENTAL SETUP

The experiments were carried out using a suction wind tunnel of cross-section 0.2×0.2 m2, Fig. 3. The axial fan is equipped with an autotransformer (variac) to change the voltage-input to the fan-motor. Thus, the air speed inside the tunnel can be controlled. A single-wire hot-wire anemometry was used to measure the mean air speed inside the tunnel. Four values of Reynolds number were utilized in the experiments, namely: 0.0 (natural convection), 787, 1573 and 2060. These values of Reynolds number are believed to lie in the laminar regime. They were chosen to be as close as possible to those of the numerical study. Six scaled-up models were used in the experiments. The scale is 2.5:1. The models represent rectangular blocks, each one has dimensions of 2.5 × 5.0 × 5.0 cm3 (h × ℓ × w, respectively). Scaling-up was necessary to facilitate the insertion of the heater and thermocouples on the surface of the model. The models were fabricated from 4 mm-Plexiglas sheets. A heater and a group of thermocouples (K-type) were inserted on the top surface of one block. Thirty three thermocouples are distributed along the centerline and two side lines of the model as shown in Fig. 3.

4

L

u = 0, v = 0

Downstream ∂ u/∂ x = 0, ∂ v/∂ x = 0

H=4h qw

Y

B

X

C

A

F

DE

G HI

Lin = 5.5 ℓ

J

ℓ

K

N

LM

R

O PQ

S

V TU

W X

u = 0, v = 0

h

Lout = 16 ℓ

S

Upstream Parabolic Profile

Fig. 1. The computational domain and boundary conditions (Not to scale).

Fig. 2. Computational mesh with quadrilateral elements for three-block arrangement.

Upper plate Flow

ℓ Measuring of velocity profile

ℓ

h

4h

Fan (a) Side view.

Flow w

8h

20 ℓ w/9 (b) Top view.

Right line Centerline Left line

Fig. 3. Side and top views of the suction wind tunnel (Not to scale).

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The heater is inserted between two layers of a non-conducting material to resemble the actual case. The models were aligned in an arrangement of six blocks. The model with the heater and thermocouples was positioned as the first, second, or third, etc., element in the arrangement. Then, temperature measurements were recorded after reaching steady state (thermal equilibrium between the heater and cooling air). The distance (gap) between any two successive models (S) was kept at 5.0 cm. To resemble a real-case of printed circuit boards, a sheet of Plexiglas was placed at 10 cm above the bottom of the wind tunnel; Fig. 3. Thus, the flow passes between two horizontal printed circuit boards and perpendicular to the blocks. 4. RESULTS AND DISCUSSION 4.1 Numerical Predictions

Figures 4 and 5 show the flow vectors, and contours of Cp and dimensionless temperature for three and six IC components, respectively, at Re = 750 and 2000. In Fig. 4, two values of the dimensionless gap were investigated (s = 0.25 and 0.5). For s = 0.25, the maximum temperature (θmax = 1.8) is found in the second gap between the second and third blocks at Re = 750. Temperature values drop on the other faces of the blocks especially the top ones. As Re increases to 2000, the value of θmax drops to 1.7. This is obviously due to the greater air cooling rate with the higher value of air velocity. When s increases to 0.5, θmax drops to 1.173 and 0.9 for Re = 750 and 2000, respectively. This may be attributed to the increase of flow activity in the gaps between the blocks when s increases from 0.25 to 0.5, Fig. 4a. Increasing s to 0.5 changes the pattern of velocity vectors directly above the three blocks and in the gaps between them. This causes the change of the negative values of Cp on the top surfaces of the three blocks (Fig. 4b). Also, the change of temperature from the top surfaces of the blocks to the far field becomes more gradual. A horseshoe vortex is seen in front of the first block for Re = 2000 and s = 0.25, Fig. 4a-ii. When considering the six-block arrangement (Fig. 5), it is obvious that θmax is found on the side surfaces of the third, fourth and fifth blocks for s = 0.5. The value of θmax reduces from 1.22 for Re = 750 to 0.691 for Re = 2000.

6

(a)

(b)

(c) 0.0 0.202 0.403 0.605 0.806 1.008 1.210 1.410 1.610 1.800

(i) Re = 750, s = 0.25. 0.0 0.189 0.377 0.566 0.754 0.943 1.131 1.320 1.510 1.697

(ii) Re = 2000, s = 0.25. 0.0 0.130 0.261 0.391 0.522 0.652 0.782 0.913 1.043 1.173

(iii) Re = 750, s = 0.5. 0.0 0.100 0.200 0.300 0.400 0.500 0.602 0.702 0.800 0.900

(iv) Re = 2000, s = 0.5. Fig. 4. Numerical predictions of flow vectors (a), pressure coefficient (Cp) contours (b), and dimensionless temperature contours (c) for forced convection from three IC components (blocks).

7 7

(a)

(b)

(c) 0.0 0.135 0.271 0.406 0.541 0.677 0.813 0.948 1.084 1.219

(i) Re = 750, s = 0.5. 0.0 0.077 0.153 0.230 0.307 0.384 0.460 0.237 0.614 0.691

(ii) Re = 2000, s = 0.5. 0.0 0.088 0.176 0.264 0.352 0.440 0.527 0.615 0.703 0.791

(iii) Re = 750, s = 1.0. 0.0 0.067 0.135 0.202 0.269 0.336 0.404 0.471 0.538 0.606

(iv) Re = 2000, s = 1.0. Fig. 5. Numerical predictions of flow vectors (a), pressure coefficient (Cp) contours (b), and dimensionless temperature contours (c) for forced convection from six IC components (blocks).

8 8

For s = 1.0, the values of θmax drop to 0.791 (Re = 750) and 0.606 (Re = 2000). The maximum values of θ are found on the rear surfaces of the third and sixth blocks for s = 1.0. Vortex-like motions dominate in the gaps between the successive blocks. These motions become more obvious and stronger for s = 1.0. Negative values of Cp prevail on and around the surfaces of the last three blocks for s = 1.0. Figure 6 shows the distributions of θ for three- and six-block arrangement, respectively, for Re = 100, 750, 1000, 1500, and 2000. 3

Re = 100 Re = 750 Re = 1000 Re = 1500 Re = 2000

2.5

Dimensionless Temperature


3

2 1.5 1 0.5

Re = 100 Re = 750 Re = 1000 Re = 1500 Re = 2000

2.5 2 1.5 1 0.5 0

0 A

B

C

DE

F

G

HI J

K

A

L

B

C

DE

F

(a) s = 0.25 - Three blocks. Dimensionless Temperature


Re = 100 Re = 750 Re = 1000 Re = 1500 Re = 2000

2.5 2 1.5 1 0.5 0 A

B

C

DE F

G

HI

J

K

LM

HI

J

K

L

(b) s = 0.5 - Three blocks. 3

3

G

X/L

X/L

N

O

PQ R

S

TU

V

W

Re = 100 Re = 750 Re = 1000 Re = 1500 Re = 2000

2.5 2 1.5 1 0.5 0

X

A

B

C

DE F

G

HI

J

K

LM N

O

PQ R

S

TU V

W X

X/L

X/L

(c) s = 0.5 - Six blocks.

(d) s = 1.0 - Six blocks.

Fig. 6. Numerical predictions of dimensionless wall temperature. Generally, temperature increases on all surfaces as Re decreases. The differences of the temperature values for the range of Re from 750 to 2000 are much smaller than the temperature differences for Re from 100 to 750. An interesting remark is that, for the six-block arrangement, Re = 100, and s = 1.0, θ varies almost linearly on the top surfaces of the blocks from the first to the last block. Maximum values of θ are always

9

found on the side walls of the blocks. Thus, the most critical overheating points are located on the side walls of blocks rather than on the top surfaces. Figure 7 illustrates the variation of the maximum dimensionless temperature (θmax) with Reynolds number 2.6 2.4 2.2 2 1.8 1.6 1.4 1.2 1 0.8 0.6 0.4 0.2

MaximumDimensionless Temperature


(Re) for different blocks.

Block (1) Block (2) Block (3) 0

250

500

750 1000 1250 1500 1750 2000

2.6 2.4 2.2 2 1.8 1.6 1.4 1.2 1 0.8 0.6 0.4 0.2

Block (1) Block (2) Block (3)

0

250

Reynolds Number

250

500

(b) s = 0.5 – Three blocks. MaximumDimensionless Temperature


Block Block Block Block Block Block

0

750 1000 1250 1500 1750 2000

Reynolds Number

(a) s = 0.25 – Three blocks. 2.6 2.4 2.2 2 1.8 1.6 1.4 1.2 1 0.8 0.6 0.4 0.2

500

(1) (2) (3) (4) (5) (6)

750 1000 1250 1500 1750 2000

Reynolds Number

2.6 2.4 2.2 2 1.8 1.6 1.4 1.2 1 0.8 0.6 0.4 0.2


0

250

500

(1) (2) (3) (4) (5) (6)

750 1000 1250 1500 1750 2000

Reynolds Number



Fig. 7. Numerical prediction of dimensionless maximum temperature as a function of Reynolds number. As can be seen in Figs. 7a and 7b, block (1) has the lowest values of θmax for all Reynolds numbers. Blocks (2) and (3) have almost equal values of θmax. Thus, the second and third blocks in three-block arrangement are more subjected to overheating. Figure 7c demonstrates that blocks (5) and (6) have the largest values of θmax from Re = 100 to 550. However, for Re = 550 to 2000, block (4) has the largest value of

θmax. Over the whole range of Re, block (1) has the lowest values of θmax. These dramatic changes of θmax over blocks with Re can be attributed to the changes of flow field as seen in Figs. 5a and 5b for s = 0.5. Figure 7d shows that blocks (5) and (6)

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have the largest values of θmax for Re between 100 and 750. Then, blocks (3) and (6) have the largest values of θmax for Re between 750 and 2000. Block (1) has the lowest

θmax for Re = 100 to 750. Then, block (4) has the lowest value of θmax for Re between 750 and 2000. Comparing Figs. 7a, 7b, 7c, and 7d, it is clear that the values and locations of θmax depend on a combination of many parameters, namely: (i) number of blocks in the arrangement, (ii) block order, (iii) Reynolds number, and (iv) gap

26 24 22 20 18 16 14 12 10 8 6 4 2 00


250

500

Mean Nusselt Number

Mean Nusselt Number

between blocks. Generally, θmax decreases with the increase of Re and gap (s).

750 1000 1250 1500 1750 2000

26 24 22 20 18 16 14 12 10 8 6 4 2 0


0

250

Reynolds Number

0

250

500

(b) s = 0.5 – Three blocks.

(1) (2) (3) (4) (5) (6)

Mean Nusselt Number

Mean Nusselt Number


750 1000 1250 1500 1750 2000

Reynolds Number

(a) s = 0.25 – Three blocks. 26 24 22 20 18 16 14 12 10 8 6 4 2 0

500

750 1000 1250 1500 1750 2000

Reynolds Number

26 24 22 20 18 16 14 12 10 8 6 4 2 0


0

250

500

(1) (2) (3) (4) (5) (6)

750 1000 1250 1500 1750 2000

Reynolds Number



Fig. 8. Numerical predictions of mean Nusselt number. The variations of mean Nusselt number (Num) with Reynolds number for different blocks are shown in Fig. 8. The mean Nusselt number is found by numerical integration of local Nusselt number over the whole surfaces of the block. For all cases, block (1) has maximum Num. This means that block (1) has the best cooling in all

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cases. Num increases with Re for all blocks in all cases. For the three-block arrangement, block (3) has the minimum values of Num for all values of Re. This means that the last block (3) has the worst cooling. For six-block arrangement, Figs. 8c and 8d, block (5) has the lowest value of Num. This means that the most critical block for the design issue is block (5). Values of Num are considerably increased with the increase of the gap (s). 4.2 Experimental Results

Due to technical difficulties, only one block is heated and its position is altered from block (1) to block (6). To facilitate the temperature measurement and increase the accuracy of measurement, a higher temperature range was utilized in the experiments than in the numerical predictions. Measurements were restricted to the top surface only of the block. Figure 9 shows the temperature distributions with the eleven measuring positions along the model centerline with s = 1.0. Naturally, dimensionless temperature (θ) reaches the highest values for Re = 0.0 (natural convection). For all cases, at any measuring position, θ decreases as Reynolds number increases. For Re = 0.0, and 787, maximum values of θ are found on the heated third block. For Re = 1573 and 2060, maximum values of θ are found on the fourth heated block. When comparing Fig. 6d with Fig. 9, it is seen that very similar trends are found by both numerical predictions and experimental results for the distributions of temperature on the top surface of the blocks. Also, the present results compare very well to others’ (e.g. Ref. [1]). In all cases, θ tends to decrease near the ends of the top surface of the block. Figure 10 compares the temperature distributions along the three lines of measurements for Re = 787 and 2060. In all the six cases (Not all shown), the values of θ along the side lines are greater than those along the centerline especially for Re = 2060. This may be attributed to the concentration of cooling in the middle section of the block. Side vortices along the side surfaces of the block reduce the cooling rate along the side measuring lines. Thus, three-dimensional investigations are very important when design is based on the maximum temperature.

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1.4

D im ensionless Tem perature

D im ensionless T em perature

1.4 1.2 1 0.8 0.6

Re = 0.0 Re = 1573

0.4

Re = 787 Re = 2060

1.2

0

Re = 1573

Re = 2060

1 0.8 0.6 0.4

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

0

1

0.1

0.2

Measuring Position (X/l)

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0.9

1

0.9

1


(a) First block is heated.

(b) Second block is heated. 1.4


1.4


Re = 787

0.2

0.2

1.2 1 0.8 0.6

Re = 0.0 Re = 1573

0.4

Re = 787 Re = 2060

0.2

1.2 1 0.8 0.6

Re = 0.0 Re = 1573

0.4

Re = 787 Re = 2060

0.2 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0

0.1

0.2


0.3

0.4

0.5

0.6

0.7

0.8


(c) Third block is heated.

(d) Fourth block is heated. 1.4


1.4


Re = 0.0

1.2 1 0.8 0.6

Re = 0.0 Re = 1573

0.4

Re = 787 Re = 2060

0.2

1.2 1 0.8 0.6

Re = 0.0 Re = 1573

0.4

Re = 787 Re = 2060

0.2 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8



(e) Fifth block is heated.

(f) Sixth block is heated.

Fig. 9. Experimental measurements of dimensionless wall temperature along the block centerline for the arrangement of six blocks at different Reynolds numbers: s = 1.0. 5. ARTIFICIAL NEURAL NETWORKS (ANN) 5.1 ANN Architecture

Two artificial neural networks (ANN) were used to predict the values of the mean Nusselt number (Num) of the blocks for the three- and six-block arrangements. The Neural Network Toolbox of the Matlab 6.1 package [14] was chosen to train the ANNs.

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1.4



1.4 1.2 1 0.8 0.6 0.4

Re = 787 : Right-Line

Re = 2060 :Right-Line

Re = 787 : Center-Line

Re = 2060 : Center-Line

Re = 787 : Left-Line

Re = 2060 : Left-Line

0.2

1.2 1 0.8 0.6 Re = 787 : Right-Line Re = 787 : Center-Line Re = 787 : Left-Line

0.4

Re = 2060 : Right-Line Re = 2060 : Center-Line Re = 2060 : Left-Line

0.2 0

0.2

0.4

0.6

0.8

1

0


0.2

0.4

0.6

0.8

1


(a) First block is heated.

(b) Third block is heated.

Fig. 10. Comparisons of experimental measurements of dimensionless wall temperature along three measuring lines at two Reynolds numbers: s = 1.0, six blocks. Each ANN consisted of two layers (a hidden layer and an output layer) with the “Back Propagation Learning Rule”, Fig. 11. Each ANN has three input vectors (Reynolds number (Re), gap (s) and block order (1, 2, …, 6)) and one output vector (Num). The transfer function “purlin” was used for the output layer. Each ANN was trained for 50 different cases. Training proceeds until the ANN reaches a certain sumsquared error goal (0.01). After the ANNs have been trained, a separate set of unseen test patterns was supplied as input to the ANNs and their performance was evaluated. After determining the optimum architecture for each ANN, the two ANNs were used to predict the values of Num for some cases that have not been predicted numerically. 5.2 Results of ANNs

Figure 12 shows the number of training epochs for different numbers of neurons (S1) and two types of transfer function in the hidden layer of the two neural networks. An epoch is the presentation of the set of training (input and/or target) vectors to a network and the calculation of new weights and biases. It is seen that, for the logsig transfer function, the number of training epochs for the six-block arrangement is much more than the training epochs of the three-block arrangement. This indicates that the training of the six-block arrangement is much tougher than the three-block arrangement. An opposite situation is noticed for the tansig transfer function.

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Number of Training Epochs

120000 100000

Three IC Components (Blocks) Six IC Components (Blocks)

80000 60000 40000 20000 0 S1=500 logsig

S1=600 logsig

S1=700 logsig

S1=800 logsig

S1=500 tansig

S1=600 tansig

S1=700 tansig

S1=800 tansig

Number of Neurons and Type of Transfer Function in the Hidden Layer

Fig. 11. The back-propagation of two-layer network [14].

Fig. 12. The number of training epochs for different numbers of neurons.

Table 1. The cases used to test the artificial neural network (ANN). (a) 3-block arrangement. (b) 6-block arrangement. 0.25 0.25 0.5 0.5 Gap 1 1 2 1 Block No. 750 2000 1000 1500 Re 8.2 12.57 8 14.63 Num

0.5 Gap 1 Block No. 750 Re 11.3 Num

0.5 3 1000 7.51

1.0 4 1000 9.5

1.0 6 1500 10.3

For the latter transfer function, the number of epochs of the six-block arrangement is less than those of the three-block arrangement. Generally, the number of epochs of the tansig transfer function is much less than those of the logsig transfer function. Table 1 gives the numerical cases that were used to test the two ANNs for three- and six-block arrangements, respectively. Figure 13 shows the results of the testing for many training cases for three- and six-block arrangements, respectively. The best results are obtained for the logsig transfer function with S1 = 800 for the two ANNs. Figure 14 illustrates the sum-squared error and learning rate of the ANN of the three-block arrangement for S1 = 800. Table 2 shows the predictions of ANNs for completely new cases that were not calculated numerically for three- and six-block arrangements, respectively. This is the powerful advantage of ANN. Once it is well trained, predictions of new cases can be carried out with minimum computational effort and run-time. Moreover, ANNs can be used to predict other important parameters (e.g. θmax).

15

Neural Results

14 12

14

S1=500-logsig S1=600-logsig S1=700-logsig S1=800-logsig S1=500-tansig S1=600-tansig S1=700-tansig S1=800-tansig

13

Neural Results

16

10 8

12 11

S1=500-logsig S1=600-logsig S1=700-logsig S1=800-logsig S1=500-tansig S1=600-tansig S1=700-tansig S1=800-tansig

10 9 8 7

6 6

8

10

12

14

Numerical Predictions

6 6

16

(a) 3-block arrangement.

8

10

12

Numerical Predictions

(b) 6-block arrangement.

Fig. 13. Results of the testing for many training cases.

(a) logsig transfer function.

(b) tansig transfer function.

Fig. 14. The sum-squared error and learning rate of the artificial neural network, three-block arrangement, S1 = 800. Table 2. ANN predictions of the mean Nusselt number for completely new cases. (a) 3-block arrangement. 0.25 Gap 1 Block No. 120 Re 3.36 Num

0.3 2 900 5.98

(b) 6-block arrangement. 0.5 0.7 Gap 1 3 Block No. 130 800 Re 4.93 7.364 Num

0.5 3 1500 7.92

16

1.0 6 1800 9.64

14

6. CONCLUSIONS

A numerical and experimental investigation was carried out to study the flow and thermal fields of two arrangements of IC components. Neural networks were also utilized to predict the values of mean Nusselt number of each IC component. From the above discussions, the following points can be concluded: 1- The present numerical predictions compare (qualitatively) very well to the experimental results that were obtained by the authors. 2- For solving such viscous flows using the finite element technique, careful clustering should be applied next to the solid boundaries for accurate prediction of both the flow and thermal fields. 3- Heat transfer from the block arrangement is greatly affected by the combined effect of: (i) Reynolds number, (ii) gap, (iii) block order, and (iv) number of blocks. 4- The thermal field on and around the IC components is mainly affected by the characteristics of the flow field around them. 5- Maximum temperatures on all blocks are found on the side surfaces of the blocks. However, values of θmax decrease as Reynolds number increases. 6- For the three-block arrangement, maximum values of θmax are found on both blocks (2) and (3). 7- For the six-block arrangement and s = 0.5, the highest values of θmax are found on the fifth and sixth blocks for Re between 100 and 550. Then, for Re between 550 and 2000, the highest values of θmax are found on the fourth block. 8- For the six-block arrangement and s = 1.0, the highest values of θmax are found on the fifth and sixth blocks for Re between 100 and 750. Then, for Re between 750 and 2000, the highest values of θmax are found on the third block. 9- For six-block arrangement, minimum temperature values are obtained near the ends of the top surface of the block.

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10- The values of the mean Nusselt number (Num) on all IC components increase with increasing both the Reynolds number (Re) and the gap between the blocks (s) for both the three- and six-block arrangements. 11- For the three-block arrangement, the highest values of Num are found on the first block. The lowest values are found on the last (third) block. 12- For the six-block arrangement, the highest values of Num are found on the first block, and the lowest values are found on the fifth block. 13- The three-dimensional measurements showed that, on the top surface, the temperature values on the side lines (near the block side edges) are greater than the temperature values along the centerline. Thus, three-dimensional investigations are essential for thermal-reliable design. 14- The performance of ANN depends greatly on its architecture. Careful design and testing of ANN should be carried out to get the optimum design of ANN. 15- The values of Num that were predicted numerically and by ANNs are very close to each other. Thus, ANN is an effective tool in predicting the thermal parameters such as Num and/or θmax. REFERENCES

1. Davalath, J., and Bayazitoglu, Y., “Forced Convection Cooling Across Rectangular Blocks”, J. Heat Transfer, Vol. 109, pp. 321-328, 1987. 2. Nakajima, M., Yanaoka, H., Yoshikawa, H., and Ota, T., “Numerical Simulation of Three-Dimensional Separated Flow and Heat Transfer around an Array of SurfaceMounted Rectangular Blocks in a Channel”, Proceedings of ASME 2000 Fluids Engineering Division Summer Meeting, Boston, USA, June 11-15, 2000. 3. Majumdar, D., and Amon, C. H., “Oscillatory Momentum Transport Mechanisms in Transitional Complex Geometry Flows”, J. Fluids Eng., Vol. 119, pp. 29-35, 1997. 4. Liou, T.-M., and Chen, S.-H., “Turbulent Flow Past an Array of Bluff Bodies Aligned along the Channel Axis”, J. Fluids Eng., Vol. 120, pp. 520-529, 1998. 5. Gavalis, S., Karki, K. C., Patankar, S. V., and Miura, K., “Effect of Heat Sink on Forced Convection Cooling of Electronic Components: a Numerical Study”, Proceedings of ASME Int. Electronics Packaging Conference, Binghamton, NY, USA, 1993. 6. Malhammar, A., “Cooling Efficiency Concept-A Tool for Fast Thermal Analysis of PCBs”, Circuit World, Vol. 19, No. 3, pp. 46-48, 1993.

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7. Olivos, T., and Majumdar, P., “Computational Model for Forced Convection Cooling in Electronic Components”, J. Electronics Manufacturing, Vol. 5, No. 3, pp. 183-192, 1995. 8. Ilegbusi, O. J., “Calculation of Force-Air Cooling of Electronic Modules with A Two-Fluid Model of Turbulence”, J. Electronic Packaging, Vol. 118, No. 4, pp. 250257, 1996. 9. Sridhar, S., Faghri, M., Lessmann, R. C., and Schmidt, R., “Heat Transfer Behavior Including Thermal Wake Effects in Forced Air Cooling of Arrays of Rectangular Blocks”, Thermal Modeling and Design of Electronic Systems and Devices, ASME Heat Transfer Division, Vol. 153, pp. 15-26, 1990. 10. Lehmann, G. L., and Pembroke, J., “Forced Convection Air Cooling of Simulated Low Profile Electronic Components. Part 1. Base Case”, J. Electronic Packaging, Vol. 113, No. 1, pp. 21-26, 1991. 11. Lehmann, G. L., and Pembroke, J., “Forced Convection Air Cooling of Simulated Low Profile Electronic Components. Part 2. Heat Sink Effects”, J. Electronic Packaging, Vol. 113, No. 1, pp. 27-32, 1991. 12. Carlos, A. C. A., and Luciano, L. M., “Enhanced Convective Cooling of a PCB in a duct”, Proceedings of the Int. Intersociety Electronic packaging Conference, Part 2, Maui, Hi, USA, 1994. 13. Tou, K. W., Xu, G. P., and Tso, C. P., “Direct Liquid Cooling of Electronic Chips by Single-Phase Forced Convection of FC-72”, J. Experimental Heat Transfer, Vol. 11, No. 2, pp. 121-134, 1998. 14. Demuth, H., and Beale, M., “Neural Network Tool box – For Use with Matlab, User’s Guide V. 4”, The Math Works, Inc., 2001. LIST OF SYMBOLS B1 & B2 = biases of first and second ANN layers, respectively. Cp = pressure coefficient = P/( 0.5×ρ ×Uo ×Uo) F1 & F2 = transfer function of the first and second ANN layers, respectively. H & h = heights of channel and component (block), respectively. L & ℓ = streamwise lengths of channel and block, respectively. Lin & Lout = length of plate upstream and downstream of the blocks, respectively. Nu & Num = local and mean values of Nusselt number (α h/λ), respectively. P & p = dimensional and non-dimensional (P/(ρ ×Uo ×Uo)) pressures, respectively. Pr = Prandtl number. qw = heat flux. R = input to the ANN. Re = Reynolds number = Uo H/ν. S = streamwise block space. S1 & S2 = number of neurons in the ANN first and second layers, respectively. s = non-dimensional streamwise block space (gap) = S/ℓ. T & To = local and upstream temperatures, respectively. U & Uo = local and upstream streamwise mean velocities, respectively. u & v=non-dimensional streamwise (U/Uo) and normal velocity components, respectively.

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‫‪W = spanwise length of channel.‬‬ ‫‪W1 & W2 = weights of the first and second ANN layers, respectively.‬‬ ‫‪w = spanwise length of block.‬‬ ‫‪X & x = dimensional and non-dimensional (X/h) streamwise coordinate, respectively.‬‬ ‫‪Y & y = dimensional and non-dimensional normal coordinate, respectively.‬‬ ‫‪Greek:‬‬

‫‪α = heat transfer coefficient = qw/(Tw – To).‬‬ ‫‪λ = thermal conductivity.‬‬ ‫‪ν = kinematic viscosity.‬‬ ‫‪ρ = density.‬‬ ‫‪θ = non-dimensional temperature = [(T – To) λ]/(qw h).‬‬ ‫‪Abbreviations:‬‬ ‫‪ANN = Artificial Neural Network.‬‬ ‫‪DNS = Direct Numerical Simulation.‬‬ ‫‪IC & PC = Integrated and Printed Circuit, respectively.‬‬ ‫‪Subscripts:‬‬ ‫‪in = inlet to IC components.‬‬ ‫‪max = maximum.‬‬ ‫‪o = upstream flow.‬‬ ‫‪out = outlet from IC components.‬‬ ‫‪w = wall.‬‬

‫ﺩﺭﺍﺴﺔ ﺭﻗﻤﻴﺔ ﻭﺒﺎﺴﺘﺨﺩﺍﻡ ﺍﻟﺸﺒﻜﺎﺕ ﺍﻟﻌﺼﺒﻴﺔ ﻟﻠﺴﺭﻴﺎﻥ ﻭﺍﻨﺘﻘﺎل ﺍﻟﺤﺭﺍﺭﺓ‬ ‫ﺨﻼل ﻤﺼﻔﻭﻓﺔ ﻤﻥ ﻤﻜﻭﻨﺎﺕ ﺍﻟﺩﻭﺍﺌﺭ ﺍﻟﻤﺘﻜﺎﻤﻠﺔ‬ ‫ﺘﻬﺘﻡ ﻫﺫﻩ ﺍﻟﺩﺭﺍﺴﺔ ﺒﺎﻟﺴﺭﻴﺎﻥ ﺍﻻﻨﺴﻴﺎﺒﻲ ﻭﺍﻻﻨﺘﻘﺎل ﺍﻟﺤﺭﺍﺭﻱ ﺨﻼل ﻤﺼﻔﻭﻓﺔ ﻤﻥ ﺍﻟﻜﺘل ﺍﻟﻤﺴﺘﻁﻴﻠﺔ ﺍﻟﺸـﻜل‬

‫ﻭﺍﻟﺘﻰ ﺘﻤﺎﺜل ﻤﺼﺎﺩﺭ ﺤﺭﺍﺭﻴﺔ ﻤﺤﺩﺩﺓ ﻋﻠﻰ ﺃﻟﻭﺍﺡ ﻤﺘﻭﺍﺯﻴﺔ ﻜﻤﺎ ﻫﻭ ﺍﻟﺤﺎل ﻓﻲ ﻤﻜﻭﻨﺎﺕ ﺍﻟﺩﻭﺍﺌﺭ ﺍﻟﻤﺘﻜﺎﻤﻠﺔ‪ .‬ﻭﺘﻌﺘﻤـﺩ‬

‫ﻫﺫﻩ ﺍﻟﺩﺭﺍﺴﺔ ﻋﻠﻰ ﺍﻟﻤﺸﺎﺒﻬﺔ ﺍﻟﺭﻗﻤﻴﺔ ﻭﺍﻟﻌﻤﻠﻴﺔ ﻟﻤﺠﻤﻭﻋﺘﻴﻥ ﻤﻥ ﺜﻼﺜﺔ ﻭﺴﺘﺔ ﻜﺘل ﻤﺘﺸﺎﺒﻬﺔ ﻤﺘﺭﺍﺼﺔ ﻓﻲ ﺼﻑ ﻭﺍﺤﺩ‪.‬‬

‫ﻭﻗﺩ ﺘﻤﺕ ﺍﻟﺩﺭﺍﺴﺔ ﺍﻟﺭﻗﻤﻴﺔ ﺒﺎﺴﺘﺨﺩﺍﻡ ﺒﺭﻨﺎﻤﺞ ‪ ANSYS 5.4‬ﺍﻟﻤﻌﺘﻤﺩ ﻋﻠﻰ ﻁﺭﻴﻘﺔ ﺍﻟﻌﻨﺎﺼﺭ ﺍﻟﻤﺤـﺩﺩﺓ‪ .‬ﻜﻤـﺎ ﺘـﻡ‬ ‫ﺍﺴﺘﺨﺩﺍﻡ ﻨﻔﻕ ﻫﻭﺍﺀ ﻟﻠﺩﺭﺍﺴﺔ ﺍﻟﻌﻤﻠﻴﺔ ﻟﺤﺎﻟﺔ ﺴﺘﺔ ﻜﺘل ﻤﺘﺭﺍﺼﺔ ﻓﻲ ﺼﻑ ﻭﺍﺤﺩ‪ .‬ﻜﻤﺎ ﺍﺴﺘﺨﺩﻤﺕ ﺍﻟﺸﺒﻜﺎﺕ ﺍﻟﻌﺼـﺒﻴﺔ‬ ‫ﻟﻠﺘﻨﺒﺅ ﺒﻘﻴﻡ ﻤﻌﺎﻤل ﻨﺎﺴﻠﺕ ﺍﻟﺤﺭﺍﺭﻱ ﻟﻤﻜﻭﻨﺎﺕ ﺍﻟﺩﺍﺌﺭﺓ ﺍﻟﻤﺘﻜﺎﻤﻠﺔ‪ .‬ﻭﺒﻨﺎﺀ ﻋﻠﻰ ﻫﺫﻩ ﺍﻟﺩﺭﺍﺴﺔ ﺘﻡ ﺍﺴﺘﺨﻼﺹ ﻤﺠﻤﻭﻋـﺔ‬ ‫ﻤﻥ ﺍﻟﻨﺘﺎﺌﺞ ﻭﺍﻻﺴﺘﻨﺘﺎﺠﺎﺕ ﺍﻟﻤﻔﻴﺩﺓ ﻓﻲ ﻋﻤﻠﻴﺎﺕ ﺍﻟﺘﺼﻤﻴﻡ ﺍﻟﺤﺭﺍﺭﻱ ﻟﻤﻜﻭﻨﺎﺕ ﺍﻟﺩﻭﺍﺌﺭ ﺍﻟﻤﺘﻜﺎﻤﻠﺔ‪.‬‬

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