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December 2005
library  >  PAPERS  >  Analysis

Fan cooled enclosure analysis using a first order method


introduction

 

most electronics packaging engineers and analysis specialists have access to a wide range of high quality analysis tools. while a few computer programs use analytical methods, the majority are based on numerical analysis techniques. although these programs are becoming easier to use, they typically require considerable skill, and they are certainly capable of producing results with a high order of accuracy. however, even with these elegant tools at his/her disposal, the design engineer should have a working knowledge of less sophisticated methods.1

 

a first order analysis may, for example, predict temperatures sufficiently high so as to indicate that further design consideration is more necessary than in-depth thermal analysis. additionally, many engineers work in small companies that cannot afford sophisticated analysis tools. although these smaller companies have the option of hiring a consultant to perform the most complex calculations, it is in the interest of the responsible design engineer to perform a first order analysis in order to ascertain the magnitude of the thermal design problem.2 an example of a first-order analysis of a fan cooled enclosure is the subject of the following paragraphs.

 

the problem 

 

the fan-cooled enclosure shown in figure 1 is used to illustrate the method. the forward portion of the bottom panel is slotted (about 50% open) to provide an inlet grill. the internal geometry consists of five circuit board channels and a power supply. the power supply is totally sealed with the exception of the front and rear panels, each of which is perforated in a manner that provides about 35% open area for airflow. it shall be assumed that the power supply is approximately 50% filled with typical electronic components on a 0.025 m pitch.

 

s = circuit board spacing = 0.025 m.
w = power supply width = 0.075 m.
l = power supply and circuit board length = 0.250 m.
l = enclosure length = 0.300 m.
w = enclosure width = 0.200 m.
h = enclosure height = 0.125 m.
qps = power supply dissipation = 25 w.
qi = heat dissipation for circuit board bi = 20, 20, 20, 20, 30w; i=1.5.
figure 1: forced air cooled enclosure with five circuit board channels and a power supply.

 

the five circuit boards are on 0.025 m centers and a single fan on the rear panel negatively pressurizes the enclosure. a simple, non-flow restricting, wire grill is placed over the external fan face.

 

the fan characteristics are illustrated in figure 2 as fan static pressure vs. mass flow rate. such a curve is required for a system analysis and is usually obtained from the fan manufacturer's product catalog. the dashed curve indicated as system pressure loss will be discussed later, but it should be mentioned here that one of the desired results of any system analysis is to determine the system operating point as indicated by the intersection of the fan static pressure and system pressure loss curves.

 


figure 2: vendor-provided fan static pressure curve and calculated system pressure curve at sea level conditions.

 

the model and analysis

 

the typical first-order system analysis of a forced-air cooled enclosure uses a circuit representation where pressures (relative to the external ambient) may be calculated at node points and air flow may be calculated in resistive elements, (see [1] for additional detail). it should be clear that the accuracy of this method is dependent on the ability of the analyst to:

 

(1) correctly determine the location of the elements and also

(2) to calculate the element values.

 

admittedly, such modeling may be somewhat subjective, but with a little care, the analyst will usually obtain quite reasonable results, particularly in view of the fact that little effort is required to perform such an analysis. furthermore, most people have access to some form of network solver such as an electronic circuit analyzer, a modest thermal network analyzer or even a mathematical "scratch pad" program. these computerized network methods are very useful for parametric analysis and sensitivity studies, thus providing considerable insight into the relative importance of the various flow and thermal phenomena in the problem.

 

a suggested circuit for the present problem is shown in figure 3. the five circuit board channels are represented by air flow resistances r1-r5; the inlet grill by resistance r6; the power supply inlet, internal members, and exit by resistances r7, r8, and r9, respectively. the resistance of the wire finger guard at the fan exit is ignored. since each card channel is presumed to have the same geometry, e.g. card spacing and component height, the five circuit boards could also have been modeled as a single card cage represented by a single resistor. in the present case, the card cage was subdivided into five elements primarily to illustrate that non-identical card channels may also be modeled.

 

figure 3: airflow/pressure circuit for fan-cooled enclosure.

 

the flow resistances for this problem were selected from [1], although there are more specialized texts that the reader may find useful [2]. the relevant formulae are listed in table a1 and the actual calculation of each resistance is shown in table 1.3 a noteworthy feature of all of the resistances is the inverse-square dependence on a cross-sectional area. in the case of the inlet grill and the power supply inlet and exit panels, the relevant area is the free-cross-sectional area within the plane of the element, i.e. the actual area through which the air flows.

 

table a1: some formulae for calculating airflow resistances at sea level altitude and modest average temperatures. perforated or slotted plate:

 

once each of the various element values have been determined, they must be combined into a single element for the entire system. the appropriate rules for adding elements in series and parallel are easily derived by assuming that a forced-air cooled system can be expected to behave as though all air flow is of a turbulent nature4. these rules are listed in table a2 (the derivation may be found in [1]).

 

 

table a2. formulae for combining and using airflow resistances.

 

 

the three elements of the power supply combine to form:

 

rps = r7 + r8 + r9
  = 7.70x104 + 3.76x105 + 7.70x104
  = 5.30x105 (n/m2)/(kg/s)2

 

the reader will note that in table 1, the internal components of the power supply have been approximated by a series addition of 10 (pitch = 0.250 m/0.025 m = 10), 50% slotted panels.

 

the five circuit board channels are combined in parallel to form a single resistance rcb:

 


 

the power supply and five circuit board resistances are combined to give a single resistance for the entire interior of the enclosure.

 

 

the airflow resistance of the entire enclosure system is then:

 

rsys = r6 + r1 = 1.28x105 + 3.60x103 = 1.32x105 (n/m2)/(kg/s)2

 

the system loss pressure is finally computed from

 

psys = rsysm2

 

and plotted as shown in figure 2.

 

the total system airflow is determined by the intersection of the fan static pressure and the system loss pressure curves. reference to figure 2 shows that the total system flow is therefore m = 0.0069 kg/s. the various branch flows are:

 

 

the well-mixed, board-exit air temperature rises above the inlet air temperature are readily calculated:

 

 

conclusions concerning the sample problem

 

most electronic equipment designers would consider the calculated well-mixed air temperature rises to be too large. furthermore, it would not be surprising to expect temperature hot-spots considerably greater than the values calculated. individual component surface temperatures could also be estimated using an appropriate heat transfer coefficient and the component power dissipation (this problem would be best treated in a separate discussion).

 

clearly, the design needs to be re-evaluated in terms of a more appropriate fan or perhaps even more fans. the designer should also check with the electronic engineers on the project to ascertain if the provided heat dissipation values are indeed realistic. it is not uncommon for initial estimates to be of a worst case nature that may never actually occur.

 

footnotes:

  1. application of first order methods is also recommended for problems such as conduction solutions using fixed temperature or convection/radiation boundary conditions. in addition, a first order method may often be used to determine a boundary condition value for input into a finite element or finite difference program.
  2. the reader is cautioned that a first order analysis may not have sufficient resolution to permit detection of all problem areas.
  3. the author has provided formulae and performed the analysis in si units, which are not yet in full usage in the us. fan vendor literature still indicates some confusion as to what should be considered standard with regard to presentation of fan static pressure and fan airflow. the reader will note that fully consistent with si units, the fan and system pressures are computed in the si units of n/m2 and the fan air flow in kg/s.
  4. an assumption of turbulence is not necessary for derivation of rules for adding resistors, although the rules may depend on the nature of the assumed flow. the square root sign used for addition of parallel flow resistors follows directly from the turbulent model represented by δp = rm2

 

gordon n. ellison
thermal computations inc
3876 s. e. bliss ct. hillboro, or 97123 usa
tel: +1 (503) 648 5385 fax: +1 (503) 648 5385
email: [email protected]

 

references

  1. ellison, gordon n., thermal computations for electronic equipment, robert e. krieger publishing co., malabar, florida, 1989.
  2. fried, erwin and idelchik, i.e., flow resistance: a design guide for engineers, hemisphere publishing corporation, new york.

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