24. Conduction Cooling for Chassis and Circuit Boards

Transcription

1 4. Cnductin Cling fr Chassis and Circuit Bards 4. Intrductin Cnductin cling is imprtant methd used in many practical electrnic systems such as spacecraft system as shwn in Figure 4.. The heat is generated in active cmpnents whenever the electrnic system is in peratin. As the heat is generated, the temperature f the cmpnent increases and heat attempts t flw thrugh any path it can find. If the heat surce is cnstant, the temperature within the cmpnent cntinues t rise until the rate f the heat being generated is equal t the rate f the heat flwing away frm the cmpnent. Steady state heat transfer then exists the heat flwing int the cmpnent is equal t the heat flwing away frm the cmpnent. Heat always flws frm high temperature areas t lw temperature areas. When the electrnic system is perating, the electrnic cmpnents are its httest parts. T cntrl the ht spt cmpnent temperatures, the heat flw path must be cntrlled. If this is nt dne prperly, the cmpnent temperatures are frced t rise in an attempt t balance the heat flw. Eventually, the temperatures may becme s high that the cmpnent is destryed if a prtective circuit r a thermal cutff switch is nt used. Cnductin heat transfer in an electrnic system is generally a slw prcess. Heat flw will nt ccur until a temperature difference has been established. This means that each member alng the heat flw path must experience a temperature rise befre the heat will flw t the next pint alng the path. This prcess cntinues until the final heat sink is reached, which is ften the utside ambient air. This prcess may take many hurs, perhaps even many days fr a very large system, depending upn its size. The materials alng the heat flw path sharply influence the temperature gradients develped alng the path. Heat can be cnducted thrugh any material: slid, liquid, r gas. The ability f the heat t flw thrugh any material is determined by the physical prperties f the material and by the gemetry f the structure. The basic heat flw relatin fr steady state cnductin frm a single cncentrated heat lad is shwn belw in Equatin.4.. Q ka (4.) L 5

2 Figure 4. Cnductin-cled electrnic bx designed t carry the heat dwn the vertical walls t a base plate, fr munting in a spacecraft 4. Unifrmly Distributed Heat Surces, Steady State Cnductin Identical electrnic cmpnents are ften placed next t ne anther, n circuit bards, as shwn in Figure 4.. When each cmpnent dissipates apprximately the same amunt f pwer, the result will be a unifrmly distributed heat lad. Figure 4. Printed circuit bard with flat pack integrated circuits When any ne strip f electrnic cmpnents is cnsidered, as shwn in sectin AA, the heat input can be evaluated as a unifrmly distributed heat lad. On a typical printed circuit bard (PCB), the heat will flw frm the cmpnent t the heat sink strip under the cmpnent, and then t the uter edges f the PCB, where it is remved. The heat sink strip is usually made f cpper r aluminum, which have high thermal cnductivity. The maximum temperature will ccur at the center f the PCB and the minimum temperature 5

3 will ccur at the edges. This prduces a parablic temperature distributin, as shwn in Figure 4.3. L L Unifrm heat input dq q dq dq 3 x t t+dt Temperature rise 3 4 La/ L/ x a Figure 4.3 Parablic temperature distributins fr unifrm heat lad n a circuit bard When nly ne side f ne strip is cnsidered, a heat balance equatin can be btained by cnsidering a small element f the strip, alng the span with a length f L. Then Where: dq q heat input dt dq - ka heat flw d(t + dt) dq 3 - ka ttal heat Then dq dt q - ka + dq dq3 dt -ka - ka d (dt) Then d t q ka 53

4 This is a secnd-rder differential equatin, which can be slved by duble integratin. Integrating nce yields t dt qx + C ka The secnd integrating yields t qx t + Cx + C ka The cnstant C is zer because at x 0, the plate is adiabatic, and n heat is lst. The slpe f the temperature gradient is therefre zer. The cnstant C is determined by letting the temperature at the end f the plate be t e ; Then ql ka + t e C The temperature at any pint alng the plate (r strip) is qx ql t + + t e ka ka q (L x ) + t (4.) e ka This equatin prduces the parablic shape fr the temperature distributin; which is shwn in Figure 4.3. When x 0. This results in the equatin fr the maximum temperature rise in a strip with a unifrmly distributed heat lad. ql ka The ttal heat input alng the length L is Then Q ql QL ka (4.3) When the temperature rise at the midpint alng the heat sink strip f length L is desired, then x L/ Substituting this value int Equatin.4..Will result in the temperature rise at the midpint f the strip. 3qL midpint 8kA 54

5 Cnsidering nly the strip with a length f L, the rati f the strip midpint temperature rise t the maximum temperature rise is shwn in the fllwing relatin: midpint 3qL ql 3 / maximum 8kA ka 4 Example 4.: A series f flat pack integrated circuits are t be munted n a multilayer printed circuit bard (PCB) as shwn in Figure 4.. Each flat pack dissipates 00 milliwatts f pwer. Heat frm the, cmpnents is t be remved by cnductin thrugh the printed circuit cpper pads, which have unces f cpper [thickness is in (0.007 cm)]. The heat must be cnducted t the edges f the PCB, where it flws int a heat sink. Determine the temperature rise frm the center f the PCB t the edge t see if the design will be satisfactry. Nte that the typical maximum allwable case temperature is abut F. Slutin: The flat packs generate a unifrmly distributed heat lad, which results in the parablic temperature distributin shwn in Figure 4.4. Because f symmetry, nly ne half f the system is evaluated. Equatin 4.3 is used t determine the temperature rise frm the center f the PCB t the edge fr ne strip f cmpnents. Figure 4.4 Unifrmly distributed heat lad n ne cpper strip Q 3(0.) 0.3 Watt heat input, ne half strip L 3 in 7.6 cm (length) k 345 W/m.K A (0.) (0.008) in cm (crss-sectinal area) Substitute int Equatin 4.3 t btain the temperature rise frm the center f the PCB t the edge. (0.3)(0.076)0000 Ο 9.7 C 97 F (345)(0.0036) The amunt f heat that can be remved by radiatin r cnvectin fr this type f system is very small. The temperature rise is therefre t high. By the time the sink temperature is added, assuming that it is 80 F, the case temperature n the cmpnent will be 77 F. Since the typical maximum allwable case temperature is abut F, the design is nt acceptable. 55

6 If the cpper thickness is dubled t 4 unces, which has a thickness f in (0.04 cm), the temperature rise will be 4.5 F (45.85 C) then the case temperature n the cmpnent will be abut 95 F s that the system can be perated safely. Fr high-temperature applicatins, the cpper thickness will have t be increased t abut 0.0 in (0.084 cm) fr a gd design. 4.3 Chassis with Nnunifrm Wall Sectins Electrnic chassis always seem t require cututs, ntches, and clearance hles fr assembly access, wire harnesses, r maintenance. These penings will generally cut thrugh a bulkhead r ther structural member, which is required t carry heat away frm sme critical highpwer electrnic cmpnent. The cututs result in nnunifrm wall sectins, which must be analyzed t determine their heat flw capability. One cnvenient methd fr analyzing nnunifrm wall sectins is t subdivide them int smaller units that have relatively unifrm sectins. The heat flw path thrugh each f the smaller, relatively unifrm sectins can then be defined in terms f a thermal resistance. This will result in a thermal analg resistr netwrk, r mathematical mdel, which describes the thermal characteristics f that structural sectin f the electrnic system. The basic cnductin heat flw relatin shwn by Equatin. 4. can be mdified slightly t utilize the thermal resistance cncept. The thermal resistance fr cnductin heat flw is then defined by Equatin L (4.4) ka Substituting this value int Equatin 4. results in the temperature rise relatin when the thermal resistance cncept is used as shwn in Equatin 4.5 Q (4.5) The thermal resistance cncept is very cnvenient fr develping mathematical mdels f simple r cmplex electrnic bxes. Analg resistr netwrks can be established fr heat flw in ne, tw, and three dimensins with little effrt. Cmplex shapes can ften be mdeled with many simple thermal resistrs t prvide an effective means fr determining the temperature prfile fr almst any type f system. Tw basic resistance patterns, series and parallel, are used t generate analg resistr netwrks. A simple series pattern netwrk is shwn in Figure 4.5. The ttal effective resistance ( t ) fr the series flw netwrk is determined by adding all the individual resistances, as shwn in Equatin Figure 4.5 Series flw resistr netwrk. 56

7 t (4.6) A simple parallel flw resistr netwrk is shwn in Figure 4.6. Figure 4.6 Parallel flw resistr netwrk. The ttal effective resistance fr the parallel flw netwrk is determined by cmbining the individual resistances as shwn in Equatin t (4.7) A typical electrnic system will nrmally cnsist f many different cmbinatins f series and parallel flw resistr netwrks. Example 4.: An aluminum (505) plate is used t supprt a rw f six pwer resistrs. Each resistr dissipates.5 watts, fr a ttal pwer dissipatin f 9 watts. The bulkhead cnducts the heat t the ppsite wall f the chassis, which is cled by a multiple fin heat exchanger. The bulkhead has tw cututs fr cnnectrs t pass thrugh, as shwn in Figure 4.7. Determine the temperature rise acrss the length f the bulkhead. Figure 4.7 Bulkheads with tw cututs fr cnnectrs 57

8 Slutin: A mathematical mdel with series and parallel thermal resistr netwrks can be established t represent the heat flw path, as shwn in Figure 4.8a. Figure 4.8 Bulkhead thermal mdels using a series and a parallel resistr netwrk. Firstly must determine the values f each resistr. Determine resistr : L in 5.08 cm k 58 W/m.K A (5) (0.06) 0.3 in.935 cm (0.0508)0000 (.935)(58).666 C/W Determine resistr : L.5 in 3.8 cm K 58 W/m.K A (0.375) (0.06) 0.05 in 0.45 cm (average area) (0.038) C/W (0.45)(58) Determine resistr 3 : L 3.5 in 3.8 cm K 3 58 W/m.K A 3 () (0.06) 0.06 in cm (0.038)0000 (0.387)(58) C/W Determine resistr 4 : L 4.5 in 3.8 cm K 4 58 W/m.K A 4 (.5) (0.06) 0.09 in 0.58 cm (0.038)0000 (0.58)(58) C/W Determine resistr 5 : L 5 in.54 cm K 5 37 W/m.K A 5 (4.75) (0.06) 0.85 in.839 cm 58

9 (0.054)0000 (.839)(58) C/W After getting all resistrs we can simplify the netwrk frm Figure4.8a t as shwn in Figure4.8b.Where resistrs, 3 and 4 are in parallel, which results in resistr The ttal thermal resistance is C/W 4 t C/W The temperature rise acrss the length f the bulkhead is then determined frm Equatin 4.5. t (9)(4.7) 4.3 C 4.4 Circuit Bard Edge Guides Plug-in PCBs are ften used with guides, which help t align the PCB cnnectr with the chassis cnnectr. These guides, which are usually fastened t the side walls f a chassis, grip the edges f the PCB as it is inserted and remved. If there is enugh cntact pressure and surface area at the interface between the edge guide and the PCB, the edge guide can be used t cnduct heat away frm the PCB. A typical installatin is shwn in Figure 4.9. Figure 4.9 Plug-in PCB assembly with bard edge guides Plug-in PCBs must engage a blind cnnectr, which is usually fastened t the chassis. If the chassis cnnectr is rigid, with n flating prvisins, the edge guide must prvide that flat, r many cnnectr pins will be bent and brken. igid chassis cnnectrs are generally used fr electrical cnnectins because wire-wrap harnesses, flex tape harnesses, and multilayer 59

10 master intercnnecting mther bards are being used fr prductin systems. These intercnnectins cannt withstand the excessive mtin required fr a flating cnnectr system. Therefre, the flating mechanism is ften built int the circuit bard edge guides. Many different types f circuit bard edge guides are used by the electrnics industry. The thermal resistance acrss a typical guide is rather difficult t calculate accurately, s that tests are used t establish these values. The units used t express the thermal resistance acrss an edge guide are C in/watt. When the length f the guide is expressed in inches and the heat flw is in watts, the temperature rise is in degrees Celsius. Figure 4.0 shws fur different types f edge guides, with the thermal resistance acrss each guide. Figure 4.0 Bard edge guides with typical thermal resistance, (a) G guide, C in/watt; (b) B guide, 8 C in/watt; (c) U guide, 6 C in/watt; (d) wedge clamp, C in/watt. These bard edge guides are generally satisfactry fr applicatins at sea level r medium altitudes up t abut 50,000 ft. At altitudes f 00,000 ft, test data shw that the resistance values fr the guides in Figure 4.0a-c will increase abut 30%. The wedge clamp shwn in Figure 4.0d will have abut a 5% increase. Fr hard-vacuum cnditins, where the pressure is less than 0-6 trr (mm hg), as nrmally experienced in uter space wrk, sme f these edge guides may nt be satisfactry, except fr very lw pwer dissipatins. Outer space envirnments generally require very high pressure interfaces, with fiat and smth surfaces, t cnduct heat effectively. Wedge clamps are very effective here because they can prduce high interface pressures. Example 4.3: Determine the temperature rise acrss the PCB edge guide (frm the edge f the PCB t the chassis wall) fr the assembly shwn in Figure 4.9. The edge guide is 5.0 in lng, type c, as shwn in Figure 4.0. The ttal pwer dissipatin f the PCB is 0 watts, unifrmly distributed, and the equipment must perate at 00,000 ft. Slutin: Since there are tw edge guides, half f the ttal pwer will be cnducted thrugh each guide. The temperature rise at sea level cnditins can be determined frm Equatin 4.8. Q (4.8) L 6 C in/watt (U guide) Q0/ 5 watt L 5 in 60

11 (6)(5) 5 At altitude f 00,000 ft, the resistance acrss the edge guide will increase abut 30%. The temperature rise at this altitude will then be. 6 t.3(6) Heat Cnductin thrugh Sheet Metal Cvers Lightweight electrnic bxes ften use sheet metal cvers t enclse the chassis. Smetimes these cvers are expected t cnduct the heat away frm the chassis fr additinal cling. T effectively cnduct heat frm the chassis t the cver, a flat, smth, high-pressure interface must be prvided. The nrmal surface cntact btained at the interfaces f sheet metal members will nt prvide an effective heat cnductin path. Hwever, if a lip can be frmed in the cver r n the sidewalls f the chassis, the heat cnductin path can be substantially imprved. Figure 4. shws hw lips may be frmed in the chassis and cver t imprve the heat transfer acrss the interface. C C Figure 4. Different types f sheet metal cvers n electrnic bxes, (a) Pr; (b) gd; (c) gd. 4.6 adial Heat Flw Electrnic supprt structures are nt always rectangular in shape. If an electrnic system is enclsed within a cylindrical structure, such as a small missile, it wuld be a waste f space t use a rectangular bx fr the electrnics. The packaging frm factr wuld prbably cnfrm t the natural cylindrical shape. Electrnic cmpnents munted n the inside surface f a cylindrical chassis wuld require a radial heat flw path t remve the heat when the heat sink is n the uter surface f the structure. The temperature rise frm the inside surface t the utside surface f the cylindrical structure can be determined frm Furier s law as fllw. dt Q -ka cnstant dr dt k(πa) (4.9) dr Hwever, in a radial heat flw system, the crss-sectinal area is cnstantly changing as the radius changes, as shwn in Figure 4.. S that we integrate the Equatin 4.9, yields t 6

12 Q ut in d πka(t Q ln( πka dt ut in ut πka t / ln( / in in ut ) t t ) ut in ) (4.0) Figure 4. Hllw cylinder Example 4.4: A hllw steel cylindrical shell has a grup f resistrs munted n the inside surface, as shwn in Figure 4.3. Heat is remved frm the utside surface f the cylinder, s that the heat flw path is radial thrugh the wall f the cylinder. Determine the temperature rise thrugh the steel cylinder when the pwer dissipatin is 0 watts. Figure 4.3 esistrs munted n the inside wall f a hllw cylinder Slutin: ut. in cm in in.54 cm a.5 in3.8 cm Q0 W k 60.5 W/m.K Substitute int Equatin 4.0 fr the temperature rise thrugh the steel cylindrical wall. 0 ln(./) π (60.5)(0.038) Then t 0.5 C 6