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1 THE AMERICAN SOCIETY OF MECHANICAL ENGINEERS Three Park Avenue, New York, N.Y GT-47 The Society shall not be responsible for statements or opinions advanced In papers or discussion at meetings of the Sodety or of its 0Msions or Sections, or printed in its publications. Discussion Is printed only if the paper is published In an ASME Journal. Authorization to photocopy for internal or personal use is granted to libraries and other users registered with the Copyright Clearance Center (CCC) provided $3/article is paid to CCC, 222 Rosewood Dr., Danvers, MA Requests for special permission or bulk reproduction should be addressed to the ASME Technical Publishing Department. Copyright by ASME All Rights Reserved Printed in U.SA. EFFECTS OF FLOW GAP ATOP PIN ELEMENTS ON THE HEAT TRANSFER FROM PIN FIN ARRAYS M. K. Chyu, C.H. Yen and W. Ma Department of Mechanical Engineering Carnegie Mellon University Pittsburgh, PA ,11,1E T. I-P. Shih Department of Mechanical Engineering Michigan State University East Lansing, MI ABSTRACT This study investigates the effect of gap atop an inline array of cubic fins on the heat transfer from various participating surfaces in the channel housing the array. Five different gap sizes of C/H = 0.25, 0.5, 1.0 and 2.0, as well as the baseline case without gap (C/H = 0.0) are examined and compared. The array consists of twelve rows of three columns. All tests use a unified Reynolds number at 16,000 based on the mean velocity in the channel and cube height. The heat transfer measurement uses a liquid crystal imaging technique combined with a onedimensional, transient conduction model and a lumped heatcapacity model. The results reveal that the heat transfer from the surfaces uncovered by the cubic fins in the test channel generally decreases with the size of the clearance atop the array. However, such a decreasing trend is insignificant for cases with relatively smaller gaps, i.e. C/H = 0.25 and 0.5. Under these conditions, the heat transfer from the surface of cubic fin, in fact, is higher than that of the baseline case. The vortex enriched shear layer separated from the sharp edges around the cube top is considered to be responsible for this phenomenon. NOMENCLATURE A heat transfer area C gap clearance C p constant pressure specific heat H height or width of cubic fin h local heat transfer coefficient = q/(t-t) k thermal conductivity IT man q local heat transfer rate per unit area Nu local Nusselt number = hh/k Re Reynolds number = UH/v T temperature t time U mainstream mean velocity x streamwise coordinate z spanwise coordinate Greek Symbols a thermal diffusivity T time parameter p fluid density Subscripts i initial m mainstream, mixed-mean p pin surface s smooth surface r reference t total wetted surface u uncovered endwall w wall INTRODUCTION Pin-fm arrays are widely used as compact heat exchangers for heat transfer from relatively small areas. Known as Presented at the International Gas Turbine & Aeroengine Congress & Exhibition Indianapolis, Indiana June 7 June

2 pedestals, pin fins are used for cooling of turbine airfoils, particularly near the trailing edge where its thinness prohibits the use of other cooling schemes. Pin fins are also found in heat sinks for cooling of electronic devices. Geometrically, pin fins are small cylindrical-type elements that arranged in a specific array form, e.g. inline or staggered, with proper spacing among the neighboring elements. Forced flow passes around a pin-fm array in a crossflow fashion, which promotes the turbulence level as well as the transport phenomena in the channel housing the array. Extensive research in studying the heat transfer and pressure characteristics has been performed in the past two decades. In the context of turbine airfoil cooling, Armstrong and Winstanley (1987) compiled a review on the array-averaged heat transfer and frictional loss for short pin-fins of staggered arrays. The data compiled suggest that arrays made of short pin-fm (height-to-diameter ratio, HID 1) have significantly lower heat transfer than the long tube bundle, typically referred to as "cylinder-in-crossflow" (Zukaskas, 1972). One of the main reasons for such a reduction in heat transfer is the presence of endwall on which the pin fins are situated. Detailed local heat transfer distribution on the endwall as well as rowresolved results are later reported in a series of studies by Chyu et. al. (Chyu, 1990; Chyu and Goldstein, 1991; Chyu et. al., 1992). In addition, Chyu et al. (1996) examined the performance of cubic and diamond shaped pin elements in narrow channels and suggested that the sharp-edge pins can produce higher heat transfer than the conventional, circular pins. More recently, they made a study to quantify the heat transfer contribution from the pin surface and the endwall (Chyu et al. 1998b). One area pertaining to pin fin performance that is practically important, but has limited information available, is concerned with the effect of the gap between the pins and one of the endwalls. For turbine airfoil cooling, the pedestals are part of the mechanical structure which bridge the pressure-side and suction-side of airfoil surfaces near the trailing edge, and consequently, the aforementioned gap effect should never be an issue of concern. In reality, however, to alleviate the stress concentration in such a very thin airfoil structure, one end of pin is intentionally made loose and unattached to the endwall. A gap may be formed at this loose junction and its size may increase as the airfoil deteriorates progressively. Aerodynamically, the gap provides an additional passage for the coolant flow in the array, the coolant passing through this gap would otherwise be flowing around the pin fins if the gap is nonexistent. One possible effect induced by this phenomenon is the reduction of heat transfer from the array and detrimental to the overall heat exchanger performance. However, the exposure of the sharp edge on one end of pin fin may generate additional vortices and promote wake shedding in the system, by which, the heat transfer may be increase with the presence of the gap. One representative study of this subject in the past was performed by Sparrow and Ramsey (1978). They studied the effects of gap on heat transfer enhancement and pressure loss for 10 rows of staggered circular fins in a rectangular duct. The fin height-to-diameter ratio in their study is larger than that for modem day turbine applications. They found that the presence of gap has only a modest influence on the magnitude of heat transfer from the array, and the general trend of heat transfer from the array, as a fimction of Reynolds number and array geometry, is virtually insensitive to the gap existence. In the context of cooling of electronic components, Garimella and Eibeck (1990) studied the effects of gap on the heat transfer from an array of rectangular elements (25.4 mm x 25.4mm and 10 nun high). Their results reveals that the magnitude of heat transfer from the array decreases with gap size and would eventually reach a limiting value when the gap size is sufficiently large. They also suggested that streamwise spacing among the elements is a more predominating geometric parameter on the heat transfer from the array than the spanwise spacing. The range of Reynolds number for this study, 150-5,150, is relatively low for other heat exchanger applications and far lower than that for cooling of turbine airfoils. The present study marks an attempt to further extend our understanding and database concerning the issue of gap atop pin-fins. The experimental setup for this investigation is an inline array of short cubic-fin arrays. One unique feature of this study is the measurement technique in attaining the local heat transfer coefficient on both the fm surface as well as the remaining wetted surface in the system. The technique is based on transient liquid crystal thermography (Chyu and Ding, 1997a) with a modification in the post-nur image processing for determining the heat transfer from the pin elements. The present study also serves as a test bench for such a measurement approach. EXPERIMENTAL APPARATUS AND PROCEDURES The experiment uses a rectangular channel made of 12.7mm thick Plexiglas, which provides good optical accessibility as well as low thermal conductivity for liquid crystal transient test. Figure 1 shows the schematic of top view and cross-sectional view of the test channel. While the overall length and the width of the test section are fixed at 332.2mm and 47.6mm, respectively, the height of the channel is variable, i.e., 6.35mm, 7.94mrn, 9.53mm, 12.7mm, and 19.1mm. With the size of the cubic fin fixed at 6.35 mm on each side, these five channel heights corresponds to five different ratios of clearance-to-height, i.e. C/H=0.0, 0.25, 0.5, 1.0, and 2.0. Thirty-six cubic fins, made of aluminum, are arranged in a twelve rows by three columns inline array and mounted on the bottom wall of the test channel. Longitudinal (x-direction) spacing and transverse (z-direction) spacing among the centers 2

3 Figure 1 Schematic of Test Section Figure 2 Schematic of Experiment Setup of adjacent fins are kept the same at 15.88mm. This gives the inter-pin-spacing-to-height ratio, i.e., S t/h and S1/L, approximately 2.5. For typical pin-fin applications, this ratio falls within the range of optimal pin fin performance (Armstrong and Winstanly, 1987). Mounting of each cubic fin on the test surface is made by inserting a small positioning pin, about 1.5 mm in diameter and 3.2 mm long and made of aluminum, into the pre-drilled holes on both the pin element and the channel wall. Figure 2 shows schematic sketch of experiment setup. As shown in Fig. 2, compressed air, filtered, dried, and metered by standard ASME orifices is used as working fluid in this study. Located upstream to the test section are a pair of tubular in-line heaters that control the temperature of airflow stream to the desired level. Prior to the actual transient test, the compressed air flow is diverted away from the test section by two solenoid valves. A test starts only when the flow rates and temperatures of both streams have reached steady state. Flow rate is controlled to have the same Reynolds number, based on the mean velocity in the channel and cube height, i.e., Re = 16,000, for all test cases in this study. The local heat transfer coefficient is determined by the socalled transient liquid crystal technique. This technique requires the entire test surface, that includes the pin-fm surface and uncovered endwall on the channel bottom wall, to be coated with a thin layer ( mm) of encapsulated therrnochromic liquid crystals (TLC). Since TLC reflects different colors in response to temperature change as a result of lattice reorientation of the crystal structure, it serves as a local temperature indicator over the entire test surface. The particular type of TLC used in the present study is a wide band liquid crystal with a range of color variation from 36 C to 41 C. As test starts by switching the solenoid valves simultaneously and routing the heated compressed air into the test section, two thermocouples situated at the inlet and outlet of the test channel, respectively, are also set to measure the flow temperatures. An A/D signal acquisition system, sampling at. 10Hz, records these temperature readings. The time-varying TLC images on the test surface are recorded by a CCD video camera at a rate of 30 frames per second. After the transient test is completed, which normally takes less than two minutes, the TLC images are then digitized by a 24-bit video capture card, saved in the hard disk of a personal computer, and further processed for attainment of the local heat transfer coefficient. As an explicit relation between the surface temperature and time is required for solving heat transfer coefficients, the present system traces the lap-time to reach the maximum green-intensity of the TLC for each pixel in the viewing domain. While the temperature of this special point is calibrated against thermocouple readings for any batch of TLC purchased, it is approximately 37.7 C for the present case. IMAGING PROCESSING AND DATA REDUCTION The post-run image processing and data reduction procedure is to calculate the local heat transfer coefficient based on the relation of the lap-time required for a temperature change from the initial temperature to the temperature exhibited by the liquid crystals at every viewing pixel. One way to facilitate this procedure is the use of the solution of one-dimensional, transient heat conduction model over a semi-infinite slab with a time-varying convection boundary condition (Metzger and Larson, 1986; Chyu et. al., 1997b). To alleviate the error incurred by the assumption of one-dimensionality and semiinfinite domain, this approach generally requires that the test section be made of low-conductive material and reasonably thick. Flat Plexiglas is a viable choice that meets such requirements. In the present study, however, the onedimensional model may be invalid on the surface of cubic pins which have sharp edges and perpendicular faces. The heat paths inside such elements can be highly multi-dimensional. In addition, much detailed local heat transfer information on the 3

4 pin surface is considered to be unnecessary from the standpoint of practical applications. As a result, a "lumped model" that renders the element-averaged heat transfer coefficient over the pin surface is implemented in the post-run data reduction procedure. The overall data reduction procedure here is a combination of two approaches: (I) One-dimensional transient model for uncovered endwalls, and (2) lumped-heat-capacity model for the individual pin elements. Outlined below are brief introductions of both approaches. One-Dimensional Transient Model The one-dimensional transient model treats the substrate (Plexiglas channel wall) beneath the surface as a semi-infinite solid domain. This is a reasonable assumption provided that the transient test completes before the heat penetrates through the channel wall. When the surface is suddenly exposed to a forced flow stream, with a steady convective heat transfer coefficient, h, prescribed on the surface, the temperature field in the solid domain can be modeled by the following one-dimensional, transient heat conduction equation, i.e. The boundary and initial conditionsare k a 2 T ar where Ti is the initial temperature of the test section, T, is - k = h(tv, -T, ) ay y= 0 =T. t=0 = Ti the local surface temperature, and T, is the flow reference temperature. The difference between T, and T, represents the driving potential for the convective heat transfer in the system. eqs. (1)44) leads a solution of T w expressed as In a typical heat convection system, the reference Tw -Ti Tr -Ti 1 exp h 2at er f k2 t hrali temperature T, is readily avalable, i.e. equal to the temperature of the mainstream. As the time-varying TLC images provides a relation between T and t over the entire viewing domain, the distribution of local heat transfer coefficient, h, can be resolved from the above equation. True step changes of the applied flow temperatures in reality are usually not possible, and the reference temperature, in fact, is a function of time. This can be accounted for by (I) (2) (3) (4) (8) modifying the solutions via superposition and Duhamel's theorem. The solution becomes: T-T; = Eu(t - t i )AT, (6) i=1 Where 1 h 2 k 2 U(2 - Ti ) = 1- exp a(t - T 1 ) erfcth irri c )) i. (7), and AT, is the stepwise temporal increment of reference temperature for Duhamel integration. Lumped-Heat-Capacity Model One key feature of the lumped model is the assumption that the temperature inside the domain of interest shows no spatial variation and is a function of time only. To facilitate this model in an actual test, the heat transfer system under consideration must have a small magnitude of Biot number. This is the reason why the cubic fins in the present study are made of aluminum, rather than Plexiglas as used for the rest of the system. The Biot number for the aluminum fin is on the order of to Considering an element with a mass m and initial temperature T 1 is suddenly exposed to a flow stream which has dt ha(t -T1 ) = - mcp (8) a steady temperature T, and imposes a convective heat transfer T (9) coefficient, h, on the element's surface. If the element is of low Biot number, its temperature, T(t), can be modeled by an initial value problem, i.e., T lukt - 1 exp(--) mc P (10) and where A is the effective heat transfer area and ; is the constant pressure heat capacitance of the element. The solution to the above equation is To a great extent, this solution is similar to, yet simpler than, Eq. (5). This resemblance makes it possible to implement T -11 = Eu(t - ti)at, (6) the two solutions together in the same numerical procedure for 4

5 h 2 U(t al expfa(t TO) k2 the post-run data reduction. For imperfect step changes in flow temperature, superposition and Duhamel's integral can also be applied, as in eqs. (6) and (7), i.e. where RESULTS AND DISCUSSION Most of the measured results present below are in the form of dimensionless heat transfer coefficient, i.e., Nusselt number. The uncertainty analysis with a 95% confidence level on the measured parameters uses the method of Kline and McClintock (1953). Nu measured in the present liquid-crystal-based system depends strongly on the temperatures of the test surface, inlet, and exit. The uncertainties of these temperature readings are about C, which correspond to 0.5%, 0.3% and 0.7%, respectively. In addition, the uncertainty of Nu is also affected by the errors in the temperature-color calibration of liquid crystal, the lap-time for the liquid crystal reaching the designated color, and the thermal diffusivity of the substrate. The errors on these three parameters are estimated at 0.5%, 0.4%, and 1% respectively. Mother major error contributing to the uncertainty of Nu is the error in measuring the flow rate or Reynolds number in the air supply system, which is about 5%. Combining all these error factors leads to the overall 8% uncertainty in Nu. Figure 3 presents the spanwise-averaged, streamwiseresolved Nusselt number on the uncovered section of the endwall (Nu.) where the cubic pin-fms are mounted. As mentioned earlier, all the cases tested are under the same Reynolds number at 16,000. Here the variation of Nu. is plotted against the row number. The domain of a specific row is defined as a region bounded by one half the longitudinal (stnamwise) distance upstream and downstream from the center of a cubic fm located in that row. The data shown in Fig. 3. reveal that, regardless of the size of clearance atop the cubic pins, Nu declines gradually along the streamwise direction. This is typical for the inline array, as observed by Chyu and Goldstein (1991). For the baseline case without gap, the spanwise spacing among adjacent pins forms a somewhat straight path that permits the flow passing through the array without much interaction with the pins, particularly in the spanwise direction. The transport phenomena under this condition reveal a characteristic of flow in a smooth channel. Although Nu exhibited in Fig. 3 shows a slightly declining trend even after twelve periods, it should eventually approach a constant, fully developed value for each case provided that a proper reference temperature in the channel is chosen (Chyu et al., 1997b). The key information revealed in Fig. 3 is a quantitative measure of the gap effects on the heat transfer from the array. The results overall indicate that the heat transfer from the arraymounted wall decreases with an increase in the gap-to-height ratio, C/H. Compared to the baseline case without gap present, the reduction of Nu avenged over the entire twelve rows is 1.6%, 13%, 24%, and 45% for C/H=0.25, 0.5, 1.0 and 2.0, respectively. This reduction by and large is caused by the flow diversion from the array toward the gap through which the flow passes with less resistance. The portion of flow diversion is expected to increase as the gap widens, hence the heat transfer reduces accordingly. Figure 3 also reveals an interesting and somewhat unexpected phenomenon that the Nu for C/H = 0.25, in fact, is generally higher than that of the baseline case, C/H =0, except for the upstream most region where the first few rows of pins are located. One plausible explanation is attributable to the shear layers generated near the sharp edge atop the cubic fins. The vortex enriched shear layer promotes overall turbulence level in the system, hence increases the heat re,cefl-lrr* I tt tt (1) C/H=0.50 Figure 3 Heat Transfer from Uncovered Endwall (2) C/F1.25 Figure 4 Live Images (in Grayscale) of Liquid Crystals on the Smooth Wall 5

6 - C/HW).00 /De 04* CO1W).00 rte C/HW).25 en H=2.00 Figure 5 Heat Transfer from Smooth Channel Wall Figure 6 Heat Transfer from Cubic Fin Surface transfer even on the endwall. To illustrate the existence of the shear layer atop a pin element, Fig. 4 displays live images (in grayscale) of liquid crystals on the smooth inall opposite to that mounted with cubic fins in the channel for C/H = 0.25 and 0.5. The brighter regions with sharp contrast in these images, typically implying higher local heat transfer coefficient, corresponds to locations directly atop the cubic pins. Based on authors' experience in liquid crystal imaging, these brighter spots, particularly for the case of C/H = 0.25, appear to bear the similar characteristics of jet impingement or shear layer reattachment after separation. Figure 5 shows the spanwise-averaged, streamwise-resolved Nusselt number on the smooth wall (Nu,). The shear layer impingement apparently diminishes for the cases of large gap; i.e. C/H = 1 and 2, possibly due to a combination of increased depth for shear layer penetration and excessive amount of through flow diverted upward from the array. For C/H = 0.25 and 0.5, although the heat transfer coefficient is lower than that of the baseline case C/H = 0 near the entrance region, it all becomes comparable toward downstream. Similar to the finmounted wall, an increase in gap size decreases the average Nu, over the entirety of the smooth wall. The reduction compared to the baseline case is 10.2%, 10.9%, 36.6%, and 51.3% for C/H = 0.25, 0.5, 1.0 and 2.0, respectively. One of the important parameters for evaluating the array performance as a heat exchanger is the heat transfer coefficient exclusively from the pin surface. Figure 6 shows the spanwiseaveraged, row-resolved Nusselt number of the cubic fins (Nu n). Similar to the results on the channel walls, the magnitude of Nu p for a given C/H generally decreases toward downstream or with 100 SO 70 Present study In-line cubic tin array Tr Genmene & Elbeck, 1990 In-line low-profile block any Re=2 DO sparrow a Ramsey Staggered circular pin.tin array Figure 7 Heat Transfer from Cubic Fin Surface vs. C/H Figure 8 Heat Transfer from Entire Wetted Area 6

7 C/H Endwali Pin Pin & Endwall Smooth Wall All _ _33.6 Table 1 Array Avenged Heat Transfer C/H Endwall Pin Pin & Endwall Smooth Wall All Unit: % Table 2 Array Avenged Heat Transfer Relation to the Baseline Case the row number. However, for the cases C/H = 0, 1.0 and 2.0, where the effect of shear layer domination over the gap may be insignificancnu p shows a moderate, local maximum at the third row after a sharp decline from the first row to the second row. Similar observation has also been reported in earlier studies on circular pin fins without gap clearance (Chyu, 1990). Such a rise. in Nup is attributable to vortex shedding initiated from the upstream rows and increase in the local turbulence level. An interesting and somewhat surprising finding revealed in Fig. 6 that, except for the first row, the magnitudes of Nu t, for the cases with relatively small gap clearance, i.e. C/H = 0.25 and 0.5, are significantly higher than that of the baseline case with no gap. In fact, Nut, for C/H = 1.0 is also higher than the baseline case from the sixth row and further downstream, although the difference is rather modest. This observation overall implies that the vortex generation atop a cubic element may extend its domain of influence beyond the vicinity of the top surface, particularly when the value of C/H is sufficiently small. Figure 7 shows the average Nu p over the entire array vs. C/H. Compared to the baseline case, the value of Nth, increases about 14% and 9% for C/H = 0.25 and 0.5 respectively. For C/H = 1.0 and 2.0, the difference is approximately 4% and 36% lower, respectively. Also shown in Fig. 7 are results from earlier studies by Sparrow and Ramsey (1978) and Garimella and Eibeck (1990). Although the actual magnitudes of Nu p vary among different cases, the general trends between the pin-resolved heat transfer and the clearance size are agreeable. Sparrow and Ramsey (1978) used circular pins in a staggered array. While staggered array generally produces a higher heat transfer than its inline counterpart, an array of circular pins may result in a relatively lower heat transfer than the corresponding cube array (Chyu et. al., 1998a). A cubic element, with sharp edges and corners, can induce excessive vortex shedding and higher turbulent mixing than a circular element. Garimella and Eibeck used an array of low-profile, rectangular blocks to simulate electronic packages under flow conditions of relatively lower Reynolds number. Both studies did not perform the baseline case and make comparisons. Figure 8 shows the average Nusselt number over virtually the entire wetted surface in the test channel (Nu,), which consists of the entire cube surface exposed to the flow, the uncovered endw-all, and the smooth surface adjacent to the gap clearance. The overall trend here is similar to that of the smooth wall displayed in Fig. 5. Except for the first four rows, the magnitudes of Nu, for = 0.25 and 0.5 are comparable to that of the baseline case C/H = 0. Since the pressure drop for the cases with gap present is expected to be lower than that without gap, the overall performance of an array, if measured as heat transfer enhancement per pressure loss, may be superior to the baseline case. Further studies in this aspect, as well as for different array configurations, are recommended. Table 1 lists all the key avenge Nusselt numbers over the entire array and Table 2 gives corresponding percentage variations compared to the baseline case. CONCLUSION AND SUMMARY An experimental heat transfer study has been performed to investigate the effects of different sizes of gap clearance atop an inline cubic-fin array. Using a liquid crystal imaging technique combined with a one-dimensional transient model and a lumped heat capacity model, detailed heat transfer contributions from all the participating surfaces in the test channel housing the array can be realized. Key conclusions drawn from this study are as follows: Except for the pin elements, heat transfer from all the participating surfaces in the housed channel, i.e., the uncovered endwall and the smooth wall adjacent to the gap clearance, generally decreases with an increase in the size of the clearance. Such a reduction.trend is much more significant for the cases with relative larger clearances, i.e., C/H = 1.0 and 2.0, than that of the smaller clearances. In fact, the heat transfer from the 7

8 uncovered endwall downstream to the sixth row is comparable between the case of the smallest gap (C/11 = 0.25) and the baseline case (C/H = 0.0). In terms of spatial variation, the most significant drop of heat transfer compared to the baseline case exists in the entrance region involving the first four rows of the array. A slight opening of gap atop the cubic fins (C/Fi = 0 25 and 0.5) elevates the heat transfer from the fin surface, by about 10 to 15% higher than the baseline case. The shear layer separated from the sharp edges near the top surface of a cubic fin is considered to be responsible for this phenomenon. When the gap is sufficient wide, say C/H > 1, the heat transfer from the pin surface shows the similar trend to that prevailing on other surfaces; i.e., to decrease with the gap size. This observation is generally agreeable with the findings reported in the literature. As a result of the aforementioned two effects combined, the average heat transfer over the entire wetted area in the channel are very comparable for C/H = 0.0, 0.25 and 0.5. The implication is that a properly sized clearance atop a fm array may be desirable from the standpoint of increased heat transfer coefficient, if the pressure loss for such a case is lower than that without the gap. Chyu, M.K., Hsing, Y.C., Shill, T. LP., and Natarajan, V., 1998b, "Heat Transfer Contributions of Pins and Endwall in Pin-Fin Arrays: Effects of Thermal Boundary Condition Modeling,", ASME Paper 98-GT-175. Garimella, S.V., and Eibecic, P.A., 1990, Heat Transfer Characteristics of an Array of Protruding Elements in Single Phase Forced Convection, Int. J. Heat Mass Transfer, vol. 33, no. 12, pp Kline, Si., and McClintock, F.A., 1953, "Describing Uncertainties in Single-Sample Experiments," Mechanical Engineering, 75, pp Metzger, D.E., and Larson, D.E., 1986, Use of Melting Point Surface Coatings for Local Convection Heat Transfer Measurements in Rectangular Channel Flows with 90-Deg Turns, J. Heat Transfer, vol. 108, pp Natarajan, V., and Chyu, M.K., 1996, Heat Transfer on the Base Surface of Three-Dimensional Protruding Element," hit. J. Heat Mass Transfer, vol. 39, no. 14, pp Sparrow, E.M., and Ramsey, J.W., 1978, Heat Transfer and Pressure Drop for a Staggered Wall-Attached Array of Cylinders with Tip Clearance, hit. J. Heat Mass Transfer, vol. 21, pp Zukauslcas, A., 1972, Heat Transfer from Tubes in Crossflow, Advances in Heat Transfer, vol. 8, pp REFERENCE Armstrong, J., and Winstanley, D., 1987, A Review of Staggered Array Pin Fin Heat Transfer for Turbine Cooling Application, ASME paper 87-GT-201. Chyu, M.K., 1990 "Heat Transfer and Pressure Drop for Short Pin-Fin Arrays with Pin-Endwall," I Heat Transfer, Trans. ASME, vol. 112, pp Chyu, M.K., and Goldstein, R.J., 1991, Influence of an Array of Wall-Mounted Cylinders on the Mass Transfer from a Flat Surface, Int. J. Heat Mass Transfer, vol. 34, no.9, pp Chyu, M.K., Natarajan, V., and Metzger, D.E., 1992, Heat/Mass Transfer from Pin-Fin Arrays with Perpendicular Flow Entry, Fundamental and Applied Heat Transfer for Gas Turbine Engines, ASME HTD 226, pp , Chyu, M.K., Hsing, Y.C., and Natarajan, V., 1996, Convective Heat Transfer of Cubic Fin Arrays In a Narrow -Channel, ASME Paper 96-GT-201. Chyu, M.K., and Ding, H., 1997a, Heat Transfer in a Cooling Channel with Vortex Generators, Heat Transfer Gallery, J. Heat Transfer, vol. 119, p.206. Chyu, M.K., Ding, H., Downs, J.P., and Soechting, F.O., 1997b, Determination of Local Heat Transfer Coefficient Based on Bulk Mean Temperature Using a Transient Liquid Crystals Technique, 97-GT-489. Chyu, M.K., Hsing, Y.C., and Natarajan, V., 1998a, Convective Heat Transfer of Cubic Fin Arrays in a Narrow Channel, J. Turbomachinery, vol. 120, pp