Effects of Roughness Height in Forced Convective Heat Transfer: Macro to Micro Roughness

Transcription

1 MIE 1-03 International Conference on Mecanical, Industrial and Energy Engineering February, 013, Kulna, BANGLADESH Effects of Rougness Heigt in Forced Conectie Heat Transfer: Macro to Micro Rougness Md. J. Nine 1, *, Md. A. A. Mamun, AKM Nazrul Islam, Hyo-min Jeong 1 1 Department of Mecanical and Precision Engineering, Gyeongsang National Uniersity, Institute of Marine Industry, 445 Inpyeong-dong, Tongyeong, Gyeongnam, , Korea. Department of Mecanical Engineering, Kulna Uniersity of Engineering & Tecnology, Kulna -903, Banglades. ABSTRACT Te article is about te comparatie analysis of macro and micro type artificial rougness applied to enance conectie eat transfer performance under laminar and low turbulent regime. Circular ribs (, 0.1, 0.15) and nano particle porous layer (CuO particle) are fabricated oer te copper substrate respectiely in a rectangular duct aing 7.5 cross sectional aspect ratio. Only one rib pitc to rib eigt ratio (P/e = 10) as been cosen for all different eigt ribs. Nano and micro scale porous layer is formed on te copper substrate by an etcing wit HNO3 acid including CuO nanoparticles aing less tan 100 nm in size. Te result sows aerage turbulence intensity between two ribs decreases wit decreasing rougness eigt on te oter and nano porous layer sows significant eat transfer efficiency (about 51 % more tan bare copper plate) under laminar and low turbulent region witout te effect of ig turbulence. It appens toug te nano porous layer causes a little additional friction loss but canges te dynamic beaiors of fluids a lot in te icinity of eat transfer wall. Keywords: ctangular duct, Circular rib, Nano porous layer, Friction factor, Heat Transfer. 1. Introduction Rougness effect on friction factor and eat transfer draws a great attention of researcer. Inestigation of ig performance eat transfer surface is an important issue in te field of eat excanger were artificial rougness is te key to fabricate noel and effectie eat transfer surface. To enance eat transfer by means of enanced surface applying obstacles like fin increases turbulence on te surface as well. But friction losses get iger to create ig turbulence by suc a macro (Ribs) size rougness tat drags te system to enormous energy loss. In tis circumstance only micro rougness can be capable to sae energy and facilitates ig efficiency in te field of eat transfer. Conection is te most usual, effectie eat transfer mood greatly influenced by te artificial rougness fabricated on eat transfer surface. Te article reeals a comparatie and compreensie analysis of eat transfer efficiency between rib rougened surface and nano porous layer under laminar and low turbulent regime. Early researces [1-] just studied ery limited number of rib rougness configurations and data were also acquired from limited number of locations. Te effect of rib pitc to rib eigt ariation in a tube was first studied by Webb et al. [3] and te result was formulated into a correlation. In 1993, Okamoto et al. [4] studied about two dimensional square ribs mounted on a smoot surface and tey measured te water flow structure oer te ribs. Tey found tat te effects of ynolds number on te optimum pitc ratio for augmenting turbulence seemed to be insignificant. Tey also reported tat at te optimum pitc ratio, te pressure loss due to te ribs was maximized. Tis was te cost of augmentation of eat transfer. Han et al. [5] studied te eat transfer in square cannel wit different angle rib arrays on two walls for P/e = 10 and e/d = Tey reported tat te angle ribs and 'V' ribs proided iger eat transfer enancement tan te continuous ribs and te igest alue is at te 60 orientation amongst te angled ribs. X. Gao and B. [6] Sunden studied te rib configuration wit parallel and V-saped into different cannel aspect ratio. Tey found tat te V-ribs pointing downstream produced igest eat transfer enancement and friction factor and proided te best termal performance. Parallel ribs proided better performance tat V-ribs pointing upstream at ig ynolds number. Last few years tere ae been seeral inestigations on rib rougened surface to optimize te sape of rib and to find te effect of rib eigt. R. Kamali and A.R. Bines [7] performed a study on square, triangular, trapezoidal wit decreasing eigt in te flow direction, and trapezoidal wit increasing eigt in te flow direction. Tey found tat te eat transfer coefficient are strongly affected by te rib sape and trapezoidal ribs wit decreasing eigt in te flow direction proide iger eat transfer enancement and pressure drop tan oter sapes. M. Hu et al. [8] reports te effect of rib eigt on eat transfer in a rectangular cannel wit sarp entrance at ig rotation number. D.N. Ryu et al. [9] studied te caracteristics of turbulent flow in cannels wit two dimensional ribs and tree dimensional blocks. So oer te years te studies ae been performed to inestigate arious significant parameters of rib rougened surface tat influence te eat transfer performance suc as rib sape, rib angle, rib eigt (e), cannel aspect ratio (AR), rib eigt to cannel eigt ration (e/h) etc. In 004, T. Kunugi et al. [10] as introduced a new system of eat transfer metod between solid and fluid were tey treated te eat transfer surface wit te past * Corresponding autor. Tel.: address: mdjulker9@gmail.com

2 containing copper oxide (CuO), Carbon (C) and Alumina (Al O 3 ) nanoparticls aing te diameter of 100 nm or less and an acid or an alkali. Tey reealed tat te system proides ig efficiency wit low cost regarding te conectie eat transfer. Latter te mecanism of conectie eat transfer enancement formed by nano-poraous layer is resoled by M. Sibaara [11]. Tey calculated energy transfer numerically by using classical molecular dynamics metod to inestigate te effect of surface structure from 0.1 nm to 10 nm. Tey found tat te geometry of nanoscale structures on te surface affects te surface adsorption state and dynamic beaiors of fluid molecules. cently R. Sentilkumar [1] sowed tat ow te nanoparticle coating can cange te surface termal performance. Tey applied CNTs coating on brass extended surfaces. Tey explained experimentally te effect of CNTs coating on conectie eat transfer performance and compared te temperature distribution for coated and non coated surface. Te present study is about te comparatie analysis on macro and micro rougness in conectie eat transfer were te working fluid is air. Te study is significant to find out te effect of micro rougness on termal diffusion and adsorption beaior of fluid molecules in te icinity of eat transfer surface. Te oerall performance obtained from micro rougness as been compared wit tree different macro sizes circular ribs employed in te study. Te comparison between rib rougened and nano porous layer ae been elaborately described in terms of friction factor and conectie eat transfer. Nano porous layer does not disturb te main stream to enance eat transfer were rib rougened surface enances conectie eat transfer occurring uge pressure drop and creating large scale of turbulence. Fig. 1 Scematic diagram of deice (aboe) and real experimental set up (inset). Experiment.1 Experimental setup Te rectangular duct is directly connected to a low pressure fan (sown in figure 1). Te cannel geometry is caracterized by 10 mm cannel eigt (H) and 500 mm axial lengt wic includes 1000 mm test section wit te cannel widt of 75 mm. Te ribbed wall is copper plate of 10 mm tickness on wic circular ribs wit different rib eigt to cannel eigt ratio (, 0.1, 0.15) were mounted. Te rougness on one principle wall of cannel was created following uniform rib pitc (P) to rib eigt (e) ratio, P/e = 10. Air is tested fluid and te operating speed of te fan was aried by using a digital regulator to proide desired air flow rate. An orifice is installed just after te fan to measure constant flow rate constant for different rougness. Silicon rubber eating coil was perfectly attaced wit te elp of anoter support plate at bottom of copper test plate and coered wit cm glass wool for termal insulation in opposite of eat transfer surface. Te electric eat input was 100 Watt. Seen RTD-type termo sensors were used were two are installed at inlet and outlet of test section, fie of tem were precisely penetrated into te 10 mm tick eat transfer plate and spaced in equal distance to measure axial temperature distribution. Two static pressure taps were located at te bottom principle wall of cannel to measure axial pressure drop across te test section. One of tese tap was 45 mm upstream from te leading edge of te test section and te oter was 45 mm downstream of te test section. Digital manometer is used for taking static pressure. All manipulated data as been taken after te system getting stable and it took about an our to be stable or to be termally equilibrium.. Turbulence Test Straigt I-type probe as been calibrated and used carefully to get te stream wise flow caracteristics. Velocity profile and regarding turbulence were analyzed at inlet and middle section of te duct for different scale rougness by ot wire anemometer system. Specific location of approximately 9 < x/d < 3 as been selected from te inlet of te duct to get te aerodynamic caracteristics between two ribs at middle of duct. In Fig. 1, te position of data acquisition in te middle of duct is sown by a ertical line wic is selected at te flow separation zone just downstream of te rib. Near wall data as been taken at 0.5 mm interal for first mm from te eat transfer surface ten rest of ertical pat is taken at interal of 0.5 mm..3 Fabrication of micro scale porous layer Particle of copper oxide (CuO < 100 nm, collected from Nanostructured & Amorpous Materials Inc. Houston, Texas 77084, USA) and Nitric acid aing low concentration were mixed to prepare paste wic was ten applied all oer te surface by screen coating metod. Ten te coating is allowed to dry for next step of wasing wit ot water following te procedure described by T. Kunugi et al. [10]. A tin layer of nonoparticles were obsered as sown in figure.. MIE1-03-

3 f Smoot Surface - 1 Smoot Surface -, 1, Systems reproducibility at = Tw, o C x/d Fig. 4 producibility of Experimental Deice (Axial Wall Temperature) Fig. SEM morpology of CuO panoporous layer (a) Tickness of layer is about 0µm, (b) Porous surface Figure (a) sows te nanoporous layer formed on te copper substrate aing te uniform tickness of 5 µm and te figure (b) sows te CuO layer containing numerous porosity. Concentration of acid, amount of particle and duration of paste making are ery important factors to get a good nanoporous layer. Yun Lu et al. [13] applied 3.5 M HNO3 to create a sponge-type surface wit abundant rougness features on a nm scale on siler substrate..4 Experimental Validation Te alidation of smoot surface is sown in figure. 3 in terms of dimensionless representation of pressure drop calculated by using Darcy Weisbac equation (eq. ), were te experimental result is compared wit Blasius correlation found in open literature [14]. Te figure sows a good agreement te maximum deiation between experiment and adopted correlation is about 6.8%. Te system as been examined seeral times to ceck te data reproducibility by recording wall temperature distribution at te same ambient condition for bot of smoot and rib rougened surfaces. Figure 4 sows tat te plotted data are almost oerlapped in repeated experiment for bot smoot surface and rib rougened surface. Digital manometer (Dwyer-Series 477) aing tolerance ±0.5% at 16.6 C to 7.6 C as been used for static and differential pressure measurement. Calibration of I-type probe was done at te same of experimental ambient circumstance to be ensured te accuracy. 3. Data duction Smoot Surface Blassius Correlation ynolds number is an independent parameter to comparing results wit oter caracteristics. Te ynolds number () based on te cannel ydraulic diameter and bulk elocity is defined as eq. (1); Fig. 3 Friction factor for smoot surface (Experimental and Blassius Correlation) = D /ν = ρ D / µ (1) b Te dimensionless pressure drop caracteristics are obtained by using Darcy Weisbac equation wic can be expressed by eq. (); P f = * () L / D b ρ b Te range of ynolds number conducted by te experiment is from 3000 to For te alidation of smoot surface in tis range Blasius correlation can be MIE

4 used found in open literature [14] as mentioned in eq. (3); 0.5 f = ( ) ( 3) o Turbulent intensity as been measured only for axial component of elocity. Mean elocity ( mean ) is defined by eq. (4); mean N u( t) i= = 1 N (4) f/fo Were N is total number of data recorded in a period of time (i =1..3 N) Fluctuation elocity (U rms ) or rms alue of u component is expressed in eq. (5); N i= 1 rms = = ( mean N u( t)) (5) Turbulent Intensity (I) (%) rms I = *100 (6) mean Te eat transfer coefficients are ealuated from te measured temperatures and eat inputs. Wit eat added uniformly to fluid (Q air ) and te temperature difference of wall and fluid (T w T b ), aerage eat transfer coefficient will be ealuated from te experimental data ia te following equations- Q = Q = mc ( T T ) VI (7) air con p out in = and conectie eat transfer coefficient can be calculated as function of aerage wall temperature T w, fluid bulk temperature (T b ) - Qcon A( T T ) b = Were, w T b ( T ) out Tin Aerage Nusselt number is defined as eq. (9); Nu D K = (8) = (9) Were is conectie eat transfer co-efficient and K is termal conductiity of working fluid. Te comparison in termal performance (η) ealuation of te increased eat transfer and pumping power is considered as following expression (9); Nu Nuo η = (9) 1/ 3 f fo Fig. 5 Friction factor ratios for different rougness eigt 4. sult and Discussion 4.1Effect of Rougness eigt on friction factor Generally pressure drop can be canged by different factors like te rougness eigt, rougness spacing, rougness sape and type. Pressure drop across all along te cannel is sown in figure 5 regarding te rougness eigt in terms of dimensionless friction factor. Here only te rougness eigt is considered to calculate te normalized pressure drop following te optimized rib spacing (P/e = 10) reported by early researcers. Te figure sows tat te friction factor ratio differs remarkably wit arying te eigt of rougness een te rib pitc to rib eigt ratio (P/e) is kept constant. To keep te parameter P/e constant te number of ribs must be increased for te lower eigt ribs comparing tat of iger. So it is clear tat te effect of rougness eigt on pressure drop is more tan te effect of rougness spacing or number of rougness. Te figure is clearly sowing tat wit decreasing rougness eigt te friction factor ratio approaces to lower magnitude. Rib rougened surface causes muc pressure drops because of aderse pressure gradient grown between two ribs. Aderse pressure gradient occurs wen static pressure increases in te direction of flow. Te reason of aderse pressure gradient is flow blockage caused by periodic ribs and it depends upon te type of surface rougness. Rib eigt greatly affects pressure gradient. Anoter significant penomenon is noticeable tat te transient state between laminar and turbulent sows least alue of friction factor ratio. It obiously proes tat te effect of transient regime between laminar and turbulent does not causes muc pressure drop for roug surfaces as a result te eat transfer witin tis region is not significant. So tis flow caracteristic of transient state can be utilized for uge mass transfer from one place to anoter place troug a cannel aing macro scale surface rougness witout extra pressure loss. Te comparison among all of rougness sows tat te nanoporous layer does not disturb te main flow as rib does and it causes no extra pressure loss in te system. MIE

5 y/h y/h a) Inlet Velocity Profile at = 4700 ± Veloicity -m/s b ) Velocity profile in middle of te duct at = 4700 Smoot Duct CuO nano porous layer Veloicity -m/s Smoot Duct CuO nano porous layer were te elocity profile is totally canged in te middle of duct influenced by different rougness eigt toug te elocity profile obtained from nano porous layer is almost same as smoot surface weter it is at te inlet or middle of te duct. Figure 6(b) sows tat more tan alf of te duct perpendicular to te direction of main stream is subjected to te effect of rougness eigt. Te result sows rib eigt influences te flow a lot at te near wall region. Te total turbulence between two ribs depend upon te eigt of ribs/rougness because of te large flow recirculation zone created by flow separation beind te rib and te flow impingement on te surface just in front of next rib as sown in figure 8. Te impingement of flow at upstream te rib occurs ig pressure gradient tat causes backflow. So because of back flow and sudden pressure difference at flow separation zone tere creates large scale turbulence near te wall. Figure 7(b) sows wit decreasing rib eigt te magnitude of turbulence decreases simultaneously at te near zone. Nano-porous layer sows te lowest turbulence but found still iger tan tat of smoot surface near te wall. So te nano-porous layer does not elp to generate near wall turbulence tougt it is found tat te nano-porous layer still capable to transfer eat more tan smoot surface. It implies tat te eat transfer mecanism troug nano-porous layer is not because of turbulence. Fig. 6 Velocity profile a) Inlet elocity profile, b) Velocity profile in te middle of duct at = no 4700 (Turbulence in te Middle of Duct) y/h Turbulence % Smoot Duct CuO nano porous layer Fig. 7 Turbulent intensity measured in te middle of duct for different rougness eigt Tw, o C Fig. 8 Flow pattern between two ribs b) Wall temperature distribution at. 197 Smoot Surface 4. Effect of rougness eigt on elocity profile and turbulence Velocity and Turbulence is measured in ertical direction for only stream wise flow (u direction). It can be seen from figure 6, ow te rougness eigt disturbs elocity profile. Figure 6(a) sows te inlet elocity profile wit maximum tolerance ±50. Te flow is not disturbed because of smootness at te inlet x/d Fig. 9 Comparison of wall temperature distribution among arious rougness eigts MIE

6 Nu/Nu o Fig. 10 Nusselt number ratios arying rougness eigt Enancement Factor Fig. 11 Enancement factor arying and rougness eigt 4.3 Effect of rougness eigt on conectie eat transfer It can be obsered from Figure 9 tat te surface temperature distribution canges wit different rougness eigt in axial distance. Wit increasing te rougness eigt surface temperature is decreasing significantly. Een for nano porous layer te decline of surface temperature is remarkable under same ynolds number at constant eat flux. Te ratio of augmented Nusselt number to Nusselt number of smoot cannel plotted against te ynolds number alue is displayed in figure 10. Heat transfer enancement is clearly noticeable for rougened surface toug it seems to be constant at low turbulent region and te reason of increasing eat transfer can be compreensie from figure 7 and 8. Higer turbulence generated in te icinity of wall by macro scale rougness and it appens because of recirculation and reattacment as well as flow separation around te ribs. It is found tat te enancement by nano porous is not tat muc as macro scales rougness but te oerall enancement factor (sown in figure 11) efficiency is reasonably better because of low pressure loss caused by nano porous layer. In te laminar zone te nusselt number ratio and enancement factor bot exibit muc improed result obtained from nano porous layer toug at iger ynolds number it goes down by sudden decline. Te query is wy and ow te nano porous layer can be effectie to transfer eat from ig temperature solid to low temperature fluid een te material of porous layer is not te same as substrate. Figure 5 sows tat te nano porous layer causes a little additional pressure drop comparing smoot surface wereas about 51% of termal enancement as been acieed under laminar regime by nano porous layer sown in figure 11. So a significant improement as been acieed in te eat transfer mecanism witin laminar iscous sublayer aing numerous nano size pores formed by nano particles and eentually conectie eat transfer co-efficient increases. T. Kunugi et al. te eat transfer performance is ynolds number dependency, te temperature recoery of porous layer is incapable to catc up wit a ery fast temperature fluctuation, so tat te porous layer migt be a termal resistance wen te main stream is strongly turbulent. Tey found te expansion and contraction of air bubble-foam in te nanoporous layer to transfer eat from solid to liquid. But te present experimental study uses just air as a working fluid so in tis case te mecanism of bubble expansion and contraction in nano porous layer does not attract attention. Te dynamic beaior of fluid molecules in te icinity eat transfer surface can be canged by te surface aing numerous nano pores. So ere te reason wy conectie eat transfer is enanced by nano porous layer is te desorption capability affected by energy stored in nanoporous layer tat releases te air molecules quicker tan te smoot surface. So te enanced dynamic moement of air molecules may transfer energy gained by nano porous layer. And It as been reported by M. Sibaara [11], tat te nano porous layer is ery muc capable to recoer energy ery quickly from substrate. Tus te conectie eat transfer co-efficient increases at lower ynolds number by creating nanoporous layer on te smoot substrate wic occur least pressure drop comparing macro type rougness. But te nano porous layer is not suitable for turbulent eat transfer. 5. Conclusion Te study compares te mecanism of conectie eat transfer performance between macro and micro type rougness. Macro rougness like rib rougened surfaces works as fin and causes uge pressure drop and facilitates large scale turbulence into te cannel were te nano porous layer enances conectie eat transfer performance by improing te surface caracteristics in te icinity of wall witout disturbing main stream of flow and witout occurring extra pressure loss. All te results can be concluded as; i. Wit decreasing rougness eigt friction factor ratio decreases but te transient state between laminar and turbulent does occurs extra pressure loss een te surface contains macro scale rougness. So if mass transfer is only becomes te MIE

7 main issue for any system, transient state is more suitable for only mass transfer troug a cannel aing roug surface. ii. Rib rougened surface affects te main stream elocity by creating more turbulence. Were te nano porous layer does not ae any impact on turbulence toug tere occur a little additional pressure droop. Te rib aing 1/7t of cannel eigt can disturb te full cannel flow were te nano porous layers sere witout any disturbance. iii. Surface temperature decreases significantly wit increasing te rougness eigt. Nano porous layer can release eat more tan smoot surface. i. Under laminar regime nano porous layer can sere superb conectie eat transfer performance wit maximum 51% enancement. But at low turbulent region it goes down but still can manage about 18 % enancement witout causing significant pressure drop wereas te rib rougened surface can enances almost twice of nano porous layer occurring uge energy loss. Acknowledgements Tis researc was supported by Basic Science Program troug te National searc Foundation of Korea (NRF) funded by te Ministry of Education, Science and Tecnology ( ). NOMENCLATURE AR : Aspect ratio of rectangular cannel C p : Specific eat capacity, J/Kg. C D : Hydraulic diameter of duct, mm e : Rib eigt, mm f : Augmentatie Friction factor f o : Friction factor for smoot surface : Conectie eat transfer coefficient H : Cannel eigt, mm I : Current, amp K : Termal conductiity of fluid, W/m.K L : Lengt of calculation domain, mm m : Mass, Kg Nu : Augmentatie Nusselt number Nu o : Nusselt number for smoot surface P : Rib pitc, mm P/e : Rib pitc to rib eigt ratio t : Time, sec T : Temperature, C : elocity, m/s (t) : Instantaneous elocity, m/s mean : Mean elocity, m/s rms : Stream wise elocity fluctuation, mm V : Voltage, Volt P x µ ρ ν η : Pressure drop, Pa : Axial distance into cannel, mm Greek Letters : dynamic Viscosity, Kg/ms : air density, kg/ m 3 : kinematic iscosity [m /s] : termal performance factor REFERENCES [1] Antonia, R., Luxton, R.E., Te sponse of a Turbulent Boundary to an Upstanding Step Cange in Surface Rougness, ASME J. Basic Eng. Vol. 93, pp. 34, 1971 [] Siuru, W.D., Logan Jr., E., sponse of a Turbulent Pipe Flow to a Cange in Rougness, J. Fluids Eng. Vol. 99, pp , 1977 [3] R.L. Webb, E.R.G. Eckert and R.J. Goldstein, Heat Transfer and Friction in Tubes wit peated-rib Rougness, Int. J. Heat Mass Transf. Vol. 14, 4 pp , 1971 [4] Hanjalic, K., Launder, B.E., Fully Deeloped Asymmetric Flow in a Plane Cannel. J. Fluid Mec. Vol. 51 pp , 197 [5] J.C. Han, Y.M. Zang, C.P. Lee, Augmentatie Heat Transfer in Square Cannels wit Parallel, crossed and V-saped angled ribs, ASME, J. Heat Transf. ol. 113, pp , 1991 [6] X. Gao, B. Sunden, Heat Transfer and Pressure Drop Measurement in Rib-rougened ctangular ducts, Experimental Termal and fluid Science, ol. 4 pp. 5 34, 001 [7] R. Kamali, A.R. Bines, Te Importance of Rib Sape Effects on te Local Heat Transfer and Flow Friction Caracteristics of Square Ducts wit Ribbed Internal Surfaces, Int. Commun. Heat Mass Transf. Vol. 35, pp , 008 [8] Micael Hu, Yao-Hsein Liu, Je-Cin Han, Effect of Rib Heigt on Heat Transfer in a Two Pass ctangular Cannel (AR = 1:4) wit a Sarp Entrance at Hig Rotation Numbers, Int. J. Heat Mass Transf. Vol. 5, pp , 009 [9] D.N. Ryu, D.H. Coi, V.C. Pate, Analysis of Turbulent Flow in Cannels Rougened by Two- Dimensional Ribs and Tree-Dimensional Blocks. Part I: sistance, Int. J. Heat Fluid Flow, Vol. 8 pp , 007 [10] T. Kunugi, K. Muko, S. Muko, US Patent no A1, 005 [11] Masaiko Sibaara,Tomoaki Kunugi, Masasi Katsuki, Molecular Dynamics Study on Effects of Surface Structures in Nanometer Scale on Energy Transfer from Fluid to Surface, Heat Transfer- Asian searc, Vol. 34 (3), 005 [1] Rajendran Sentilkumar, Seturamalingam Prabu, Marimutu Ceralatan, Experimental inestigation on CNTs coated brass rectangular extended surfaces, ttp://dx.doi.org/ / j.appltermaleng [13] Yun Lu, Gi Xue, Jian Dong, HNO 3 Etced Siler Foil as an Fffectie Substrate for Surface Enanced Raman Scattering (SERS) Analysis, App. Surface Sci. Vol. 68, , 1993 [14] Frank P. Incropera, Daid P. De Witt, Introduction to Heat Transfer, nd Edition, Jon Wiley & Sons, Inc. pp. 408, 1990 MIE