Design of Electronic Equipment Casings for Natural Air Cooling: Effects of Height and Size of Outlet Vent on Flow Resistance

As the power dissipation density of electronic equipment has continued to increase, it has become necessary to consider the cooling design of electronic equipment in order to develop suitable cooling techniques. Almost all electronic equipment is cooled by air convection. Of the various cooling systems available, natural air cooling is often used for applications for which high reliability is essential, such as telecommunications. The main advantage of natural convection is that no fan or blower is required, because air movement is generated by density differences in the presence of gravity. The optimum thermal design of electronic devices cooled by natural convection depends on an accurate choice of geometrical configuration and the best distribution of heat sources to promote the flow rate that minimizes temperature rises inside the casings. Although the literature covers natural convection heat transfer in simple geometries, few experiments relate to enclosures such as those used in electronic equipment, in which heat transfer and fluid flow are generally complicated and three dimensional, making experimental modeling necessary. Guglielmini et al. (1988) reported on the natural air cooling of electronic boards in ventilated enclosures. Misale (1993) reported the influence of vent geometry on the natural air cooling of vertical circuit boards packed within a ventilated enclosure. Lin and Armfield (2001) studied natural convection cooling of rectangular and cylindrical containers. Ishizuka et al. (1986) and Ishizuka (1998) presented a simplified set of equations derived from data on natural air cooling of electronic equipment casings and showed its validity. However, there is insufficient information regading thermal design of practical electronic equipment. For example, the simplified set of equations was based on a ventilation model like a chimney with a heater at the base and an outlet vent on the top, yet in practical electronic equipment, the outlet vent is located at the upper part of the side walls, and the duct is not circular. Therefore, here, we studied the effect of the distance between the outlet vent location and the heat source on the cooling capability of natural-air-cooled electronic equipment casings.


Introduction
As the power dissipation density of electronic equipment has continued to increase, it has become necessary to consider the cooling design of electronic equipment in order to develop suitable cooling techniques.Almost all electronic equipment is cooled by air convection.Of the various cooling systems available, natural air cooling is often used for applications for which high reliability is essential, such as telecommunications.The main advantage of natural convection is that no fan or blower is required, because air movement is generated by density differences in the presence of gravity.The optimum thermal design of electronic devices cooled by natural convection depends on an accurate choice of geometrical configuration and the best distribution of heat sources to promote the flow rate that minimizes temperature rises inside the casings.Although the literature covers natural convection heat transfer in simple geometries, few experiments relate to enclosures such as those used in electronic equipment, in which heat transfer and fluid flow are generally complicated and three dimensional, making experimental modeling necessary.Guglielmini et al. (1988) reported on the natural air cooling of electronic boards in ventilated enclosures.Misale (1993) reported the influence of vent geometry on the natural air cooling of vertical circuit boards packed within a ventilated enclosure.Lin and Armfield (2001) studied natural convection cooling of rectangular and cylindrical containers.Ishizuka et al. (1986) and Ishizuka (1998) presented a simplified set of equations derived from data on natural air cooling of electronic equipment casings and showed its validity.However, there is insufficient information regading thermal design of practical electronic equipment.For example, the simplified set of equations was based on a ventilation model like a chimney with a heater at the base and an outlet vent on the top, yet in practical electronic equipment, the outlet vent is located at the upper part of the side walls, and the duct is not circular.Therefore, here, we studied the effect of the distance between the outlet vent location and the heat source on the cooling capability of natural-air-cooled electronic equipment casings.Ishizuka et al. (1986) proposed the following set of equations for engineering applications in the thermal design of electronic equipment: where Q denotes the total heat generated by the components, S eq is the equivalent total surface of the casing, T m is the average temperature rise in the casing, A o is the outlet vent area of the casing, h is the distance from the heater position to the outlet, K is the flow resistance coefficient arising from air path interruption at the outlet, T o is the air temperature rise at the outlet vent, and  is the porosity coefficient of the outlet vent.K was approximated as a function of : Ishizuka et al. (1986Ishizuka et al. ( , 1987) ) obtained the following relation for wire nets at low values of the Reynolds number (Re):

Set of equations
where Re is defined on the basis of the wire diameter used in the wire nets.However, since the effect of Re on K is less prominent than that of , K can be approximated as a function of  only.Therefore, Eq. ( 2) is considered to be a reasonable expression for practical applications.The h term in Eq. ( 1) refers to chimney height, as Eq. ( 1) assumes a ventilation model like a chimney with a heater at the base and an outlet vent on the top (Fig. 1).However, as practical electronic equipment is nothing like a chimney, we took practical details into account in the following experiments.

Experimental apparatus
The experimental casing measured 220 mm long  230 mm wide  310 mm high (Fig. 2).The plastic casing material was 10 mm thick and had a thermal conductivity of 0.01 W/(m•K).A wire heater (2.3-mm gauge) was placed inside (Fig. 3).The size, location, and grille patterning of a rectangular vent on one of the side walls were varied (Fig. 4).Experiments

Estimation of heat removed from casing surfaces
The amount of heat removed from the casing surfaces was estimated by experiment.For this purpose, the casing was considered to be a closed unit with no vents except at the base.Using the natural convective heat transfer equations for individual surfaces presented by Ishizuka et al. (1986), we expressed the amount of heat removed from the casing surfaces, Q s , as: Eq. ( 6) shows the first term on the right-hand side of Eq. ( 1).Where, D 1 is the constant coefficient.The coefficient D 1 includes a radiative heat transfer factor and determined by the experiment.The amount of heat generation was within the Q s = 6-40 W range (Fig. 5) when the room temperature T a was 298 K.The results are shown in Fig. 5 and are well expressed by Eq.( 7).where D 1 was determined to be 0.445.The temperature distribution in the casing was relatively uniform, within ±5%.Hereafter, the amount of heat removed from the outlet vent, Q v , was calculated as: Fig. 5. Relationship between Q s and T m

Influence of outlet vent size on temperature rise in the casing
The experiment was carried out by varying the outlet vent size of the reference casing at outlet vent position H v = 275 mm and heater position at H h = 25 mm (Fig. 2).The porosity coefficient  o (Fig. 4) was defined as the ratio of the open area of each individual vent to the area of the reference vent (150 mm  50 mm).
At each value of input power, Q, as  o decreased, T m increased linearly on the logarithmic plot (Fig. 6).As Q increased, T m also increased.

Influence of outlet vent position on mean temperature rise in the casing
The relationship between T m and outlet vent position H was investigated at two opening sizes with the heater at the bottom.T m decreased as H increased at both opening sizes (Fig. 7).It decreased faster at lower H.

Influence of distance between outlet vent position and heater position on mean temperature rise in the casing
The relationship between T m (average of temperatures measured only above the heater position) and the distance between the outlet vent position and the heater position, h, was investigated by varying opening size and input power while the outlet height was fixed at H v = 275 mm.As h increased, T m decreased at all values of input power (Fig. 8).9) for the overall energy balance and Eq. ( 10) for the balance between flow resistance and buoyancy force: where Q v is dissipated power, c p is specific heat of the air at constant pressure, A is the cross-sectional area of the duct, u is airflow velocity, T is temperature rise,  is air density ( a is atmospheric condition), g is acceleration due to gravity, h is the distance between the outlet and the heater, and K is the flow resistance coefficient for the system.Since the pressure change in the system is small, the expression can be rewritten to assume a perfect gas: K is defined in terms of hand Q v as: In this study, H value was used in spite of h to arrange the present data.

Porosity coefficient
Generally,  o is defined as the ratio of the area of the opening to the reference opening (Fig. 4).Here, as the top surface area is an ideal outlet vent area for a casing cooled by natural convection, we defined the porosity coefficient  as:  = open area in outlet vent / inner casing top surface area (13)

Reynolds number Re
The velocity u was obtained using Eq. ( 9) and the hydrodynamic equivalent diameter of an opening with height A and width B was used as a reference length: Thus, Re is defined as: This multiplier has previously been used for higher values of Re, for example, in the case of forced air convection (Collar 1939).In the empirical correlation of K with X, all the K values obtained under the reference condition (outlet vent in the upper position and heater at the bottom) lie on the line, but others lie slightly below the line (Fig. 9).The reason for this discrepancy is likely to be measurement uncertainty, due to: 1. errors in the estimation of mean temperature rise from the temperature measured at the flow location 2. errors in the estimation of the amount of heat removed from the casing surface 3. the method of estimating the mean temperature rise when the heater position was varied.The best-fit line was: where the coefficient of 0.4 is inherent in this apparatus and is not a general value.This fit indicates that h can be considered as chimney height in practical equipment as well, and that the definition of  is reasonable.A more detailed discussion requires 3-dimensional thermofluid analysis and more precise measurement .H o w e v e r , w e c o n s i d e r t h a t a u s e f u l relationship among K, Re, and  can be determined from a practical point of view.

Conclusion
Experimental analysis of the effects of the size of the outlet vent opening and the distance between the outlet vent and the heater location on the flow resistance in a natural-air-cooled electronic equipment case revealed the following relationship among the flow resistance coefficient K, Reynolds number Re, and the outlet vent porosity coefficient  (defined on the basis of the top surface area): .5   where X = Re( 2 /(1 -) and B is an inherent coefficient of the casing in question.

Fig. 6 .
Fig. 6.Influence of vent porosity and input power on mean temperature rise in the casing

Fig. 8 .
Fig. 8. Influence of distance between outlet vent position and heater position on mean temperature rise in the casing