The importance of the heat transfer coefficient - Simulation of reflow soldering profiles: Possibilities and limitations

Measuring temperature profiles is still part of everyday business in the production of electronic assemblies. Although the software for measuring systems and reflow soldering systems is constantly improving, it is not yet possible to completely replace the manual measuring effort with a temperature simulation. This article aims to shed some light on why this is the case.

Introduction

Today, software tools use so-called confirmation runs, i.e. real temperature measurements on the assembly to be produced, to compare the data required for the temperature simulation. The use of AI, which draws on large databases to link material data, processing parameters etc. with the thermodynamic algorithms in order to create a precisely fitting new reflow soldering profile for the current assembly in a matter of seconds, remains a dream of the future. Adam et al [i] have taken a first step in this direction by linking a geometric model of the PCB with a numerical description of the heat transfer system (two digital twins). This software uses the 3D geometry of the assembly known from databases (ODB++ data: Layer structure and layout, drill holes, placement, SMD component description) as well as an existing tool for temperature simulation of reflow soldering systems.

1. thermodynamics or the interaction between reflow soldering system and assembly

With the help of thermodynamics (thermodynamics), we can describe the interaction between the reflow soldering system and the assembly. It is known from physics that heat is transported in the direction of the negative temperature gradient via the following mechanisms

• heat conduction (within a material)
• convection (heat transfer from one material to another) and
• thermal radiation (electromagnetic waves between opposing surfaces)

and thus strives for temperature equalization up to thermal equilibrium. The three mechanisms always work together (also in the reflow soldering system), any simplification must be understood as a compromise and requires good justification in order to describe the true processes sufficiently well with an idealized formula.

Tab. 1: Symbols used

Symbol	Parameter	Unit
	Heat flow	J/s = W
m	mass	kg
c	Specific heat capacity	J/kgK
ε	Emissivity, absorptivity	Without
Tm	Mean temperature of the radiation environment	K (273.15 K = 0 °C)
s	Stefan-Boltzmann constant	5.67*10-8 W /m2 K4
λ	Thermal conductivity	W/mK
TU	Ambient temperature, heating zone temperature	K
TK, TK0	Assembly temperature	K
TP	Maximum temperature at the measuring point	K
A,AK,AL	Area of the assembly, cross-sectional area	m²
t	time	s
τ	thermal time constant	s
DLP	Thickness of the printed circuit board	m
d	Length or distance	m
PK	Material density (total)	kg/m³
	Heat transfer coefficient, or mean W.	W/m²K

Nevertheless, we want to present a largely simplified view here. How the temperature profile in the reflow soldering process can be simulated with the help of a spreadsheet is described in the appendix.

Below are some equations and algorithms that are helpful in simulating temperature-time profiles and optimizing soldering parameters.

The interaction of the reflow soldering system as a supplier of heat with the assembly and its heat requirement can be described using the following relationships (1):

Therein are:

The temperature difference dT in (2), considered here as a derivative with respect to time t, is the difference (_TK - _TK0) between the temperature of the assembly after heating (e.g. soldering temperature) and the temperature before heating. It is assumed that complete temperature equalization has taken place within the thermal mass m⋅c. This condition is considered fulfilled if the dimensionless Biot number is significantly less than 1.

The Biot number describes the ratio of the temperature differences between the heat conduction λ in the volume V and the heat transfer via the surface A. The ratio of volume V to surface A of a printed circuit board is approximately half the thickness (D/2). In practice, Bi smaller than approx. 0.1 appears to be sufficient for a largely homogeneous temperature in the volume. This is fulfilled for a PCB thickness of approx. 1.5 mm with a thermal conductivity of approx. 0.5 W/mK and a heat transfer coefficient of approx. 70 W/m²K (reflow under convection). This means that thermal conduction can be neglected in many cases.

(_TU - _TK) in (3), on the other hand, is the difference between the environment, e.g. the heating gas of the reflow soldering system and the assembly. This shows that a heat transfer to the assembly can only take place if the temperature difference (_TU-TK) > 0, in general a driving temperature difference exists. If the driving temperature difference is set in relation to the transferred heat per unit area, a measure of the quality of the heat transfer is obtained, which is referred to as the heat transfer coefficient h; see Herwig [ii]. In other words, h describes the ability / efficiency of the reflow soldering system to transfer heat.

The solution of the differential equation (1) generally has the form (5):

The thermal time constant t summarizes the geometry and material data of the thermal mass (assembly) and the heat transfer characteristics (soldering system) in an idealized form. Accordingly, (5) is used to calculate the assembly temperature _TK at the end of a period t under constant conditions (heat transfer coefficient h = constant, ambient temperature_TU = constant), starting with _TK0 (initial temperature of the assembly at the beginning of the period t).

To illustrate the exponential function (5), after t = τ approx. 63 % of the original temperature difference has been reduced, and from t = 3⋅τ approx. 95 % of the thermal equilibrium is practically reached. By rearranging (5), the temperature of the environment (6) can be determined if a change in the temperature profile (t, _TK) is to be calculated under the given conditions of a reflow soldering system.

Typical heat transfer coefficients for different soldering processes have been determined by Poech [iii]. For convection reflow soldering systems, which transfer heat by means of heating gas, h can assume values in the range of 40 to approx. 80 W/m²K, for condensation reflow soldering systems (vapor phase) the values are around 300 W/m²K.

In purely mathematical terms, the derivation from (5) can be used to determine an average heat transfer coefficient (7), see Moschallski [iv].

This mean heat transfer coefficient can be understood as the mean value between the heated top and bottom of the assembly on the one hand, and as the mean value over time under sufficiently uniform ambient conditions (gas flow, temperature) on the other. A convection reflow soldering system in particular is not a heating cabinet with only one ambient temperature; it consists of several heating and cooling zones arranged one behind the other. This results in different temperature differences (_TU - _TK)1...n in each zone. The required heat results from the sum of the heat flows of all heating zones that act on the surface of the assembly per time unit (8):

The final temperature profile of the assembly (t, _TK)1...n along all zones results from the multiple application of (5), whereby the assembly initial temperature TK0_(n) in the respective zone corresponds to the final temperature TK_(n-1) in the preceding zone.

In a reflow soldering system, the heat absorbed by the assembly does not result exclusively from the primary energy source; in convection reflow soldering systems this is convection (flow of the heating gas), in vapor phase reflow soldering systems it is the latent heat of the working medium (e.g. Galden). There is always a small amount of radiation in the systems (9). However, it is difficult to separate this radiation component from the heat flow that reaches the assembly by 'natural convection'. Natural convection' is understood here to mean the state of stationary fan motors, i.e. no forced movement of the heating gas. According to Poech [iii], a heat transfer coefficient h of 5 to 10 W/m²K can be assumed in this state, to which a radiation component of a similar magnitude must be added, or even considerably more if radiators are installed in the system specifically for this purpose.

If the relationships (3) and (9) are combined with each other, a temperature-dependent heat transfer coefficient for the radiation component hr can be defined (10), see Poech [iii]. The emission coefficient ε (also used here for absorption) still poses a challenge for the application of (9, 10), as it can vary between approx. 0.1 for bare metal surfaces and approx. 0.9 for ceramic or polymer surfaces and is also dependent on the wavelengths.

Finally, the thermal conductivity of the assembly must also be taken into account (11). Heat is transported from the surface of the material (printed circuit board, components) to the interior by means of thermal conduction. However, the heat flow that impinges homogeneously on the surface of the assembly can be distributed inhomogeneously. This is due to the design of the module, e.g. its copper distribution, which is usually inhomogeneous, as well as the arrangement of the components and their thermal masses.

As already mentioned at the beginning, heat conduction can be neglected in many cases, as heat conduction strives for temperature equalization, especially with small dimensions. Thermal masses at a distance from each other can be considered approximately as isolated from each other, so that the neglect of heat conduction is justified. To simplify matters, we will therefore neglect thermal conduction in the following examples.

2. examples for determining the heat transfer coefficient

2.1 The fitting method

First, the heating and cooling behavior of a defined thermal mass (material data and surface properties are known) is measured in the reflow soldering system and the ambient temperature is also determined. In the second step, the temperature of the thermal mass per heating zone can be calculated again using (5) by manually inserting a heat transfer coefficient in (5) where the measured and calculated temperatures are the same.

Here is an example: Instead of an assembly, we use a 34x34x2 mm³ blackened stainless steel sheet in a 6-zone reflow soldering system for the measurement. The sheet has the advantages of having no topography and that all material data is known and does not have to be partially estimated as with an assembly. For the fitting, the real measured ambient temperatures TU were used here and not the set heating zone temperatures (settings).

This corresponds to nature, as the heat transfer takes place from the near-surface layer to the body (the assembly). The interaction of the assembly with the heating gas environment in the reflow soldering system leads to a slight cooling of the heating gas in a small layer around the assembly. The fitting achieves a good match between the simulated temperature (red) and the measured temperature (gray); Figure 1 and Table 2. An individual h was determined for each heating zone.

It would certainly be easier to have a fixed heat transfer coefficient for all heating zones of the reflow soldering system, but thermodynamics cannot be outwitted. If, in the simulation of our example, we only calculate with an average heat transfer coefficient of h = 76 W/m²K for all heating zones, large temperature deviations from the measured value must be accepted in some cases, see green curve.

Fig. 1: Temperature profiles of a stainless steel sheet

2.2 The reverse calculation

The following calculation is based on a 210x300x2.1 mm³ module with small components such as 0201 chips and large, high-mass components such as a 31 g choke. Mixed assemblies, which lead to large mass differences on the module, are not uncommon with increasing power electronics. Figure 2 shows the temperature curves for various measuring points on this module. For further discussion, only the values of the 0201 chip and the relatively heavy choke are considered here.

Fig. 2: Temperature profiles of a module

An assembly is made up of different inhomogeneous materials and its topography influences the flow, which means that the individual measuring points (soldering points) can differ greatly from one another. As a result, different temperature profiles are also measured; on our example assembly, a maximum temperature_TP = 259 °C was measured on the 0201 chip and the choke reached_TP = 232 °C, Figure 3.

It inevitably follows that there is no absolutely uniform system variable h and that the heat transfer coefficient must be determined individually for each measuring point and heating zone of the system. Using the relationship (7), an average heat transfer coefficient can be determined for each temperature profile per heating zone. For the ambient temperatures_TU, the heating gas temperatures (settings) of the reflow soldering system used (with seven heating zones) are simply used here. It is not surprising that the temperatures calculated in this way (see Table 3) used in Formula (5) are a good approximation of the measured temperatures, Figure 4.

3. temperature simulation

At first glance, these mathematical considerations do not simplify everyday reflow work, as the large number of heat transfer coefficients required for a reflow soldering system is rather confusing. However, it is still useful for everyday production practice. The determined h can be used for simulations of temperature profiles of comparable thermal masses (assemblies) or they can be very helpful for the optimization / adaptation of temperature profiles. This will be shown using the example of the 0201 chip (the choke is not considered), for which we set ourselves the following optimization task (example A):

The maximum temperature_TP on the 0201 chip should not exceed 245 °C, the profile geometry should be approximated to a saddle geometry. How should the reflow soldering system temperatures (settings)_TU be changed in order to achieve this goal?

We use equation (5) for the calculation. The new temperature profile with the pronounced saddle can be seen in Figure 5 and Table 4. The modern software of reflow soldering systems can take over the calculation tasks presented here and thus helps the employee on site to determine the correct system parameters promptly. In Table 4, a new setting of 389 °C has been calculated for zone P2. Whether the reflow soldering system can technically realize such a high setting temperature or also maintain such zone temperature differences must of course be clarified; this is not always the case in terms of design.

Example B: A double-sided FR4 mainboard weighing approx. 500 g has so far been successfully soldered on a 10-zone convection reflow soldering system, Figure 6. Production is now to be relocated to another site. A 10-zone system is also available at this location, but from a different manufacturer. Task: Which settings of the other system are required to achieve a reflow soldering profile that is as similar as possible? To solve the problem, the first step is to determine the heat transfer coefficients h for each zone of the other system using defined masses (blackened stainless steel plates) according to the fitting method, Table 5.

In the second step, the determined h were used in the formula (5), whereby the dwell time per zone corresponded to the transport speed of v = 750 mm/min. The heating gas temperatures_TU were adjusted manually; Figure 7 shows the result.

4. influence of radiation

General experience shows that a small influence of thermal radiation is definitely present in reflow soldering systems. However, this influence cannot be separated from natural convection (flow), which is always to be expected in heated reflow soldering systems. The following test results describe this 'natural' heat transfer. A temperature measuring board (PTP 250 mm wide) was first run through the reflow soldering system at the usual settings (set, Table 6). Before a second measurement run, the fans of the individual heating and cooling zones were switched off in order to record the 'natural' heat transfer of the system. The second measurement (fan OFF) took place immediately after the first measurement, so that the system did not suffer any significant temperature losses. Under forced convection (fan ON), the large mass reaches a maximum temperature of_TP = 209 °C, but_TP = 136 °C when the fans are switched off. The heat transfer coefficient for the radiation component can be estimated using (10). For Tr, the setting temperatures of the system are used here and ε is set to 0.8. Although the heating chamber of the reflow soldering system is made of stainless steel (with ε approx. 0.4), it can nevertheless be assumed that ε tends towards 1 in the discussed case of a very small area ratio of the assembly to the cavity area of the system and the almost closed heating chamber. Figure 8 shows the simulated temperature curves of the two masses. Table 6 shows the calculated heat transfer coefficients for both states 'ON and OFF' of the reflow soldering system. As expected, the heat transfer coefficients for the 'OFF' state of the blowers are significantly lower than those for the normal 'ON' state; they correspond to the values found in the literature for natural convection (e.g. 16 W/m²K in Herwig [ii], p. 35). The heat transfer coefficients marked '*' in the peak and cooling zones are significantly higher. This is the only way to simulate the steeper rises in these zones, which are due to the influence of an additional gas flow in the reflow soldering system, which circulates the gas for cleaning purposes independently of the heating fans. This gas circulation generates local forced convection.

Fig. 8: Measured (line) and simulated (symbol) temperature curves of the masses (M.) in comparison: fan ON and OFF

Estimating the possible proportion of radiation, or rather the proportion of natural heat transfer, initially only appears to be of academic value. Nevertheless, it provides additional information about the heat transfer system of the reflow soldering system and the ability to control reflow soldering processes.

5 Conclusion

Moschallski writes in [iv] that the heat transfer coefficient depends on the body geometry, the type of flow around the body (velocity, direction, flow shape ...) and the properties of the heating gas, but not on the material properties of the body. In reflow soldering systems, the top and bottom sides of the assemblies are exposed to heating gas differently, vertical and horizontal flows vary, and the material data of the heating gas also depend on the temperature. Illés described the influence of the flow in convection reflow soldering systems on the heat transfer coefficient in detail in [vi]. He calculated considerable differences in the magnitude of h both vertically across the assembly and across its width of 15 - 25 %. The considerations presented in this article also show considerably greater differences from heating zone to heating zone. Furthermore, a small proportion of temperature equalization due to heat conduction within the assembly must be added to each measuring point.

Unfortunately, the heat transfer coefficient is not a constant of the reflow soldering system. Nevertheless, the known thermodynamic algorithms are suitable for simulating temperature profiles for the production of electronic assemblies. Deviations from the true temperature value must be tolerated; they can be corrected by so-called confirmation runs (real measurements). However, it must also be pointed out that a measurement must always be carried out with the utmost care in order to come as close as possible to the true temperature. Adam [i] points out that the sum of all tolerances in the measurement may well be ± 5 K, which also influences the congruence between simulation and real measurement.

Automated learning (AI) will certainly help to make simulations of reflow soldering profiles more convenient in the future. Whether this technology will then be reliable and affordable is another matter.

Literature

[i] Adam, J.; Reichhart,S.; Schill, J.; Wild, P.: Praktikable Reflow-Simulation von Leiterplattenbaugruppen - Zwei Digitale Zwillinge, EBL 2024 - 12th GMM/DVS-Tagung March 04 - 06, 2024 Fellbach.
[ii] Herwig, H.; Moschallski, A.: Wärmeübertragung, Vieweg Verlag, ISBN-10 3-8348-0060-0, p. 4 ff.
[iii] Poech, M.: The reflow soldering profile with a restricted process window, FhG ISiT soldering seminar, Itzehoe 17.09.2015.
[iv] Moschallski, A.; Rückert, J. Ph.; Herwig, H.: Praxisnahe Bestimmung von Wärmeübergangskoeffizienten an Körpern unterschiedlicher Geometrie, Chemie Ingenieur Technik, August (2011) and www. Researchgate.net, publication, 258218053.
[v] DIN EN ISO 13789 ISO 13789, 2018-04, Thermal performance of buildings - Transmission and ventilation heat transfer coefficient - Calculation method.
[vi] Illés, B.: Distribution of the heat transfer coefficient in convection reflow oven, Applied Thermal Engineering 30 (2010), pp. 1523 -1530.

Appendix

The following Table 7 shows that a physically based calculation of the temperatures (simulation) in the reflow soldering process is feasible with little effort in a spreadsheet (MS-Excel, LibreOfficeCalc).

Fig. 9: Simulated temperature profile from the spreadsheetThe necessaryentries (values or formulas, without decorative accessories such as cell descriptions and units) in the cells (column, row) of the spreadsheet are for the example shown above:

• C1: Density in kg/m³
• C2: Specific heat capacity in J/kgK
• C3: Thickness in mm
• C4: Transport speed in mm/min (set value on the reflow soldering system)
• G5: Initial temperature in °C
• B6 to B11: Zone length in mm (dimensions in the reflow soldering system)
• C6 to C11: Zone temperature in °C (setting values on the reflow soldering system)
• D6 to D11: Heat transfer coefficient in W/m²K (property of the system, influenced by flow conditions on the component surface)
• E6 to E11[*]: = 60*B6/C$4 (calculated dwell time t in the zone in s)
• F6 to F11[*]: = C$1*C$2*C$3/2000/D6 (calculated time constant τ in the zone in s)
• G6 to G11[*]: = G5+(C6-G5)*(1-EXP(-E6/F6)) (simulation, calculated temperature _TK at the end of the zone in °C)

The zones can be defined with corresponding values, e.g. as inlet, preheating, heating, peak, transition, cooling and outlet zones over the entire length of the system. The above example of a "virtual" system does not refer to a real furnace; the numerical values must be adapted to the respective case (soldering system, assembly) or extended or shortened line by line.

[Lines 7 to 11 (columns E to G) are to be filled in automatically or copy&pasted with correspondingly adapted formulas