Heat-transfer effectivenesses of shrouded, rectangular-fin arrays

Applied Energy 46 (1993) 99-112

Heat-Transfer Effectivenesses of Shrouded, Rectangular-Fin Arrays R. F. B a b u s ' H a q , S. D. P r o b e r t & C. R. T a y l o r Department of Applied Energy, Cranfield University, Bedford, UK, MK43 0AL

ABSTRACT The thermal and h.v~h'aulic characteristics ~/i/brced-convective transfers from arrays of ~'ertical, tm([brmly spaced, rectangular fins, aligned parallel to an undisturbed air stream, have been hwestigated experimentally. For a constant temperature of the fins' base, at each airflow rate and shroud clearance gap to l~'n-height ratio, optimal inter-l~n separations, corresponding to the maximum steady-state rate of heat trans/'er, hare been determined. The thermal conductivity of the material q['the.fins had on O, a relatively small effect on the rate of heat transfer through the array of.fins. So optimal geometrical configurations of even relative O' low thermal-conductivity plastic material could be usefulO' employed as covers /br rapidly heat-dissipating enclosures .[br electronic O,stems.

NOMENCLATURE A C H

Area, m 2 Vertical clearance gap between top of fins and shroud (see Fig. 1), m. Vertical protrusion upwards of the rectangular fin from the horizontal base (see Fig. 1), m. h Convection heat-transfer coefficient of air, W m - 2 K - i . k Thermal conductivity of the fin material, W m - ~ K - 1 L Length o f the finned assembly (see Fig. 1), m. P Perimeter of the fin [ = 2(t + L)] (see Fig. 1), m. p Pressure, N m - 2 Steady-state rate of heat transfer, W s Uniform separation between adjacent fins (see Fig. 1), m. 99 Applied Energy 0306-2619/93/$06.00 © 1993 Elsevier Science Publishers Ltd, England. Printed in Great Britain

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Steady-state temperature, K. Uniform thickness of each fin (see Fig. 1), m. Mean inlet velocity, ms-1. Horizontal width of the wind-tunnel, i.e. orthogonal to the air-stream direction (see Fig. 1), m. Horizontal width of the fins' assembly, i.e. orthogonal to the air-stream direction (see Fig. 1), m.

Subscripts b c opt

for the base of the fins' array for the horizontal cross-section of the fin optimal value free-stream condition HEAT E X C H A N G E R FINS

The operation of many engineering systems results in the generation of heat. This often unwanted by-product can cause serious overheating problems and sometimes leads to failure of the system. This is especially important in modern electronic systems, in which the packaging density of integrated circuits can be as high a s 10 6 chips per cubic metre. 1 For example, the temperature of semiconductor components should not exceed the manufacturer's recommendations, typically ~65°C, in order that reliable operation is achieved. A 10°C increase, above 65°C, for a micro-electronic device approximately halves its mean-time-to-failure. 2 In order to overcome this problem, thermal systems with effective emitters (e.g. fins) are desirable. Also, optimisation of the heat-exchanger design leads to less material being used and/or the exchanger occupying less volume for a required heatdissipating performance. Heat exchanger fins are manufactured in a wide variety of forms, ranging from relatively simple shapes, such as rectangular, cylindrical, annular, tapered or pin fins (protruding from either a rectangular or a cylindrical base), to a combination of different geometries (as used throughout the electronics industry). Plate fins, which are to be discussed in this paper, are often made of duralumin, and formed by extrusion. (Pin-finned heatexchangers usually exhibit better heat transfer performances per unit mass of material used, but for mass production, usually have to be individually moulded and so are often more expensive. There is surprisingly little information available concerning the influence of the geometry of a fin array on the local heat-transfer coefficient and hence on the total rate of heat transfer from that fin assembly. Only a few studies,3-7 either experimental or analytical, have established unequivo-

Heat transfers from shrouded rectangular-fin arrays

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cally the geometric configuration which produces, for a given set of environmental conditions, the maximum rate of heat flux out of the surface from which the fins protrude. The present investigation involved studying, experimentally, the forcedconvective thermal-hydraulic characteristics of arrays of uniformly spaced, shrouded, rectangular fins. The effect of varying the fin spacing on the rate of heat dissipation from the heat exchanger for different air-flow rates was examined. The aim was to increase the rate of heat flow through the array, while reducing the viscous losses experienced by the air flow. In addition, the effect of changing the thermal conductivity of the fins on their optimal uniform-spacing was assessed.

E X P E R I M E N T A L HEAT-TRANSFER RIG

Assembly of fins This consisted of 250-mm long rectangular fins protruding vertically upwards from a 250 mm × 159 mm horizontal rectangular base. One set of

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fins was manufactured from duralumin, each being 250 mm long, 3.26 mm thick and 21 mm high. The other set of fins was made of mild steel, each being 250 mm long, 3"05 mm thick and 33 mm high. Rectangular-sectioned spacerbars (each 250 mm long) were employed between adjacent fins in order that the uniform separations could be changed by predetermined amounts. Four different thicknesses of spacer bars were produced, i.e. 1.65, 3.22, 6.55 and 12-26 mm.

Heating system Heating of the base of the exchanger was achieved by four electric resistor strips, each rated at 400W: this was the main heater. The assembly was firmly bolted together through the spacers and the roots of the fins thereby forming a rectangular base (see Fig. 2). The presence of thin layers of high thermal-conductivity heat-sink putty ensured that good thermal contacts existed between the main heater and the rectangular base, as well as between the fin roots and the spacer bars. The lower horizontal surface and sides of the main-heater block (when operational) were insulated thermally with 80-mm thick mineral-wool blankets. A horizontal guard heater, rated at 500 W, was positioned, parallel to the main heater, below the mineral-wool blanket, with yet another 80-mm layer of mineral-wool placed below it (see Fig. 2). The whole system of heatexchanger base, heaters and guard heater, with associated thermal insulation, was located in and protected by a well-fitting open-topped wooden box. The horizontal upper edges of this box and the top surfaces of the laterally placed thermal insulant, during each experiment, were flush with the upper surface of the multi-component rectangular base from which the fins protruded upwards. The power supplied to the main heater could be adjusted by altering the variac setting and was measured by an in-line electronic Wattmeter. The dissipation in the guard heater was adjusted until the steady-state temperature difference across the layer of insulant, sandwiched between the heaters, was zero. Then, under all the test conditions employed, more than 98% of the heat generated in the main heater passed, to the air of the surrounding environment, through the finned heat-exchanger. The steadystate temperatures at the base of the fin array were measured by an appropriately distributed set of six copper-constantan thermojunctions embedded within the rectangular base. Each thermojunction was bonded in position with a thin layer of epoxy resin so as to ensure good thermal contact. The average value from these appropriately located thermojunctions was regarded as the mean overall base temperature. This was maintained constant during each experiment at 40 ( + 0.5)°C.

104

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For the mild-steel fin array, one fin was manufactured incorporating narrow, shallow slotted grooves over one side of the fin surface, into which twelve thermocouples were buried (so that they were not proud of the fiat surface of the fin) at various positions in order to enable the fin temperature distribution to be ascertained. The gaps around the thermocouple wires grooves were filled with heat-sink putty and polished so as to be flush with the surface of the unadulterated fin. The inlet and the outlet air-stream temperatures in the wind-tunnel duct were measured using eight thermocouples: four thermojunctions were located immediately before the entrance of the fin assembly and another four downstream of the array. These could be traversed across the whole inlet and outlet cross-sections of the wind-tunnel duct. All the thermocouples, as well as those indicating the ambient'air temperature were connected, through ribbon cables, to a data-logger which was used to record the temperatures each half hour until steady-state conditions were attained (see Fig. 2).

Wind tunnel The main body of the rectangular cross-sectioned wind-tunnel duct (see Fig. 2) was manufactured from wood and was 2 m long with a constant internal width of 240 mm. However, the uniform vertical height of the duct and hence the duct cross-sectional area could be varied. Different duct heights were obtained by means of an adjustable horizontal r o o f (or shroud). Approximately half-way along the length of the wind-tunnel duct was the test section. The roof and side walls of this test section were made of 6-35mm-thick Perspex, so enabling the fin array and the air (or smoke flows) around it to be observed. A bell-mouth section was fitted at the entrance of the wind-tunnel duct, followed by a resin-impregnated, low-porosity, cardboard honeycomb flowstraightener. The exhaust air from the fin assembly was passed through an insulated chamber where mixing was accomplished by two resinimpregnated cardboard honeycombs, one being of relatively low porosity and the other of higher porosity. The latter was situated upstream of the former. The two honeycombs were m o u n t e d perpendicular to the undisturbed flow-stream. At the exhaust end of the duct, a gradual areacontraction section was attached. It was connected, via a plastic pipe, to a single-speed, single-stage fan capable of providing a maximum flow rate of 0.242kgs -1, and preceded by a throttle control valve. A differential manometer was employed to measure the pressure drop across an orifice plate, which had been calibrated according to BS 1042 (see Fig. 2). The wind tunnel was operated in the suction mode, i.e. the fan sucked

Heat transfers from shrouded rectangular-fin arrays

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atmospheric air through the fin assembly and the test section via the bellmouthed entrance section, with the fan and motor assembly on the exhaust side of the system. This avoided the air-stream being heated by the motor's fins prior to its passage through the heat-exchanger assembly which would have reduced the cooling capability of the air. The overall pressure drop along the heat exchanger was obtained via four sets of four static-pressure tappings located in the roof of the test section, i.e. in a plane perpendicular to the direction of the mean air flow. The velocity profile of the inlet air-stream to the fin assembly was identified via four

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OBSERVATIONS The rate of heat loss from the fin array by convection, conduction and radiation through the air depends largely on the mean temperature and temperature distribution of the fins and the assembly base; fin geometry; airflow rate; and orientation of the heat exchanger. However, under the 101

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considered conditions of the current investigation, the steady-state rate of radiative heat losses from the fins varied very little for different assembly configurations: the absolute radiative contribution as a percentage of the total steady-state rate of heat transfer through the fins was small ( < 5%) because all the surfaces of the heat exchanger components were highly polished. Thus the optima identified can be considered to be those which occurred had only forced convection ensued. The desired mean velocity, V, of the air at the inlet of the wind tunnel was adjusted via a throttle valve, which controlled the air-flow throt~gh the fan. For a fin array with a fixed inter-fin-spacing, s, at a fixed air velocity, the steady-state rate of heat transfer, Q, from the array was measured. Optimal values of the fin separation, Sopt, corresponding to the maximum rate of heat transfer under various applied conditions have been identified by drawing the appropriate graphs (see Figs 3-7). Over the narrow ranges of variables considered, the values of the optimal inter-fin separation appear to be almost independent of both the mean inlet velocity of the air-flow and the C/H ratio for the shroud. These spacings A

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Fig. 6. As for Fig. 5, but with C/H= 0.5. were determined to be 2.0 (-I-0.1)mm and 4.1( + 0.1)mm for the duralumin and the mild-steel fin-arrays resPectively. These observations agree qualitatively with the results from a previous experimental study, 5 under similar test conditions,~ for a shrouded duralumin fin-array configuration, but for a different fin height. However, it was apparent that an increase in the fin height led to a higher value for the optimal inter-fin separation (see Figs 3 and 4). It was also observed that by decreasing the C/H ratio, the optimal inter-fin separations deduced for the duralumin fin-arrays 5 approached those optima for the mild-steel fin arrays under similar applied conditions of air flow and temperature. At each C/H ratio tested, when near coincident mean inlet velocities of the air-flow and similar fin-array surface areas were employed, the steady-state rates of heat transfer from fin-arrays of both materials were far closer than a simple consideration o f the thermal conductivities of the materials employed would suggest (see Figs 5-7 and Appendix 1). Thus, the

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prospects for optimal-shaped external surfaces of finned, plastic-moulded containers for electronic devices appear promising. Such systems will have the advantages of being electrically insulating, and cheap to manufacture. The air-flows around each fin-array led to flow disturbances and resistances which resulted in a pressure drop. For both the duralumin as well as the mild-steel fin arrays, at each C/H ratio tested, as expected the overall pressure drop increased on increasing the mean inlet velocity, whereas it declined as the inter-fin spacing increased (see Figs 8 and 9).

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CONCLUSIONS The thermal and hydraulic performances of arrays of vertical, uniformly spaced, rectangular fins attached to a heated horizontal base have been studied experimentally. The fin-arrays were aligned parallel with the undisturbed direction of a forced turbulent air-stream, in the presence of a well-insulated horizontal shroud, situated adjacent to or above the fin tips. Optimal inter-fin separations, corresponding to the m a x i m u m steady-state rate of heat transfer, of 2.0( + 0" 1) m m and4.1( + 0" 1) mm, have b~en deduced for the duralumin and the mild-steel fin arrays respectively. These optima remained invariant for each of the C / H ratios tested, but increased with fin height. At C / H ratio of zero, changing the thermal conductivity of the fin material had almost no effect on the value of the optimal inter-fin spacing. The magnitude of the overall pressure drop along the fin array was influenced by the C / H ratio, the inter-fin separation and the mean inlet velocity of the air-flow.

REFERENCES 1. Naik, S., Probert, S. D. & Wood, C. I., Natural-convection characteristics of a horizontally based vertical rectangular fin-array in the presence of a shroud. Applied Energy, 28(4) (1987) 295-319. 2. Babus'Haq, R. F., George, H. E. & O'Callaghan, P. W., A thermal-analysis template. Int. J. Computer Applications in Technology, 5(1) (1992) 67-71. 3. Sparrow, E. M., Baliga, B. R. & Patankar, S. V., Forced convection heat transfer from a shrouded fin array with and without tip clearance. J. Heat Transfer, Trans. ASME, 100(4)(1978)572-9., 4. Kadle, D. S. & Sparrow, E. M., Numerical and experimental study of turbulent heat transfer and fluid flow in longitudinal fin arrays. J. Heat Transfer, Trans. ASME, 108(1)(1986) 16-23. 5. Naik, S., Probert, S. D. & Shilston, M. J., Forced-convective steady-state heat transfers from shrouded vertical fin arrays, aligned parallel to an undisturbed air-stream. Applied Energy, 26(2) (1987) 137-58. 6. Leung, C. W. & Probert, S. D., Heat-exchanger design: optimal length of an array of uniformly spaced vertical rectangular fins protruding upwards from a horizontal base. Applied Energy, 30(1) (1988) 29 35. 7. Olson, D. A., Heat transfer in thin, compact heat exchangers with circular, rectangular, or pin-fin flow passages. J. Heat Transfer, Trans. ASME, 114(2) (1992) 373-82. 8. Incropera, F. P. & De Witt, D. P., Fundamentals of heat andmass transfer, 3rd edn., John Wiley & Sons, New York, USA, 1990.

Appendix follows

112

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A P P E N D I X 1 E F F E C T OF C H A N G I N G T H E T H E R M A L C O N D U C T I V I T Y OF T H E F I N M A T E R I A L For a fin with an adiabatic tip (i.e. the convectiveheat loss from the fin tip is negligible) and a uniform cross-sectional area, the total rate of heat transfer is: s = M tanh (mH) where M = ~ ( T b

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and m = Thus, for two identical fins exposed to identical conditions, but of different thermal conductivities, the heat transfer ratio will be: l / Q 2 = N//~I tanh [ ~ H ] / x / ~

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Under the considered conditions of the current investigation for the duralumin fin (i.e. kl = 168Wm -1 K -1) and the mild-steel fin (i.e. k 2 = 5 4 W m - l K - X ) , at H = 2 1 x 10-3m, P = 0 . 5 0 7 m , A = 0 . 8 1 5 x 1 0 - 3 m -2 and h = 5 0 W / m 2 K, the rate of heat transfer ratio would be equal to 1.05. Therefore more than 200% increase in the thermal conductivity of the fins' material led to only ,-~5% rise in the rate of heat loss through the fins.