Beating the heat: the basics of fluid flow and heat transfer and how they can be applied to electronics cooling applications.

Power dissipation of electronic devices has been rising steadily to the point that thermal management must be considered as an integral part of the design process for most products. Further, PCB component layout, which using current design methods is often decided long before cooling issues are addressed, has a major effect on junction temperature and failure rate. Yet the usual lack of involvement of electrical engineers in thermal issues means that thermal issues are normally not addressed until the later stages of the design process when component placement has been fixed and the board routed. Potential thermal issues that arise at this point are usually expensive to resolve. Substantial changes such as a cabinet redesign or board placement changes and rerouting are usually required. The need for custom or exotic thermal solutions may even wind up killing the design. By addressing thermal issues very early in the design process, problems can often be corrected by layout changes that can be made nearly without cost.

Conduction Heat Transfer

Addressing thermal issues prior to the prototyping phase first requires an understanding of heat transfer, the transfer of thermal energy due to a temperature difference. One method of heat transfer is conduction, the transfer of heat between particles in contact within a medium. Heat is transferred from hot regions to cold regions due to thermal excitation of atoms and free movement of electrons in metals following Fourier's Law:

Q = - k A [DELTA]T (W)

Q Conductive heat flux

k Material thermal conductivity (W/m-K)

[DELTA]T Temperature gradient (K or [degrees]C)

The concept of thermal resistance provides an alternative to Fourier's Law that is frequently used in board design because it is analogous to Ohm's Law:

* [R.sub.k] = [DELTA]T/Q = L/kA (K/W or [degrees]C/W)

* [R.sub.k] Thermal resistance

* Similar to [R.sub.[ohm]] = V/I (Ohms)

Thermal resistance can also be calculated in series or in parallel (FIGURES 1-3).

[FIGURES 1-3 OMITTED]

For example, the equivalent through plane thermal conductivity of a PCB can be calculated by treating the copper and FR-4 layers as thermal resistances in series (FIGURE 4).

[FIGURE 4 OMITTED]

Often it is important to know the temperature profile across an object as opposed to simply knowing the change in temperature from one side to another. In this case, the superposition principle can help determine a complex conduction temperature profile by separating the problem into two simpler conduction problems. For instance, the temperature profile within a medium subject to heat generation and an imposed temperature difference can be easily derived by superimposing the temperature profile of the heat source in the object over the temperature profile of an imposed temperature difference (FIGURE 5).

[FIGURE 5 OMITTED]

Convection Heat Transfer Convection is characterized by the transfer of heat between a solid surface and a fluid flowing over this surface. The dominant contribution is made by bulk movement of fluid particles while thermal diffusion makes a small contribution.

The convective ability is characterized by its heat transfer coefficient h. Newton's law states that:

Qh = h A(T - [T.sub.[infinity]])= h A [DELTA]T

where

Q = Convective heat flux (W)

h = Heat transfer coefficient (W/[m.sup.2] - K)

A = Surface area ([m.sup.2])

T = Surface temperature (K or [degrees]C)

[T.sub.[infinity]] = Fluid temperature away from the surface (K or [degrees]C)

Convection can also be expressed by a thermal resistance:

Rh = [DELTA]T/Qh = 1/hA (K/W or [degrees]C/W)

[DELTA]T = [T.sub.s] - [T.sub.[infinity]] (K/W or[degrees]C)

Three modes of convection are typically encountered in electronics:

* Natural convection, which occurs through the movement of a fluid caused by density variation due to the presence of temperature gradients in the fluid.

* Forced convection, where fluid is moved mechanically (e.g., fans) or naturally (e.g., wind).

* Mixed convection, a combination of natural and forced convection.

It should be noted that, in natural convection the heat transfer coefficient is highly dependent on the temperature difference, whereas in forced convection the heat transfer coefficient is dependent on the fluid velocity and surface geometry.

Knowing whether the flow is laminar or turbulent is also an important concept since convective heat transfer is improved by turbulence in the flow. The roughness of a surface may therefore be increased in order to create more turbulence at the wall, thus improving the heat transfer. Numerous formulas are available in the literature in order to derive the appropriate heat transfer coefficient (see References).

Radiation Heat Transfer

Any surface whose temperature is higher than absolute zero emits energy in the form of electromagnetic radiation so radiation is another form of heat transfer that does not require a medium. The radiation heat flux exchange between two surfaces can be derived from Stefan-Bolzmann's Law such that:

[Q.sub.12] = [epsilon]1 [sigma] [A.sub.1] [ F.sub.12] ([T.sub.14] - [T.sub.24])

[Q.sub.12] = Heat flux at surface 1 (W)

[A.sub.1] = Area of surface 1 ([m.sup.2])

[[epsilon].sub.1] = Emissivity of surface 1 (dimensionless)

[F.sub.12] = View factor between surface 1 and 2 (dimensionless)

[sigma] = Stefan Boltzmann constant (W/[m.sup.2].[K.sup.4]).

The emissivity [epsilon] of a surface characterizes its ability to radiate.

* For a black body (perfect emitter) [epsilon] = 1

* For real bodies, 0 [less than or equal to] [epsilon] [less than or equal to] 1.

When radiation hits a surface, some of the heat flux is absorbed while the rest of the heat flux is either reflected or transmitted. In electronics applications, some simplifying assumptions can be made in order to compute radiative heat transfer. Emission and reflection are considered diffuse or equal at every angle and absorptivity is considered to be independent of the incidence angle. Another important simplification is to consider the surfaces to be grey and to apply Kirchhoff's Law, which considers that the emissivity of a surface equals its absorptivity.

Within an electronics box, it should be noted that the emissivity of a surface depends on the surface condition only (such as the roughness), not on the color. For example, an anodized aluminum heat sink can radiate more heat than a polished aluminum heat sink. On the other hand, the color will be critical if the surface is subject to solar loading. This is due to the difference in wavelength spectrum.

When forced convection is the primary heat transfer mechanism, radiation can generally be neglected because it is usually small in comparison. In natural convection, however, radiation and convection are generally of comparable magnitude.

Fluid Mechanics: Conservation Principles

Heat transfer is one key component of electronics cooling but fluid mechanics, and in particular pressure drop, is another one. Three principles can be applied to a fluid flowing in a system: conservation of mass, conservation of momentum and conservation of energy.

Conservation of mass states that, for a steady state application, the mass going in a system should be equal to the mass going out. Looking at FIGURE 6, one can see that, based on that principle and assuming that the density is constant, the velocities at different sections of a duct can be determined.

[FIGURE 6 OMITTED]

The sum of all the external forces acting on a fluid (such as gravity, pressure forces) is equal to the rate of change of momentum in the fluid. This principle defines the conservation of momentum, which leads to Bernoulli's equation when viscous forces are neglected, steady flow and constant density are assumed.

p + r[V.sup.2] /2 + [rho]g z = constant

where

p = Static pressure

[rho][V.sup.2] /2 = Dynamic pressure

[rho]g z = Hydrostatic pressure.

In a similar manner that conservation of mass links areas and velocities, Bernoulli's equation links velocities and static pressures, when applied to a diffuser or a nozzle. If Bernoulli's equation is applied to the diffuser in Figure 6, the static pressure [p.sub.2] will be higher than [p.sub.1] since [V.sub.1] is bigger than [V.sub.2].

Conservation of energy is another principle that applies to the fluid. This principle is of great importance in electronics cooling as it can be easily used to assess the basic heating of a steady flow.

Q = m Cp [DELTA]t

where

Q = Power dissipated by the component (W)

Cp = Fluid specific heat capacity (J/kg-K)

[DELTA]T = Global temperature increase of the fluid (K or [degrees]C)

m = mass flow rate (kg/s).

Finally, applying the steady-flow energy equation to the fluid helps deriving an important relationship regarding pressure losses. Pressure drop experienced by a fluid come from friction and geometric losses. Geometric losses are incurred in features such as turns and sharp bends:

[DELTA]p = (K+4f/D). [rho][V.sup.2]/2g

where

K = Geometry loss coefficient

F = Friction loss coefficient.

After reviewing all these basic principles, let us see how they could be applied to electronics cooling.

Forced Convection System Design

In order to analyze a forced convection system design, certain information is needed such as the fluid ambient temperature, the number of boards, the local heat dissipations and the system orientation. The typical goals of the analysis are to determine the effect of fan and vent positions, determine flow distribution around boards, local hot spots or low flow regions and evaluate various design options.

Each constituent of the system offers some resistance to the flow of cooling fluid. The consequence of flow resistance is pressure loss through the system. The global pressure loss of an electronic system is due to the flow resistance of every component: heat sinks, card arrays, power supplies, disk drive, cabling, grills, filters, etc. The individual flow resistances of the system add together in series and in parallel. The impedance of the various sections of the system must be determined in order to determine how the flow is segmented. The pressure drop [DELTA]p of a system can then be expressed as a nonlinear function of the flow-rate [G.sub.v].

[FIGURE 7 OMITTED]

[DELTA]p = [K.sub.v] [rho] [G.sub.v.sup.N] with N between 1 and 2

Recall that the pressure drop due to the system geometry can be calculated according to the following formula

[DELTA]p = Kp x ([rho] [V.sup.2] /2)

Numerous experimental values of [K.sub.p] are available for screens, orifices, bends, expansion/contraction in the literature:

                               [K.sub.p]

Perforated plate, 40% open     8.25
50% open                       4.00
60% open                       2.00
Flush entrance aperture        0.5
Free discharge from aperture    1
Sharp bend                     1.4

Consider, for example, a simple telecom shelf with 16 cards. The model is dissected into flow paths and the flow resistances and effective areas are calculated for each flow path. Once the correct correlations for each region in the system are set up, one can calculate the system impedance and local average velocities at different flow rates by varying the flow rate and applying the conservation of momentum equation. This approach provides reasonable results for average flow rates over the cards and shows the potential impact of filters and vents but it requires many simplifications which limits its accuracy.

Fans

Fans are typically present in forced convection systems. They must balance the total system resistance by generating an equivalent pressure rise. The operating point of a fan is the intersection between the fan curve and the system resistance curve. A fan has a unique operating point for a given system delivering a finite amount of flow to each region of the system (FIGURE 8).

[FIGURE 8 OMITTED]

Note that fans are classified into three categories: axial fans, blowers and impellers. Fans can be mounted in series or in parallel to improve the system air flow. The first step in selecting a fan is determining the flow rate needed to maintain a specified change in temperature through the system:

Req. G = 1.72 Q/[DELTA]T (Sea Level) (CFM)

where

Q = System power dissipation (W)

[DELTA]T = Expected temperature gradient through the system (K or [degrees]C).

Then assess the available real estate for fan placement and check the fan curves of various fans to determine which ones will provide the needed flow. Fans can either be mounted to push or pull air into the electronics chassis. A push system provides positive pressure, reducing the risk of contamination through unsealed areas but often produces large flow variations in the system. On the other hand, a pull system generally provides more uniform flow at the cost of an increase risk of contamination and a decay in the fan life since the fan will drive a higher temperature flow.

Natural Convection System Design

When designing a natural convection system, data such as the ambient conditions, power dissipation and orientation are typically available. Solar loading can be an additional constraint to consider for the design. The typical goals are to determine the available heat sink area and come up with the appropriate heat sink. Begin the analysis by calculating the thermal resistance to the heat sink area on the surface of the system. In the initial estimate, assume that all the heat passes through this path. This will yield the maximum surface temperature and available envelope for heat sink design. Thus, the available heat sink surface area, along with the maximum allowable surface temperature and the maximum defined temperature will be determined. A more refined definition of the heat sink can be done using heat transfer correlations (*).

[FIGURE 9 OMITTED]

Package-Level Thermal Design

The primary goal of cooling an electronic system is to maintain junction temperatures of ICs at acceptable levels. For this reason it is necessary to consider heat generated on the active side of the die and thermal characteristics of the package.

A package is basically an intermediary between the die and PCB. Many different types of technologies--solder balls, leads, etc.--are used to achieve this. How can one assess how good thermally a package is compared to another? JEDEC (jedec.org), the standards group for the semiconductor industry, provides sets of standards for comparing packages. A component can be plugged in a still or forced air environment, which permits generating a resistance junction to air ([[theta].sub.ja] or [[theta].sub.jma] also commonly called [R.sub.ja] or [R.sub.jma]). Component manufacturers typically provide that data. It is useful to know about this resistance when the goal is to compare the performance of one package vs. another but these data should never be used to assess the junction temperature of a package in another environment.

A more interesting thermal resistance standard that JEDEC specified is the junction to case resistance. The junction to case resistance ([[theta].sub.jc]) is the thermal resistance from the junction to the outside surface of the package (case). The top surface of the package is mounted to a cold plate and all the other areas are adiabatic, forcing the heat to travel to the top only. A similar test exists to derive the resistance from the junction to the board ([[theta].sub.jb]).

Two-resistor compact models provide a significant improvement over single-resistor metrics. When using a two-resistor model to compute the junction temperature, the error compared to physical testing is typically less than 20%.

[FIGURE 10 OMITTED]

The goal of heat sinks is to increase the available surface area in contact with the fluid so that more is being removed by convection. Heat sinks are made of a base and fins of various height and thickness. An important concept to consider when designing a heat sink is the fin efficiency. The fin efficiency of a heat sink measures the amount of heat that is conducted from the base to the top of the fins. An ideal fin would have a fin efficiency equal to 1.

h = tanh (mL)/(mL) with m = [(2h/k[delta]).sup.0.5]

where

h = Heat transfer coefficient (W/[m.sup.2]-K)

k = Themal conductivity of fin material (W/m-K)

[delta] = Fin thickness (m)

L = Fin height (m).

Following are some quick calculations that can be used for first order approximations of heat sink performance based on laminar flow over a flat plate and air at 300K:

h = 1.26e-3 [(V/H).sup.0.5] (W/[in.sup.2] [degrees]C)

The minimum recommended fin spacing

[S.sub.min] = 1.3 [(H/V).sub.0.5] (in.)

H = heat sink length in the flow direction (in.)

V = approach velocity (ft/min).

Also consider flow in the calculation. The more fins the heat sink has the higher the pressure drops due to friction and contraction/expansion effects. Designing a heat sink is finding an optimum number of fins for a given flow rate.

Heat sinks are usually mounted on components. An interface material is needed to improve the conduction between the top of component and the heat sink base. This interface material needs to be considered as an additional thermal resistance when designing an electronics cooling system. There are many vendors on the market offering various types of interface materials including phase change, thermal paste, etc.

Other techniques. Thermo-electric coolers can deliver precisely controlled cooling but are not very efficient and generate additional heat to the system. Heat pipes are being used more often. They are essentially objects with a very high thermal conductivity that spread or move the heat very quickly away from a device. For example, they are used in laptop computers to move heat to an area where a fan and a heat sink can be placed to dissipate the heat from the system.

Cold plates, also called internal liquid cooling, is also becoming more popular. Cold plates use a fluid such as water that offers a much higher cooling capacity than air. Disadvantages of cold plates include the need for a pump and leakage issues.

Other cooling techniques such as immersion cooling, spray cooling and jet impingement are not widely used in the electronics industry but they are under investigation for future applications.

Thermal Design Tools

A variety of thermal design tools are available to expedite these calculations, particularly in real-world applications with complex geometries and many heat sources. Spreadsheets provide customized organization of empirical correlations that are an excellent tool for early design exploration. But building a spreadsheet can be time-consuming as many assumptions need to be made.

Flow network modelling represents the system as a network of flow paths providing a good tool for gross solutions. It quickly computes the system impedance, the bulk temperature rise and could be a good start for a more advanced analysis using computational fluid dynamics (CFD). It cannot accurately predict the junction and case temperatures at the component level.

Finite element analysis (FEA), which is typically used for stress analysis, can also be used mainly for heat transfer analysis. FEA tools tend to not compute fluid flow and radiation explicitly, requiring the user to apply these as boundary conditions.

CFD provides a more powerful modelling tool in which a 3D model of the system is built and the full conjugate heat transfer solution is calculated. This approach is highly accurate because it takes the full geometry of the system into account and relies on fewer assumptions compared to the other methods. CFD resolves the system flow field to a high level of detail which helps to identify recirculation and low flow regions. Numerical and graphical results provide an intuitive understanding of the characteristics of the system.

CFD can be applied to model a full range of models, from a data center room all the way down to a detailed package. At the board level, this analysis can help highlight potential thermal issues and provide engineers with more flexibility in resolving them before hundreds of hours of engineering time are invested in unusable designs. Problems identified at this early stage of the process can often be addressed by layout changes that can be made nearly without cost.

Some board-level thermal simulation tools are usually much easier for electrical engineers to use because they are designed around the same tools that they already use to define functional block diagrams and physical layouts.

Once an acceptable design is achieved using any of the tools mentioned in this article, the electronics system should be tested. Testing can be done at any stage of the design but it may not be cost effective. Putting the electronics system in the test chamber will give a good sanity check of the assumptions made during the modeling. Temperature measurements can be performed using thermocouples, an infrared camera or thermal diodes. Velocities can be measured using thermistors and anemometers.

REFERENCES

(1.) Frank White, Fluid Mechanics

(2.) Frank P. Incropera and David R Dewitt, Fundamentals of Heat and Mass Transfer, John Wiley & Sons, 2001.

(3.) E. Fried and I. E. Idelchik, Flow Resistance: A Design Guide for Engineers, Hemisphere Publishing Corp., 1989.

(4.) Dave S. Steinberg, Cooling Techniques for Electronic Equipment, second edition, John Wiley & Sons, 1991.

(5.) Kennedy, D.P., "Heat Conduction in a Homogeneous Solid Circular Cylinder of Isotropic Media," IBMTR 00.699, 1959.

(6.) Tony Kordiban, Hot Air Rises and Heat Sinks, ASME, 1998.

(7.) www.cfd-online.com

(8.) www.coolingzone.com

(9.) www.electronics-cooling.com

ALEXANDRA FRANCOIS-SAINT-CYR is thermal application engineer supervisor at Flomerics Inc. (flomerics.com); [e-mail].