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Thermal Response of Electronic Assemblies during Forced -Infrared Reflow Soldering in an Oven with Air Injection∗

Young-Seok SON∗∗ and Jee-Young SHIN∗∗∗

The thermal response of electronic assemblies during forced convection-infrared reflow soldering is studied numerically. Soldering for attaching electronic components to printed circuit boards is performed in a process oven that is equipped with porous panel heaters, through which air is injected in order to dampen temperature fluctuations in the oven. Forced convection-infrared reflow soldering process with air injection is simulated using a two- dimensional numerical model. The multimode within the reflow oven as well as within the electronic assembly is simulated. Parametric study is also performed to study the effects of various conditions such as conveyor speed, air injection velocity, and electronic as- sembly emissivity on the thermal response of electronic assemblies. The results of this study can be used in the process oven design and selecting the oven operating conditions to ensure proper solder melting and solidification.

Key Words: Numerical Analysis, Thermal Response, Electronic Assembly, Forced Convection-Infrared Reflow Soldering, Air Injection, Parametric Study

is equipped with infrared panel heaters. The energy from 1. Introduction panel heaters to the card assembly melts the solder, and Recently, electronic equipments are under rapid then the electronic components are attached to the PCB progress with the electronic components being developed permanently by solidifying the solder in the cooling zone toward the trend of small size, high performance, and high near the oven exit. density. Therefore, reliable high-density mount technol- ogy is required to attach many electronic components on the limited area of printed circuit board (PCB). To meet this requirement, surface mount technology (SMT) where soldering is performed on the surface is widely used re- cently(1), (2). Infrared reflow soldering has been a common technique used in SMT, but it is recently known that forced convection-infrared reflow soldering is easier to control heating and cooling of the electronic assemblies(3). Figure 1 shows schematic of infrared reflow ovens. (a) In a conventional infrared reflow oven shown in Fig. 1 (a), unsoldered card assemblies are supported at their edges by a conveyor, which moves them through the oven that

∗ Received 7th March, 2005 (No. 05-5026) ∗∗ Department of , Dong-Eui Uni- versity, 995 Eomgwangno, Busanjin-Gu, Busan 614–714, Korea. E-mail: [email protected] (b) ∗∗∗ Department of Mechanical Engineering, Dong-Eui Uni- versity, 995 Eomgwangno, Busanjin-Gu, Busan 614–714, Fig. 1 Schematic of (a) a conventional infrared reflow oven and Korea (b) a forced convection-infrared reflow oven

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This study is concerned with the forced convection- thermal response of electronic assemblies during forced infrared reflow oven shown in Fig. 1 (b). In this modi- convection-infrared reflow soldering in an oven with fied oven that has porous panel heaters instead of infrared air injection are predicted numerically using a two- panel heaters, the process air is introduced to, and ex- dimensional (2D) model. The advantage of forced tracted from the oven through porous panel heaters. In convection-infrared reflow soldering is identified by com- this scheme each card assembly will be subject to simulta- paring the results with those of conventional infrared re- neous radiative and convective heating and cooling, which flow soldering. The effects of oven operating conditions is not inherent in the design of Fig. 1 (a). Therefore, lo- and property of electronic assembly on the thermal re- cal excessive heating that is the main weakness of the sponse of electronic assemblies are also analyzed. conventional infrared reflow oven could be prevented by Nomenclature the additional convection effect. Moreover, selective up- flow or downflow can establish augmenting inertial and e : emissivity buoyancy forces within the oven air. This augmentation, k : thermal conductivity [W/m·K] in turn, may stabilize the air flow, which might minimize Q : heat transfer rate per unit length [W/m] product temperature fluctuation during soldering through T : temperature [K] conjugate interaction. V : velocity [m/s] Even though experimental studies on the thermal as- x : horizontal coordinate pects of the electronic components during infrared reflow y : vertical coordinate soldering process have been performed(4) – (6), heat trans- Subscripts fer mechanism related to thermal behavior has not been b : blowing (injection) closely examined. It has been required that the develop- c : conveyor ment of a numerical model that can predict thermal re- conv : convection sponse of various electronic assemblies in various pro- rad : radiation cesses because electronic packaging and soldering tech- 2. Analysis nique are under rapid progress. A simple numerical model which predicts thermal response of a electronic assem- 2. 1 Numerical model bly during infrared reflow soldering using radiative heat In this study, the flow in a forced convection-infrared transfer effect and convective heat transfer correlations has reflowovenwithairinjectionisassumedtobe2Dbycon- been developed(7), (8). To improve inaccuracy of the sim- sidering a simply populated board which consists of uni- ple model, a detailed numerical model which predicts heat form rows of electronic components. The first thing to be transfer characteristics by solving conduction, convec- considered in the geometrical modeling of the oven and tion, and radiation heat transfer equations has been devel- the card assembly is the relevant length scale. The length oped(9), (10), and analysis using this numerical model has of a typical infrared reflow oven is several meters, but that been performed(11). A numerical study reflecting the effect of solder in a card assembly which connects the lead of of forced convection by attaching a only near the exit a electronic component and PCB is several millimeters. of the infrared reflow oven has been performed(12).How- Since relevant length scales span approximately three or ever, comprehensive analyses on the forced convection- four orders of magnitude in a geometrical model, it is im- infrared reflow soldering process and the effect of the op- possible to resolve local solder temperatures by applying erating conditions on the thermal response of the elec- a single model to the entire oven or excessive computation tronic assemblies have not been performed sufficiently yet. time is required due to the tremendous number of meshes It is important to control the temperature in the oven in order to resolve local solder temperatures accurately. during reflow soldering process in order to achieve re- To solve this problem, two models, oven model and card liable soldering and to minimize thermally-induced card model, are introduced in this study. The oven model pre- assembly stresses which can cause lead-solder misalign- dicts the large scale velocity and temperature distributions ment and card assembly damage. The thermal response of within the oven, while the card model uses the results of the card assembly depending on the oven operating con- the oven model and estimates the small scale thermal re- ditions, which is governed by three coupled heat transfer sponse of a typical card assembly(10). modes of conduction, convection, and radiation, must be Figure 2 shows the oven and card models used in provided for proper thermal control. Especially stabiliza- the forced convection-infrared reflow soldering. The oven tion of air flow and minimization of temperature fluctu- model shown in Fig. 2 (a) does not account for the detailed ation in the oven by forced convection effect should be geometric features of the card assembly, but assumes a confirmed and the thermal response of the card assembly plane slab whose dimensions and thermophysical proper- should be predicted. ties are equivalent to those of the actual populated card as- In this study, heat transfer characteristics and the sembly. By defining effective thermophysical properties,

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Table 1 Velocities of injecting air at porous panel heaters (mm/s)

(a)

conduction equation(13),anda2Ddifferential, diffuse-gray radiative exchange analysis(14) are applied to the inside of the oven and card model domain shown in Fig. 2. The top and bottom panels of the forced convection- (b) infrared reflow oven with air injection are composed of 6 porous panel heaters, and each panel is 300 mm long Fig. 2 Coordinate system and geometry used in (a) the oven with an surface radiative emissivity of 0.95. The size of model and (b) the card model for the forced convection- the oven and the temperature distributions of the porous infrared reflow oven panel heaters are shown in Fig. 2 (a), and specific temper- atures used are based upon actual values taken from in- consistent oven and card model predictions can be gener- dustry. The unsoldered card assembly at 300 K enters the ated. The oven model predicts the large scale thermal re- oven at a velocity of 6 mm/s. The surfaces of the extended sponse in the oven, and generates the velocity and temper- domains at the inlet and outlet of the oven model are held ature boundary conditions for the card model as it moves at 300 K and are impermeable. through the oven. The oven model generates instantaneous The air injection velocities of inflow and outflow air velocity and temperature distributions throughout the through each porous panel heater are listed in Table 1, and computational domain of the oven, in addition to the distri- the temperatures of the injected air are the same as those of bution along the vertical planes located at the plane card’s the porous panel heaters shown in Fig. 2 (a). Three cases leading and trailing edges of the plane card. are considered in this study: air injection up, air injection The card model shown in Fig. 2 (b) accounts for the down, mixed air injection(air injection down in the up- actual card assembly geometry in a 2D fashion. The card stream half of the oven and air injection up in the down- model uses the predictions of the oven model as boundary stream half of the oven). conditions, along with the temperature and velocity distri- 2. 3 Numerical method butions of the porous panel heater in the oven, to estimate The continuity, Navier-Stokes, and energy equations heat transfer characteristics in the card assembly. The card are solved numerically using a finite volume method(15). model predicts the small scale thermal response such as The continuity equation is utilized to develop pressure temperature and velocity distributions around the card as- and pressure correction equations following the SIMPLEC sembly, heat transfer rates and temperature distribution in algorithm(16). The discretized equations are solved us- the card assembly, and solder melting and solidification. ing the ADI method in conjunction with the TDMA al- 2. 2 Governing equations and boundary conditions gorithm. The 2D differential diffuse-gray radiation heat The thermal response of electronic assemblies in an transfer equation is solved by subdividing each surface infrared reflow soldering oven with air injection is gov- into smaller elements having the same size as used in erned by three coupled heat transfer modes of conduction, the discretization of the Navier-Stokes and energy equa- convection, and radiation. The oven and card models use tions. The resulting simultaneous equations are solved nu- conservation of mass, momentum, and energy principles merically using a successive over-relaxation technique(14). to determine the air velocity and temperature distributions Additional terms associated with the net surface radia- within the oven as well as the thermal response of the card tion heat flux and variable property effects are included assembly. The 2D transient, compressible, variable prop- as sources in the discretized equations. erty Navier-Stokes and energy equations, the 2D transient Since the problem is characterized by a relatively

JSME International Journal Series B, Vol. 48, No. 4, 2005 868 complex geometry with moving surfaces, a collocated grid shown in Fig. 1 (a) and (b) air injection up in the forced is used to aid in tracking the numerical solution. Use of a convection-infrared reflow soldering oven with air injec- collocated grid requires momentum interpolation to deter- tion as shown in Fig. 1 (b) and (c) air injection down, and mine interfacial values of the conserved variables. (d) mixed air injection(air injection down in the upstream The 2D numerical model and solution algorithm was half of the oven and air injection up in the downstream validated by comparing predictions with experimental half of the oven). The oven height has been expanded by data which was obtained from an experiment on measur- a factor of 10 for clarity. ing thermal response of discrete material in a horizontal In the conventional infrared reflow oven as shown in channel similar to infrared reflow oven shown in Fig. 1 (a). Fig. 3 (a), the isotherm distribution clearly reveals the role Agreement between predicted and measured material tem- of buoyancy with notable effects at the oven inlet and out- peratures was within 7% of the benchmark data(17). let. At the inlet of the oven, heating of the incoming cool Calculations have been performed with different air at the bottom section of the oven induces buoyancy meshes and time steps to select appropriate number of force in the vertical direction which causes plumes to em- meshes and time step guaranteeing accuracy and efficient anate away from the bottom panel heater. At the exit of the computation time. From the grid and time step indepen- oven, the air entering the oven is preheated by the warm dence studies, the mesh is chosen to be 528×56 (x×y)for card leaving the oven. Hence, the preheated air is cooled the oven model and 120 × 33 for the card model, and the at the top section of the oven maintained at low tempera- time step is set to 0.05 second. A uniform computational ture, and cold plumes descend from the top panel. Overall mesh is used in the x-direction, while smoothly variable temperature field reveals that temperature gradients near mesh dimensions decreasing near solid surfaces are used the inlet and exit of the oven are steep, but temperatures in the y-direction to enhance spatial resolution. become nearly uniform near the exhaust. In the forced convection-infrared reflow oven with air 3. Results and Discussion injection as shown in Fig. 3 (b) – (d), it can be seen that The thermal response of electronic assemblies dur- predictions for the upstream oven half are nearly identical ing forced convection-infrared reflow soldering in an oven in Fig. 3 (c) and (d) and conditions in the downstream half with air injection is predicted for the standard operating condition. Thermal characteristics according to the direc- tion of air injection are examined by comparing predic- tions with those during conventional infrared reflow sol- dering(10). Afterwards, the effects of changes in the op- erating conditions, such as conveyor speed, air injection velocity through the porous panel heaters of the oven, and (a) electronic assembly emissivity, on the thermal response of electronic assemblies are analyzed. As mentioned earlier, two models(oven and card model) are developed in this study, in which thermal prop- erties of a plane card and solder(8) used are given in Table 2. (b) 3. 1 Results for the standard operating condition Figure 3 shows predicted temperature distributions within the oven for the standard operating condition. In the figure, four different cases are shown: (a) the conven- tional infrared reflow soldering oven with top exhaust as (c) Table 2 Thermal properties of a plane card and solder

(d) Fig. 3 Predicted temperature distributions within the oven for (a) conventional processing, (b) air injection up, (c) air injection down, and (d) mixed air injection (16 equally- spaced isotherms spanning 300 to 590 K)

Series B, Vol. 48, No. 4, 2005 JSME International Journal 869 are similar in Fig. 3 (b) and (d). In each case, the cards are cool at the oven entrance relative to the surrounding air and adjacent panel heaters and are warm near the oven exit. Hence, cool high density plumes fall from the cards near the inlet of the oven, and warm low density plumes rise from the cards near the exit of the oven. By consid- ering air flow direction caused by in the oven, air is injected in the same direction of the buoy- ancy forces in the mixed air injection case as shown in Fig. 3 (d). That is, air is injected down in the upstream half of the oven and injected up in the downstream half of the oven. For the mixed air injection case, inertial force (a) by air injection augments buoyancy force adjacent to the card assembly, which results in the stabilization of the air flow in the oven. Figure 4 shows the predicted total convective and ra- diative heat transfer rates delivered to the card assembly as it moves through the reflow oven, in which x repre- sents the location of the card center in the oven. As shown in Fig. 4 (a), the thermal response of the card assembly is dominated by the radiation, and the maximum heat trans- fer occurs when the cold card enters the oven. Significant convective heating and cooling occurs at the front and tail of the oven, respectively. In a conventional infrared re- flow oven, an oscillatory behavior is the strongest near the (b) oven inlet and outlet due to the fluctuation of the temper- ature field caused by the buoyancy forces. This high fre- quency behavior fluctuates the convective heat transfer to the cards, which makes it difficult to control the thermal response of the card assembly during soldering process. The fluctuation of the convective heat transfer in a conventional infrared reflow oven is amplified or dimin- ished according to the direction of air injection through the porous panel heaters in a forced convection-infrared reflow oven. For the case where air is injected up as shown in Fig. 4 (b), the counteracting buoyancy and iner- tial forces adjacent to the card at small x (oven inlet) lead (c) to fluctuation in the air flow, which in turn induces strong variations in the convection heat transfer to the card as- sembly. However, the fluctuations in air flow and convec- tion heat transfer to the card assembly are damped at large x (oven exit) because air is injected to the same direction as the warm air rising from the card. In contrast, fluctuations are shifted to the oven exit as air is injected downward as shown in Fig. 4 (c), with the fluctuations at oven inlet damped. From these results, it is known that mixed air injection, with air injection down in the upstream half of the oven and air injection up in the downstream half of the oven, results in stabilized heating (d) and cooling of the card assembly as shown in Fig. 4 (d). Fig. 4 Predicted convective and radiative heat transfer rates to Therefore, mixed air injection makes it easy to control the the card assembly for (a) conventional processing, (b) thermal response of the card assembly. air injection up, (c) air injection down, and (d) mixed air injection

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3. 2 Results for the changes in the operating condi- tions As seen in the previous results for the standard oper- ating condition, forced convection-infrared reflow solder- ing with mixed air injection is the effective soldering tech- nique in terms of stabilization of air flow and temperature fields and easiness of thermal control of the card assembly. The effects of changes in the operating conditions on the thermal responses of electronic assemblies during forced convection-infrared reflow soldering with mixed air injec- tion are also analyzed. To analyze the sensitivity of ther- mal response of electronic assemblies to the oven operat- (a) ing conditions and card assembly emissivity, calculations are performed with changes in conveyor speed, air injec- tion velocity through the porous panel heaters, and card assembly emissivity. Figure 5 shows thermal characteristics of the card as- sembly for the changes in conveyor speed. The conveyor speed for the standard operating condition is 6 mm/s, and it is changed to 3 mm/s and 12 mm/s for the sensitivity study. As shown in Fig. 5 (a) and (b) representing convec- tive and radiative heat transfer rates delivered to the card assembly as it moves through the oven, the thermal re- sponse of the card assembly is dominated by the radiation, and the heat transfer rates to the card assembly increase as (b) the conveyor speed increases. When the conveyor speed is decreased to 3 mm/s, the card assembly temperature rises quickly due to the increased time of delivering heat to the card assembly. Therefore, air flow by natural convection rises from the card assembly before it travels the 3rd porous panel heater injecting air downward, which causes rapid fluctuation of convective heat transfer rate due to the counteracting buoyancy and inertial forces. In contrast, when the con- veyor speed is increased to 12 mm/s, the card assembly temperature rises slowly due to the decreased time of de- livering heat to the card assembly. This results in descend- ing air flow from the card assembly in the downstream half of the oven where air is injected up, which is the (c) opposite direction of the inertial force. Therefore, rapid Fig. 5 Effect of the variations in conveyor speed on (a) the fluctuation of convective heat transfer rate is shifted to the convective heat transfer rates, (b) radiative heat transfer downstream of the oven. It is obvious that, during forced rates, and (c) average card assembly temperatures convection-infrared reflow soldering with mixed air injec- tion, the direction and velocity of air injection should be adjusted appropriately according to the conveyor speed in is too slow (3 mm/s), however, the card assembly tempera- order to control the thermal response of the card assem- ture rises above the solder melting temperature beneath the bly by reducing fluctuations in the air flow and convective 2nd porous panel heater, a preheat zone, since too much heat transfer rate. heat is delivered to the card assembly. And then the solder As shown in Fig. 5 (c) representing the volume- is kept molten until it is solidified near the end of the oven, averaged card assembly temperature as it moves through which could lead to poor soldering and lead-solder mis- the oven, for the standard operating condition (conveyor alignment due to the thermal stress. When conveyor speed speed is 6 mm/s), the card assembly temperature reaches is too fast (12 mm/s), reflow soldering does not occur since the solder melting temperature (453 K) beneath the 5th the card assembly temperature does not reach the solder porous panel heater, a reflow zone. When conveyor speed melting temperature due to the insufficient time of deliv-

Series B, Vol. 48, No. 4, 2005 JSME International Journal 871 ering heat to the card assembly. Therefore, the appropriate study. As shown in Fig. 6 (a) and (b), as the air injection conveyor speed should be set for each new card assembly velocity increases, the convective heat transfer rate to the to assure reliable reflow soldering when setting operating card assembly increases slightly due to the increase of the conditions of a forced convection-infrared reflow oven. convection heat transfer coefficient, but the radiative heat Thermal characteristics of the card assembly for the transfer rate hardly changes. As shown in Fig. 6 (c), the changes in air injection velocity through the porous panel card assembly temperature in a forced convection-infrared heaters are shown in Fig. 6. The incoming air velocity reflow oven increases slightly due to the increase of the to the 1st porous panel heater at the bottom of the oven convective heat transfer rate as the air injection velocity for the standard operating condition is 56.5 mm/s, and it increases, even though the card assembly temperature is is changed to 28.25 mm/s and 113 mm/s for sensitivity still dominated by the radiation. To analyze the thermal responses of card assemblies to be soldered with various materials, sensitivity of the thermal characteristics of the card assembly to variations in card assembly emissivity is shown in Fig. 7. The card assembly emissivity for base case is 0.9, and it is changed as 0.8, 1.0 and 0.5. As shown in Fig. 7 (a) and (b), the convective heat transfer rate to the card assembly hardly changes as the card assembly emissivity changes, but the radiative heat transfer rate increases as the emissiv- ity increases. As shown in Fig. 7 (c), the card assembly temperature increases as the emissivity increases because the radiative heat transfer to the card assembly increases. For the standard oven operating conditions considered in this study, reflow soldering occurs when the emissivity is (a) higher than 0.8, however, when the emissivity is low as 0.5, reflow soldering does not occur since the card assem- bly temperature does not reach the solder melting temper- ature due to the insufficient radiative heat transfer to the card assembly. Therefore, the oven operating conditions such as conveyor speed, temperature and air injection ve- locity of the porous panel heaters should be set appropri- ately according to the card assembly emissivity in order to assure reliable soldering. 4. Summary and Conclusions In this study, the thermal response of electronic as- semblies during forced convection-infrared reflow solder- (b) ing in an oven with air injection was predicted by a two- dimensional numerical model. Forced convection heat- ing and cooling is established by selective injection of air through porous panel heaters. Simultaneous radiative and convective heating and cooling of the card assembly oc- curs, and fluctuations induced by buoyancy forces were diminished by inertial effects associated with the injec- tion. Therefore, local excessive heating that is the main weakness of the conventional infrared reflow oven could be prevented. From the analysis results for the standard operating condition, it is known that forced convection- infrared reflow soldering with mixed air injection, air in- jection down in the upstream half of the oven and air injec- (c) tion up in the downstream half of the oven, is the effective Fig. 6 Effect of the variations in air injection velocity on (a) the soldering technique in terms of stabilization of air flow convective heat transfer rates, (b) radiative heat transfer and temperature fields and easiness of thermal control of rates, and (c) average card assembly temperatures the card assembly.

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ations in the air flow and convective heat transfer rate. The surface temperature and thermal characteristics of the card assembly is affected by air injection velocity through the porous panel heaters, but the temperature change of the card assembly through the oven is small. The oven oper- ating conditions such as conveyor speed, temperature and air injection velocity of the porous panel heaters should be set appropriately according to the card assembly emissiv- ity because it is revealed as one of the dominant param- eters to assure reliable forced convection-infrared reflow soldering. The results of this study can be used in the design of (a) manufacturing equipment for this industry and the selec- tion of the appropriate oven operating conditions such as conveyor speed, temperature and air injection velocity of the porous panel heaters for each new card assembly hav- ing different shape and emissivity. This enables reliable soldering and contributes to maximizing production rates while minimizing the need for manual rework. Acknowledgments This study was supported by Dong-Eui University (Project number: 2004AA132). References ( 1 ) Capillo, C., Surface Mount Technology, (1990), (b) McGraw-Hill Publishing Co., New York. ( 2 ) Classon, F., Surface Mount Technology for Concurrent Engineering and Manufacturing, (1993), McGraw-Hill Publishing Co., New York. ( 3 ) Lau, J.H., Handbook of Fine Pitch Surface Mount Technology, (1994), Van Nostrand Reinhold, New York. ( 4 ) Lichtenberg, N.R. and Brown, L.L., Component Ther- mal Management in Infrared Solder Reflow, Inter- national Journal of Hybrid Microelectronics, Vol.10, No.2 (1987), pp.19–26. ( 5 ) Miura, H., Nishimura, A., Kawai, S. and Nakayama, W., Temperature Distribution in IC Plastic Packages in the Reflow Soldering Process, IEEE Transaction on Components, Hybrids, and Manufacturing Technology, Vol.11, No.4 (1988), pp.499–505. (c) ( 6 ) Fernandes, N.J., Bergman, T.L. and Masada, G.Y., Fig. 7 Effect of the variations in card assembly emissivity Thermal Effects during Infrared Solder Reflow—Part on (a) the convective heat transfer rates, (b) radiative I : Heat Transfer Mechanisms, ASME Journal of Elec- heat transfer rates, and (c) average card assembly tronic Packaging, Vol.114 (1992), pp.41–47. temperatures ( 7 ) Whalley, D.C., Ogunjimi, A., Conway, P.P. and Williams, D.J., The Process Modeling of the Infrared Reflow Soldering of Printed Circuit Board Assemblies, In a forced convection-infrared reflow soldering oven Journal of Electronics Manufacturing, Vol.2 (1992), with mixed air injection, the effects of changes in the op- pp.23–29. erating conditions and electronic assembly emissivity on ( 8 ) Eftychiou, M.A., Bergman, T.L. and Masada, G.Y., the thermal response of electronic assemblies were ana- Thermal Effects during Infrared Solder Reflow—Part lyzed. The conveyor speed is an important parameter to II : A Model of the Reflow Process, ASME Journal of assure reliable reflow soldering. Also the direction and Electronic Packaging, Vol.114 (1992), pp.48–54. ( 9 ) Son, Y.S., Bergman, T.L. and Masada, G.Y., Detailed velocity of air injection according to the conveyor speed Card Assembly Thermal Response during Infrared Re- should be adjusted appropriately in order to reduce fluctu-

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flow Soldering, Advances in Electronic Packaging, and Mass Transfer, 4th Ed., (1996), John Wiley & Sons Vol.4-2 (1993), pp.575–581. Inc., New York. (10) Son, Y.S., Heat Transfer Analysis of Infrared Reflow (14) Siegel, R. and Howell, J.R., Heat Soldering Process for Attaching Electronic Compo- Transfer, 3rd Ed., (1992), Hemisphere Publishing Co., nents to Printed Circuit Boards, Journal of Korean Washington, D.C. Welding Society, (in Korean), Vol.15, No.6 (1997), (15) Patankar, S.V., Numerical Heat Transfer and Fluid pp.591–601. Flow, (1980), Hemisphere Publishing Co., Washington, (11) Son, Y.S. and Shin, J.Y., Parametric Study on the Ther- D.C. mal Response of Electronic Components during In- (16) Van Doormaal, J.P. and Raithby, G.D., Enhancements frared Reflow Soldering, JSME Int. J., Ser. B, Vol.46, of the SIMPLE Method for Predicting Incompressible No.2 (2003), pp.308–315. Fluid Flows, Numerical Heat Transfer, Vol.7 (1984), (12) Kim, M.R., Choi, Y.K., Lee, G.B., Chung, I.Y., Kim, pp.147–163. J.D. and Lee, J.H., Thermal Investigation of Infrared (17) Bergman, T.L. and Son, Y.S., Mixed Convection in Reflow Oven with a Convection Fan, KSME Interna- Horizontal Channels with Discrete Material and Top tional Journal, Vol.12, No.5 (1998), pp.972–979. Exhaust, International Journal of Heat and Mass Trans- (13) Incropera, F.P. and DeWitt, D.P., Fundamentals of Heat fer, Vol.38, No.14 (1995), pp.2519–2527.

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