THERMO-HYDRODYNAMICS OF DEVELOPING FLOW IN A RECTANGULAR MINI-CHANNEL ARRAY

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1 THERMO-HYDRODYNAMICS OF DEVELOPING FLOW IN A RECTANGULAR MINI-CHANNEL ARRAY Gaurav Agarwal Dept. of Mecanical Engineering Indian Institute of Tecnology Kanpur Kanpur (UP) 0016, India gaurag.agarwal@gmail.com Manoj Kumar Moarana Dept. of Mecanical Engineering Indian Institute of Tecnology Kanpur Kanpur (UP) 0016, India manojkm@iitk.ac.in Sameer Kandekar Dept. of Mecanical Engineering Indian Institute of Tecnology Kanpur Kanpur (UP) 0016, India samkan@iitk.ac.in ABSTRACT Termo-ydrodynamic performance of ydrodynamically and termally developing single-pase flow in an array of rectangular mini-cannels as been experimentally investigated. Te array consists of fifteen rectangular parallel mini-cannels of widt 1.1±0.0 mm, dept 0.77±0.005 mm (ydraulic diameter mm), inter-cannel pitc of.0 mm, macined on a copper plate of.0 mm tickness and aving an overall lengt of 50 mm. Deionized water used as te working fluid, flows orizontally and te test section is eated directly using a tin mica insulated, surface-mountable, stripe eater (constant eat flux boundary condition). Reynolds number between 00 and 300 at an inlet pressure of about 1.1 bar, are examined. Te laminar-to-turbulent transition is found to occur at Re 10 for average cannel rougness of 3.3 m. Te experimental pressure-drop under laminar (Re < 10) and turbulent flow conditions (Re > 10) closely matc wit te correlations in literature on developing flow. Te experimental Nusselt numbers for bot laminar and turbulent flow are found witin satisfactory range of values estimated from teoretical correlations existing in te literature on developing flows. Tus, te study reveals tat conventional teory, wic predicts termo-ydrodynamics of developing internal flows, is largely applicable for te minicannels used in tis study. No new pysical penomenon or effect is observed. NOMENCLATURE A cs Area of cross section (m ) C p Specific eat at constant pressure (J/kgK) D Hydraulic diameter (mm) f Friction factor (Darcy) G Mass flux (kg/m s) g Acceleration due to gravity (m/s ) Heat transfer coefficient (W/m K) k Termal conductivity (W/mK) L Lengt of te cannel (m) m Mass flow rate (kg/s) P Pressure (N/m ) Q Heat energy (W) q Heat flux (W/m ) T Temperature (K) u Velocity (m/s) w Widt of cannel (m) X Hydrodynamic entry lengt (m) X t Termal entry lengt (m) Greek symbols Heigt/widt (aspect) ratio of rectangular cannels Mass density (kg/m 3 ) μ Dynamic viscosity (Ns/m ) Surface rougness parameter (m) Wall termal conductivity (W/mK) Non-dimensional Numbers Gz Graetz number Nu Nusselt Number Po Poiseuille Number Pr Prandtl Number Re Reynolds Number Subscripts app Apparent avg Average cf Constricted flow f Fluid g Gas Hydraulic l Liquid sat Saturation t Tube, transition to turbulent w Wall x Distance from inlet INTRODUCTION In recent years, tere is a rapid growt of applications wic require ig eat transfer rates and fluid flows in relatively small passages. Some examples wic demand suc flow conditions are electronics cooling, space termal management, MEMS devices for biological and cemical analyses etc. Te development of new applications requiring cooling of components in a confined space as motivated researcers to focus on te prediction of te termoydrodynamic performance of mini and microcanels. 0t National and 9t International ISHMT-ASME Heat and Mass Transfer Conference Edited by Kannan N. Iyer Copyrigt c 0 Researc Publising Services ISBN: doi:.350/

2 0t National and 9t International ISHMT-ASME Heat and Mass Transfer Conference Nominally, microcannels can be defined as cannels wose dimensions are less tan 1 mm and greater tan 1 m [1]. Currently most researced microcannels fall into te range of 30 to 300 m. Cannels aving dimensions of te order of mm can be defined as minicanels. Despite te fundamental simplicity of laminar flow in straigt ducts, experimental studies of mini/microscale flow ave often failed to reveal te expected relationsip between te transport parameters. Furtermore, data of simultaneously developing flows, wic inerently provide ig species transport coefficients, are not very abundant. LITERATURE REVIEW Prior contributions tat are relevant to te present investigation are reviewed briefly. As regards te pressure drop caracteristics of internal flows, from a istorical perspective, Darcy (157), Fanning (177), Mises (1914), and Nikuradse (1933) did te pioneering work to relate te pressure drop in pipes to various parameters like relative rougness, Reynolds number, and transition from laminar to turbulent etc. Later Colebrook (1939) proposed a well known correlation. Moody (1944) presented te Colebrook s results in a grapical format correlating f darcy as a function of flow Re (laminar and turbulent regions) over a relative rougness (/D) range of 0 to 5%. In laminar region, relative rougness sows very little effect on te overall pressure drop. In contrast, in turbulent region, f increases wit Re and asymptotically reaces a constant value at iger Re; tis asymptotic value increases wit increasing relative rougness [-5]. As discussed earlier, now te focus as sifted from macro sized cannels/pipes to mini/micro counterparts. As regards eat transfer, te potential of microcannels in ig eat flux removal application was first igligted in 191 wen Tuckerman and Pease [6] studied te fluid flow and eat transfer caracteristics in microcannels, and demonstrated tat te electronic cips could be effectively cooled by forced convective flows of water troug microcannels fabricated eiter directly in te silicon cip or in te circuit board. In teir study a very ig eat flux removal rate was obtained as due to small caracteristic lengt of te micro-scale cannels. As regards friction factor in mini/micro systems, earliest study was reported in 193. Sortly after te initial work of Tuckerman and Pease [6], Wu and Little [7] conducted experiments to measure flow friction caracteristics alongside eat transfer caracteristics of gases flowing in silicon/glass microcannels aving trapezoidal cross-section wit a D =55.1, 55.9 and 7.3 m. Gases were used as test fluids (N, H, Ar); te measured values of f darcy were larger ( 30%) tan tose predicted by te conventional teory. Te autors concluded tat te deviations are due to te large /D and its asymmetric distribution on te cannel walls. After tese initial works, researc was carried out in te next years to study te flow and eat transfer in te microcannel or microtube. Te potential of te microcannel cooling tecnology was confirmed and evaluated in tose works. However, dissimilar and contradicting penomena of flow and eat transfer in microcannels or micro-tubes were also observed in some of tese works. Peng et al. [, 9] measured bot te eat transfer and flow friction for single pase convection of water troug rectangular microcannels aving ydraulic diameters of mm and distinct geometric configurations wit aspect ratios of Teir measurements of bot eat transfer and flow friction indicated tat te laminar eat transfer ceased at a Reynolds number of Te results indicated tat te geometric configuration ad a significant effect on te single-pase convective eat transfer and flow caracteristics. Te laminar eat transfer was found to be dependent upon te aspect ratio and te ratio of D to te center-to-center distance of te micro-cannels. Te turbulent flow resistance was usually smaller tan tat predicted by classical relationsips. Te Re corresponding to flow transition to fully developed turbulent flow became muc smaller tan te ordinary cannel flow ( ). Empirical correlations were suggested for calculating bot eat transfer and pressure drop. Wang and Peng [] also experimentally studied te forced flow convection of water and metanol in rectangular microcannels. Tey found tat te fully developed turbulent convection was initiated at Reynolds numbers in te range of , and tat te conversion from te laminar to transition region occurred in te range of Tey also observed tat te eat transfer beavior in te laminar and transition regions was quiet unusual and complicated, and strongly influenced by many factors suc as liquid temperature, velocity, cannel dimension. Te results provide significant data and considerable insigt into te beavior of te forced-flow convection in micro-cannels. Adams et al. [11] ave experimentally investigated te single pase turbulent forced convection of water troug circular cannels of diameters 0.76 and 1.09 mm. Tey found tat Nu for te microcannels are iger tan tose predicted by te traditional correlations for turbulent flows. Teir data suggested tat te extent of enancement in te convection increased as te cannel diameter decreased and te Reynolds number increased. Wu and Ceng [1] conducted experiment on laminar convective eat transfer and pressure drop of deionized water in trapezoidal silicon microcannels aving different geometric parameters, surface rougness, and surface ydropilic properties. Tey found tat laminar Nu and apparent friction constant depend greatly on different geometric parameters. Te Nu and apparent friction constant bot increase wit te increase in surface rougness. Te experimental results also sowed tat te Nu increases almost linearly wit te Reynolds number at low Re (Re < 0), but increases slowly at Re > 0. Tey furter developed dimensionless correlations for Nu and friction constant. Agostini et al. [13] ave done friction factor and eat transfer coefficient experiments wit liquid flow of R134a in rectangular mini-cannels. Two test sections made of aluminum multi-port extruded (MPE) tubes (cannels dimensions were - Tube-1: mm and Tube-: mm) were tested. Correlations available for large tubes in te literature were found to predict tere results reasonable well. Laminar to turbulent transition occurred around Re 000. Also, tey pointed out te importance of estimating uncertainties in reporting data on mini-cannels. Morini [14] as summarized te experimental work in mini/micro cannels (D 1.0 mm) done till 004. It is pointed out tat in many cases te experimental data of Po and Nu disagree wit te conventional teory but tey also appear to be inconsistent wit eac oter. Several reasons ave been proposed to account for tese differences. Rarefaction/ compressibility effects, viscous dissipation, electro osmotic effects, property variation effects, cannel surface conditions (relative rougness and morpology) and experimental uncertainties ave been invoked to explain te anomalous beavior of transport mecanisms in mini/micro cannels. 1343

3 0t National and 9t International ISHMT-ASME Heat and Mass Transfer Conference Steinke and Kandlikar [15, 16] point out te importance of specifying exact boundary conditions for comparison of data from various sources. For example, in many studies, te eat flux is only applied to tree sides of te cannel, wile, for comparative analysis, a uniformly applied eat flux is invoked. Also, since te eat transfer in microcannels is very large, te associated differential temperatures are small. Tey igligt te importance of accurate temperature measurements for estimating transfer coefficients. Tey also point out, as many oters ave done in te past tat simultaneously developing flows are te most complex and muc more accurate data is needed in tis regime. Hetsroni et al. [17, 1] ave analyzed and reviewed a large body of data in circular, triangular, rectangular and trapezoidal mini/ micro cannels wit D from 60 m m. Tey discuss te effects of geometry, axial eat flux due to termal conduction troug te working fluid and cannels walls and energy dissipation in te fluid. Tey also discuss te entrance effects (inlet and outlet manifold design), effect of wall rougness, interfacial effects and measurement accuracy. As regards surface rougness, tey also conclude tat, as done by Sclicting [19] in te classical text, te presence of rougness on te wetted pipe surface favors an early laminar to turbulent flow transition. A need for a systematic approac to quantify te effect of surface rougness is also igligted. Reynaud et al. [0] ave also undertaken pressure drop and eat transfer measurements of D mini-cannels ranging from 300 m to 1.1 mm. All teir experimental results are largely in good agreement wit classical teory of conventional cannels. Some observed deviations are explained eiter by macroscopic effects (mainly entry and viscous dissipation) or by imperfections of te experimental apparatus. Kandlikar et al. [1] and later Taylor et al. [] point out tat since te modern mini/micro fluidic systems routinely violate te 5% relative rougness tresold, as set fort by te classical works of Nikuradse, Moody etc. mentioned earlier, due to te inerent limitations of microfabrication tecniques, tere is a need to modify te Moody s Diagram. Tey propose a concept of D cf, as follows: D D (1) cf Re and f were redefined based on te constricted flow diameter; Moody diagram was replotted by using te above new definitions. Later, tey tested various mini/microcannels and found tat te transition from laminar to turbulent flow is seen to occur at Re well below 0 because of rougness effects. Caney et al. [3] tested a 1.0 mm aluminum rectangular cannel 40 mm long wit flow Re Tey found tat experimental Po and Nu sow a good agreement wit classical correlations for conventional cannels. Recently, Hrnjak and Tu [4] studied fully developed flow frictional pressure (Re ) in rectangular microcannels wit D range of m, eigt-to widt ratio range of , and relative rougness range of %. In te laminar region, Poiseuille number (Po) of bot liquid and vapor R134a flow in microcannels wit smooter surfaces (R a /D < 0.3%) agree wit te analytical solution based on te Navier Stokes equation. Te critical Reynolds numbers were found to be marginally smaller tan te conventional values (i.e. Re 300). In te turbulent region, te friction factors are found to be considerably larger tan tat predicted by te Curcill s (1977) equations for smoot tubes. t Te relatively few works available in literature in te field of microscale termal-ydraulics (especially on mini-cannel regime, 3.0 mm D 00 m) reveal contradictory conclusions and tere are still important discrepancies between te results obtained by different researcers. Tis can be largely attributed to experimental uncertainties, effect of rougness, manifold design and control of boundary conditions in te experiment. Secondly, very limited combined fluid flow and eat transfer studies are available in literature for developing flow in mini-micro cannels. No two models can be compared wit eac oter because exactly matcing sets of experimental results are also difficult to get in te literature. So, tere is a need of complete series of data for simultaneously developing flow, wic is not available in literature [5]. Te aim of te present work is to fill tis gap. EXPERIMENTAL DETAILS AND PROCEDURE Te experimental facility is designed and constructed as illustrated scematically in Figure 1-a. Te test section consists of an array of fifteen rectangular parallel minicannels (w = 1.1±0.0 mm, d = 0.77±0.005 mm; D = mm), macined on a copper plate of x9x13 mm 3 wit eac cannel lengt = 50 mm. Cannels are connected by inlet and outlet eaders of 50x0x4 mm 3. Figure 1-b sows te actual potograp of te mini-cannel test section. Te grooved cannels are covered by transparent polycarbonate seet enabling flow visualization (boiling experiments were also done but not reported ere) and aiding insulation from top of te test section. Cannel rougness parameters are measured at different locations using laser surface profilometer and ten averaged to estimate te effective rougness. Te effective value of R a is found to be 3.3 m. (b) (a) Figure 1. (a) SCHEMATIC LAYOUT OF THE EXPERIMENTAL SETUP (b) COPPER PLATE MINI-CHANNEL ARRAY (c) DETAILS OF THE MINI-CHANNEL ARRAY (c) 1344

4 0t National and 9t International ISHMT-ASME Heat and Mass Transfer Conference A mica insulated strip-eater (50x50x1 mm 3 ) is attaced below te copper plate using termal paste to eat te incoming working fluid under constant eat flux condition. Compared to te cannel size, te eater-block as a very large eat capacity. Tus, it is reasonable to assume tat te eat flux on te test specimen is constant along te tree sides of te cannels. Te top side is insulated, as sown in Figure 1 below. Te working fluid (distilled and deionized water) at a fixed temperature (maintained by a constant temperature bat) is allowed to pass troug te mini-cannel array via te inlet and outlet eaders. A digital variac controls te power supply to te strip-eater. Te fluid temperature at inlet and outlet of te test section are measured using two J-type termocouples suitably located in te inlet and outlet eaders. Two more J- type termocouples are placed 15 mm from te bot ends of cannel, centrally along te cannel lengt, in order to calculate te wall temperature, as sown in Figure 1-c. Te pressure drop across te test section is measured using a differential pressure transducer (Honeywell: FP000). It can measure in te range of Pa wit an accuracy of 0.1% of full scale reading after calibration. Data acquisition is carried out using a PCI-DAQ (NI TBX-6T) and is designed on LabView platform. Proper insulations are provided werever necessary so as to minimize te eat losses to te environment, wic are found to be below 1 %. RESULTS AND DISCUSSION Pressure Drop Te test section dimensions and experimental parameters are cosen in suc a manner tat te flow in te cannels is always developing (bot ydrodynamically and termally) eiter along te full lengt of te cannel or at least for some lengt of te cannel from te inlet. Figures -a, b, sow te ydrodynamic and termal entry lengt estimations wit respect to te flow Re, based on standard equations [4], as noted on Figure. As per te classical teory, at Re 10, te ydrodynamic entry lengt in laminar flow region is 49.9 mm, wic is approximately equal to total cannel lengt, i.e. 50 mm. If te laminar-to-turbulent flow transition is believed to take place at Re = 300, ten for all Re > 10, te flow along te entire lengt of cannel will be developing in nature. For Re < 10, te flow will fully-develop somewere inside te cannel, as igligted in Figure -a. Interestingly, experimental observations (please refer to te next section) indicate tat te slope of te Po vs Re significantly canges at Re 10, suggesting te inception of transitional flows i.e. a drift away from laminarity. Considering tat te flow is indeed starting to get turbulent (transition to turbulent flow) at Re 10, conventional teory suggests tat te ydrodynamic entry lengt will ten vary between D to 60 D. If te upper limit of X = 60 D is considered valid, ten flow along te entire lengt of cannel will remain developing in nature for all Re > 10. It sould be noted, owever, tat Figure can, at best, be treated as a teoretical guideline; in practical reality te boundaries between developing and fully developed may be fuzzy due to intrinsic perturbations and inerent system/ardware design limitations, wic induces non-ideal flow caracteristics. As regards te termal boundary layer development, since te applicable Prandtl number is in te range of Pr 3-4, under laminar flow conditions, flow is termally developing along te entire cannel lengt (refer Figure -b; unless for Re < 350, in wic case te flow will be termally developing Hydrodynamic entry lengt (mm) Termal entry lengt (mm) Hydrodynamic entry lengt (Transition Re=10) Hydrodynamic entry lengt (Transition Re=300) X =0.05ReD Cannel lengt=50mm Transition at Re=10 Transition at Re=300 X =60D X =D Pr=4 Pr=3 Pr= (a) Transition Re=10 Cannel lengt=50mm 5 X t =0.05RePrD X t =D (b) X t =60D Figure. VARIATION OF (a) HYDRODYNAMIC ENTRY LENGTH (b) THERMAL ENTRY LENGTH WITH FLOW Re for some lengt of te cannel only). For te case of turbulent flow, tere is a possibility tat flow termally fully develops witin te cannel lengt, as suggested by Figure -b. Typically, a lengt of D is considered sufficient for full ydrodynamic and termally turbulent flow development. As regards total pressure drop, it is primarily due to friction only as te acceleration component is considered to be negligible and gravitational component is equal to zero. For ydrodynamically developing flow, Poiseuille Number (Po) is not constant and can be calculated as follows: Pox x/re D () P / u x were x, te dimensionless axial distance in te flow direction for te ydrodynamic entrance region. Since in te present range of experimental Reynolds numbers te flow will be a combination of developing and fully developed, tis local Poiseuille number is integrated along te applicable developing lengt and developed lengt, to find te net average Poiseuille number across te lengt of te cannel considered, i.e., x L 1 Poavg Pox dx Podeveloped dx L (3) 0 x Figure 3 sows te observed pressure drop in te array as a function of flow Re. Te cange of slope in te trend at Re 10 is observed for all experiments. As noted earlier in Figure -a, te Reynolds number limit for te flow to remain 1345

5 0t National and 9t International ISHMT-ASME Heat and Mass Transfer Conference Experimental Teoretical Po (turbulence at Re=10) Pressure drop (Pa) Poiseuille Number (Po) 0 Blasius correlation Figure 3. EXPERIMENTAL PRESSURE DROP vs FLOW Re Figure 4. Po vs. Re FOR THE ARRAY completely developing inside te entire cannel lengt is also Re = 10. Tus, tis is a unique situation were te flow is simultaneously affected by te inception of laminar-toturbulent flow transition and te development of te velocity boundary layer. At tis stage, it is difficult to clearly differentiate between te two effects and assign explicitly discernable explanation to te cange of slope at Re 10. Also it is noted tat tere is considerable scatter in te data obtained after Re 10. Te transition from laminar to turbulent flow as been reported to occur in mini-cannels at Re considerably below 300 (e.g., Wu and Little [7], Wang and Peng [], Steinke and Kandlikar [16] etc.). Kandlikar et al. [6] conducted experiments wit SS tubes and observed an early transition occurrence for /D of 0.355%. Tey suggested te following equations to describe te effect of rougness for fully developed flow conditions: Re / D ; 0 / D 0.0 (4) t,cf.cf.cf Re / D 0.0 ;0.0 / D 0.15 t,cf.cf.cf were, D = D - (5),cf Equivalent rougness, is estimated by: = R +F (6) were, R pm is te average maximum profile peak eigt, and F p is te floor distance to te mean line in rougness carts. For te present experiments, /D,cf = application of Eq. 4 and 5 suggests transition at Re = 1750 wic is somewat less tat te observed value of Re = 10. For fully developed laminar flow in circular cannels, Poiseuille number (Po) remains constant and equals 64. For rectangular cross section, Poiseuille number decreases wit increase in aspect ratio () of te cross section. For te microcannel under study, Po is found to be 5.4 []. Te teoretical vs. experimental Po as a function of flow Re is sown in Figure 4. Te Blasius correlation for fully developed turbulent flow [4] is also sown for comparison by considering te critical Re = 10. In laminar flow regime (at low Re), flow will be fully developed for most of te part of te cannel lengt and terefore te experimental Po is in reasonable range of te predicted values. As te flow Re increases, te flow development lengt inside te cannel increases (as per Figure -a) and te deviation from te predicted fully-developed value is clearly seen. As te flow pm p drifts away from laminarity, Po becomes a strong function of flow Re. Wit te simultaneous superposition of flow development penomenon in te entire lengt of te cannel after Re 10 and incipience of transitional beavior, te experimental Po is greater tan te fully developed turbulent beavior, as predicted by te Blasius correlation. As can be seen from te figure, it is expected tat at very ig Re values, wit fully turbulent flows, te Po will indeed matc te predictions by te Blasius correlation. Since flow along te cannel is developing up to certain lengt and fully developed tereafter, te experimental results are compared wit correlations available for developing flow. Sa [7] proposed a correlation to predict pressure drop in developing laminar flow in circular ducts: Po P x x x x x ux x were x x/red (7) A duct is classified as (a) Long duct if x , (b) Sort duct if x Eq. (7) is applicable for long ducts only. Earlier Sapiro et al. [] proposed a sort duct correlation: Poiseuille Number (Po) Pox P / u x / x () Sa correlation Sapiro et al. correlation Experimental Best fit of experimental data Figure 5. Po vs. Re FOR DEVELOPING LAMINAR FLOW 1346

6 0t National and 9t International ISHMT-ASME Heat and Mass Transfer Conference Te developing laminar region in our experiments lie neiter in long duct nor in sort duct region. To te best of our knowledge no correlation exists in te literature for te range x As te ydraulic diameter increases, te working range for te same Reynolds number would ave fallen under sort duct domain. In suc case te correlation proposed by Sapiro et al. [], i.e. Eq. () need to be used. Tis correlation predicts less pressure drop tan te correlation by Sa [7], i.e. Eq. (7). From experimental observation, as depicted in Figure 5, it is found tat experimental Po is always less tan teoretical Po given by Eq. (7) or (). Tis deviation is well explained in te background of te fact tat we are working wit rectangular cannels. As mentioned earlier, for fully developed flow in rectangular cannels under consideration, Po =5.4 wile for circular cannels it is equal to 64, i.e., te former is about.5% less. Tis trend is maintained in developing flow also wen compared to te predictions of Sapiro et al. Heat Transfer Te local eat transfer coefficient for single-pase forced convection flow in mini-cannels can be calculated using: Q /A T T (9) conv cs w f were, T f is te average of te inlet and outlet fluid temperature and A cs = 0.5 D is te area of cross-section of te cannel. Te corresponding Nusselt number is given by: Nu D /k () Figure 6 depicts te complete experimental data set for te variation of local Nusselt number wit Re, at two different Pr. Nusselt numbers are found to vary between 4 and 19; corresponding eat transfer coefficient varied from W/m K. For ig Re, in all te experiments, eat transfer coefficient at location T is found to be lower tan tat at location T 1 (T 1, T at x = 15 and 35 mm respectively; refer Figure 1-c). Tis is in accordance wit te known fact tat for developing flows under uniform eat flux condition, Nusselt number decreases along te lengt of te cannel (For details refer to Figures 7 and also). An attempt is made to confirm experimental data wit existing teory for termally developing region. Experimental data in laminar region of termally developing flow are compared wit correlations proposed by Curcill and Ozoe [9], Sieder Tate [30], Stepan and Preuer [31], and Sa and London []; all tese available correlations are applicable for circular cross-section ducts wit uniform eat flux Pr=3.5 Pr= Figure 6. Nu X vs. Re AT DIFFERENT LOCATIONS f Curcill and Ozoe [9] proposed a correlation for termally developing flow in circular ducts wit uniform eat flux: Nu x 1/ Gz / 9.6 1/3 3/ (11) Gz / / 1/3 /3 1 Pr/ Gz / 9.6 were, Gz ( / 4)x* and x* x/(d Re Pr) Incropera and DeWitt [3] presented a correlation attributed to Sieder and Tate [30], wic is of te form: 1/ f w Nu 1.6 Re Pr D / L / (1) Stepan and Preuer [31] proposed a correlation as follows: Re Pr D / L Nu Pr ReD /L (13) Sa and London [] proposed a correlation as follows: 1/3 Nu RePr D / L ; Re Pr D / L 33.3 (14a) (14b) Nu Re Pr D / L ; Re Pr D / L Sieder and Tate Stepan and Preuer Sa and London Curcill and Ozoe Local Nu at T 1 Local Nu at T Pr=3.97 Nu=4.34 (Circular, developed flow) Nu=3.99 (Rectangular, developed flow) (a) Sieder and Tate Stepan and Preuer Sa and London Curcill and Ozoe Local Nu at T 1 Local Nu at T Pr=3.5 Nu=4.34 (Circular, Developed flow) Nu=3.99 (Rectangular, Developed flow) (b) Figure 7. COMPARISION OF EXPERIMENTAL AND THEORETICAL VALUES OF Nu FOR LAMINAR FLOW (a) Pr = 3.97, (b) Pr =

7 0t National and 9t International ISHMT-ASME Heat and Mass Transfer Conference Comparison of tese experimental values wit teoretical Nusselt numbers calculated using Eq are presented in Figure 7-a, b respectively for Pr = 3.97 and 3.5. Figure 7-a, b suggest tat present experimental values are in accordance wit teoretical relations as in Eq Point to remember ere is tat te above used teoretical correlations are for circular tubes in contrast to rectangular cannels used in present case. Kays and Crawford [4] suggested a correlation to find Nusselt number for fully developed laminar flow in rectangular ducts wit constant eat flux condition, i.e., Nu.35 (15) were, is te aspect ratio (=cannel eigt/cannel widt). In te considered case = 0.7, so using Eq. 15, one can find Nu = For fully developed laminar flow in circular cannels Nu = 4.34 [4]. Earlier it was sown tat Poiseuille number for developed laminar flow for rectangular duct (Po = 5.6) is less tan te value for circular duct (Po = 64) by.4%. Similarly, te Nusselt number for developed laminar flow in rectangular ducts is also less tan tat of circular ducts by.1%. Hence, our study sows a similar reduction in bot Nusselt and Poiseuille number for simultaneously developing flow in rectangular ducts, in comparison to circular ducts of same ydraulic diameter Dittus Boelter correlation Pillips correlation.5% less of Pilips correlation Local Nu at T 1 (Experimental) Local Nu at T (Experimental) 9 Pr= (a) Dittus Boelter correlation Pillips correlation.5% less tan Pillips correlation Local Nu at T 1 (Experimental) Local Nu at T (Experimental) -.5% 9 Pr= (b) For fully developed turbulent region in a circular duct, te value of Nu can be predicted using Dittus-Boelter correlation [3] as follows: Nu 0.03Re Pr (16) Here, Nu is constant irrespective of te location as flow is fully developed. Pilips [33] suggested te following correlation to predict Nu in a circular duct in te turbulent developing region. Nux D / x Re 0 Pr (17) Te teoretical Nusselt number tus obtained is compared wit te experimental value in Figure ; a satisfactory matc between te teoretical and experimental is obtained. Te experimental results are more in compliance wit Pillips correlation [33] tan Dittus Boelter correlation [3] because Pillips correlation [33] incorporates te effect of termally developing turbulent flow as well. It is clearly seen from te comparison of results presented in Figures 7 and tat eat transfer coefficient under turbulent conditions increased as compared to low Re, wen laminar flow conditions existed. SUMMARY AND CONCLUSIONS Termo-ydrodynamic study of simultaneously developing single-pase flow troug a mini-cannel array as been experimentally studied. Te mini-cannel array consists of fifteen rectangular parallel cannels (w = 1.1±0.0 mm, d = 0.77±0.005 mm, and D = mm), macined on a copper plate of mm tick. Flow Re was varied from wile flow Pr was maintained in te range of 3-4. Te main conclusions of te study are: (i) Developing flows provide very ig eat transfer coefficients in te entrance regions and terefore of interest for mini/micro scale ig eat flux removal applications. (ii) In general, te conventional teory wic predicts termo-ydrodynamics of internal flows is well applicable for te cannels used in tis study. No additional pysical effects were observed. (iii) Experimental data suggests an early laminar to turbulent transition near Re 10. Tis is primarily attributed to te cannel rougness morpology and possibly by corner swirls generated due to te construction of inlet/outlet manifolds of te array. (iv) Te experimental and teoretical Po as well as Nu are well correlated wit te available models for developing flow. Comparison was made wit circular cannels of equivalent diameter as well as wit fully developed flow conditions. ACKNOWLEDGEMENTS Te work is funded by te Department of Science and Tecnology, Government of India, under te sponsored project N: DST/CHE/ Tecnical support from Mr. C. S. Goswami is also acknowledged. Figure. COMPARISION OF EXPERIMENTAL AND THEORETICAL Nu FOR TURBULENT FLOW (a) Pr 3.97 (b) Pr

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