introduction

after selecting or designing a heat sink based upon a given air velocity or volumetric flow rate through the fins, the thermal designer needs to determine the total amount of flow which must be delivered in the duct or card passage containing the module w with heat sink. as shown in figure 1, some of the flow will go around or bypass the heat sink. in fact, depending upon the free area on the sides and above the heat sink in comparison to the flow area between the fins, a significant portion of the approaching air flow will simply bypass the heat sink.

although computational fluid dynamics codes offer a very useful tool for analyzing flow through and around the heat sink, the methodology described here provides a simple technique for obtaining an initial estimate of flow bypass for use in air moving device selection and trade-off studies. this approach is an extension of that originally described by lee [1].

\considering the geometry shown in figure 2 and applying the condition of a momentum balance across the control surfaces (1 and 2) we obtain:

where v_d is the velocity in the duct approaching the heat sink, v_f is the velocity in the fin passages, and v_b is the velocity in the bypass region. assuming the pressure drop in the bypass region, δ_pb, to be negligible compared to the pressure drop, δ_pf, in the fin passages, we combine equations 1 and 2 to obtain:

applying the condition of a mass balance across the control surfaces, we further obtain:

where, a_d is the duct cross-sectional area, a_b is the flow bypass area, and a_f is the flow area between the fins. taking into account a_hs, the frontal area of the heat sink, we have:

equation 4 may now be used to find the air velocity in the bypass region surrounding the heat sink:

squaring the bypass velocity we obtain:

which may be substituted for vb² in equation (3),

rearranging terms in equation (8) results in,

which is a quadratic equation of the form,

with,

the velocity in the duct required to achieve velocity v_f between the fins is then:

and the total required volumetric flow rate, g_d is

each of the areas required to calculate the numerical values of the quadratic coefficients may be determined readily from the geometry of the duct and heat sink. the value of velocity v_f is determined from a heat sink analysis or vendor data as that which is required to achieve the desired heat sink thermal resistance. the heat sink pressure drop (including entrance and exit effects), _pf, at velocity v_f , is determined by analysis, experimentally, or using vendor data.

this flow bypass analysis may be easily automated using a spreadsheet or similar calculation tool and provides a useful tool at the early stages of a thermal design project. an example of the analysis in the form of a mathcad file is shown in table 1.

table 1 - example of mathcad file for heat sink air flow bypass analysis.

references

1. lee, s., optimum design and selection of heat sinks, ieee trans., cpmt-a, vol. 18, no. 4, dec. 1995.