Microbial survival and heat generation during online sterilization of ...

Fig. 3. Sources of heat losses/gain for the entire sterilization system.( )q = MC T − Te pe ie oe( )q = U A T − Tt t t ia a( )q = U A T − Tb b b i a( )q = U A T − Tw w w m aqr = qgb+ qgt+ qgwwhere:A b = surface area of the reactor bottom (m 2 ),A t = surface area of the reactor top (m 2 ),A w = surface area of reactor outer walls (m 2 ),C pe = specific heat of effluent (kJ kg -1 K -1 ),M = flow rate of effluent (kg/h),(2)(3)(4)(5)(6)U wq gb = rate of heat gained by reactor bottom(kJ/h),q gt = rate of heat gained by reactor top (kJ/h),q gw = rate of heat gained by reactor walls(kJ/h),T a = ambient air temperature (K),T i = inlet temperature of cheese whey (K),T ia = temperature of air entrapped in headspace of reactor (K),T ie = inlet temperature of effluent (K),T m = mean temperature of cheese whey (K),T oe = outlet temperature of effluent (K),U b = overall heat transfer coefficient ofreactor bottom (kJ m -2 h -1 K -1 ),U t = overall heat transfer coefficient ofreactor top (kJ m -2 h -1 K -1 ), and= overall heat transfer coefficient of reactor walls(kJ m -2 h -1 K -1 ).The rate of heat gained by reactor top, bottom and walls iscalculated from Eqs. 7 -9.qqqgtgbgw( 2−1 )mtcptT T=∆tmbcbtT2 − T1=∆tmwcwT2 − T1=∆t( )( )where:C bt = specific heat of bottom material of reactor(kJ kg -1 K -1 ),C pt = specific heat of top material of reactor (kJ kg -1 K -1 ),C w = specific heat of wall material of reactor (kJ kg -1 K -1 ),T 1 = initial temperature (K),T 2 = final temperature (K),∆t = time interval (h),m b = mass of bottom of reactor (kg),m t = mass of top of reactor (kg), and= mass of walls of reactor (kg).m w(7)(8)(9)The terms m t , m b , and m w are calculated from Eqs. 10 - 12.m= A d ρt t t t(10)m= A d ρb b b b(11)Fig. 4. Heat transfer coefficients.mw = Adw Lwρwwhere:A dw = cross-sectional area of cylinder (m 2 ) ,d b = thickness of reactor bottom (m),d t = thickness of reactor top (m),L w = characteristic length, height of reactor (m),ρ b = density of material of reactor bottom (kg/m 3 ),ρ t = density of material of reactor top (kg/m 3 ), andρ w = density of the material of reactor walls (kg/m 3 ).The cross-sectional area of the cylinder is calculated as:2 2( )A = π r − rdw o i(12)(13)3.4LE GÉNIE DES BIOSYSTÈMES AU CANADA SINGH and GHALY

where:r o = outer radius of reactor (m), andr i = inner radius of reactor (m).The overall heat transfer coefficient of the reactor top (U t )is calculated as (Holman 2002):U1=1 1 dt+ +h h kitott(14)where:h it = convective heat transfer coefficient between innersurface of reactor top and air in reactor (kJ m -2 h -1 K -1 ),h ot = convective heat transfer coefficient between outersurface of reactor top and ambient air (kJ m -2 h -1 K -1 ),andk t = thermal conductivity of top material (kJ m -1 h -1 K -1 ).For laminar flow (10 4 < Gr f Pr f < 10 9 ), the convective heattransfer coefficients (h ot ) and (h it ) are calculated as (Holman2002):hhatit⎛ Tot− Ta⎞= 132 . ⎜ ⎟⎝ L ⎠⎛ Tia− Tit⎞= 132 . ⎜ ⎟⎝ L ⎠tt0.250.25(15)(16)where:Gr f Pr f = Rayleigh number,T it = temperature of inside surface of reactor top (K),T ot = temperature of outside surface of reactor top (K),andL t = characteristic length, diameter of the top (m).The value of the Prandtl number (Pr f ) is obtained from theStandard Tables (Holman 2002) while that of the Grashofnumber (Gr f ) is calculated using Eqs. 17 and 18.For the outer surface:Grf( − )3gβTot Ta Lt=2υFor the inner surface:( − )(17)3gβTia Tit LqGrf=2(18)υwhere:g = gravitational acceleration (m/s 2 ),Gr f = Grashof number,υ = kinematic viscosity (m 2 /s), andβ = volume coefficient of expansion (K -1 ).The film temperatures for the reactor top and inner surfaces arecalculated using Eqs. 19 and 20.TTffT=otT=ia+ Ta2+ T2where: T f = film temperature.it(19)(20)For ideal gases, the volume coefficient of expansion (β) isthe reciprocal of the absolute temperature of the gas while forthe other fluids it is obtained from the Standard Tables (Holman2002). For Eqs.17 and 18, the value of β is calculated fromEq. 21.β = 1 T f(21)The overall heat transfer coefficient of the reactor bottom(U b ) is calculated as (Holman 2002):Ub1=1 1 db+ +h h kibobb(22)where:h ib = convective heat transfer coefficient between innersurface of reactor bottom and cheese whey effluent(kJ m -2 h -1 K -1 ),h ob = convective heat transfer coefficient between outersurface of reactor bottom and ambient air (kJ m -2 h -1K -1 ), andk b = thermal conductivity of bottom material (kJ m -1 h -1K -1 ).The heat transfer from the cheese whey to the inner surfaceof the reactor bottom is by forced convection while that from theoutside to the air is by natural convection. Since the heattransfer coefficient due to forced convection (h ib ) is very largecompared to that of the natural convection (h ob ), the term (1/h ib )will be very small and can be neglected. Thus the overall heattransfer coefficient of the reactor bottom (U b ) is rewritten as:Ub=1hob1d+kbb(23)For laminar flow (10 4 < GrPr f

Table 2. Values of the various parameters used in theheat balance calculations for the conventionaland coil reactors.The overall heat transfer coefficient of the reactor wall (U w ),based on the outside area of the cylinder, is calculated as(Holman 2002):Uw=1 1+h howiw⎛ A⎜⎝ Aowiw1( 0 i )⎞ Aowln r / r⎟ +⎠ 2πk Lww(27)where:A iw = surface area of inside wall of reactor (m 2 ),A ow = surface area of outside wall of reactor (m 2 ),= convective heat transfer coefficient between cheeseh iwh owParameter Value UnitsA iw79482.29A ow88153.08A t2922.0C pe4.17d t2.00d w3.00g 9.81k t47.6k w47.6Lt61.0L w460.00r o30.50r i 27.50mm 2mm 2mm 2kJ kg -1 EC -1mmmmm/s 2W m -1 EC -1W m -1 EC -1mmmmmmmmwhey and reactor inside wall (kJ m -2 h -1 K -1 ),= convective heat transfer coefficient between reactoroutside wall and ambient air (kJ m -2 h -1 K -1 ), andk w = thermal conductivity of cylindrical wall (kJ m -1 h -1K -1 ).The heat transfer from the cheese whey to the inner surfaceof the reactor wall is by forced convection, while that from theouter surface to the air is by natural convection. Since the heattransfer due to forced convection (h iw ) is very large compared tothat of the natural convection (h ow ), the term (1/h iw ) (A ow /A iw ) willbe very small and can be neglected. Thus Eq. 27 is rewritten as:Uw=1how1( )Aow ln ro / ri+2πk Lww(28)For laminar flow (10 4 < Gr f Pr f < 10 9 ), the convective heattransfer coefficients (h ow ) is calculated as (Holman 2002):how⎛ Tow− Ta⎞= 142 . ⎜ ⎟⎝ L ⎠w0.25(29)where: T ow = temperature of outer surface of reactor wall (K).The value of the Prandtl number (Pr f ) is obtained from theStandard Tables (Holman 2002) while that of tthe Grashofnumber (Gr f ) is calculated using:Grf( − )gβT T L=2υ3ow a w(30)For Eq. 30, the value of β is obtained from tables Holman2002). The film temperature in this case is calculated as:TfTow+ T=2Table 3. Effect of flow rate on final cell number, destruction efficiency, and Dean number.(31)The values of the various parameters used in the heatbalance calculations are presented in Table 2.RESULTS and DISCUSSIONMicrobial survivalThe final microbial populations in the effluents and thedestruction efficiencies of the conventional and coil reactors areshown in Table 3. The results are the average of the threereplicates. The coefficient of variation varied from 0.0 to 9.3%.The survival curves for both reactors are shown in Fig. 5.Flow rate(mL/min)Residencetime(min)Reynoldsnumber*(Re)Deannumber**(De)Conventional reactorFinal cell number(x 10 6 )Destructionefficiency (%)Final cell number(x 10 6 )Coil reactorDestructionefficiency (%)510152025303540506070168.084.056.042.033.628.024.021.016.814.012.01.392.794.185.586.978.379.7011.1613.9516.7520.101.092.233.344.465.576.697.768.9311.1613.4015.410.0460.1220.2360.5471.0031.7182.3643.0104.0284.6695.20099.4098.4096.9092.8086.8077.4068.9060.4047.0038.5631.582.9032.3141.0960.2850.1250.0020.0080.4371.8303.8004.08060.7769.5285.5696.2498.3599.9890.9075.8053.5150.5146.20Initial cell number is 7.6 x 10 6 cells/mL* For both reactors** For coil reactor3.6LE GÉNIE DES BIOSYSTÈMES AU CANADA SINGH and GHALY

Fig. 5. Survival curves for the coil and conventional reactors.Survival curves are plots of the ratio of the concentration of thefinal number of microorganisms found after the treatment (N) tothe initial number of microorganisms (N o ) and are used tointerpret the inactivation kinetics of microorganisms. For theconventional reactor, the survival curve is described by:NNo= exp − .( 0 0319t)while for the coil reactor the relationship is:NNo= − t + × − 3 2 −4 32. 137 0196 . 65 . 10 t − 1× 10 t +− − −8 × 10 t − 3× 10 t + 6 × 10 t7 4 9 5 12 6(32)(33)Based on Eqs. 32 and 33, it would require more than 496minutes (1.69 mL/min) to destroy the whole initial populationin cheese whey in the conventional reactor while the optimumresidence time is 28 minutes (30 mL/min) in the coil reactor.Mahmoud and Ghaly (2004) found that the destruction ofmicrobial cells present in cheese whey in conventional UVreactors could be described by a first order equation. Koch(1995) and Mitscherlich and Marth (1984) reported thatmicroorganisms exposed to ultraviolet germicidal irradiation(UVGI) experience an exponential decrease in populationsimilar to other methods of disinfection such as heating,ozonation, and exposure to ionizing radiation.Generally the flow is laminar when the Reynolds number(Re) is less than 4000 and is turbulent when it is greater than4000 (Cengel 2003). Reynolds number calculations wereperformed on conventional and coil reactors using Eqs. 34 - 37.UdRe = h(34)υ(35)dh= do− diU =qA c(36)⎛De Re r x ⎞= ⎜ ⎟⎝ Γ ⎠rx =rΓ =0,5a ⎛ 1 2δ⎞⎜ − ⎟2 ⎝ 2 π a⎠+ br2 2Acπ=2 2( do− di )4(37)where:A c = annular section area (m 2 ),d h = hydraulic diameter (m),d i = inner diameter (m),d o = outer diameter (m),q = volumetric flow rate (m 3 /s),Re = Reynolds number, andU = mean velocity (m/s).The results (Table 3) show that theReynolds number was 1.39 for thelowest flow rate of 5 mL/min and 20.1for the highest flow rate of 70 mL/min,indicating that the flow was laminar inboth reactors.Dean number has been used as ameasure of the magnitude of thesecondary flow and is calculated fromEqs. 38-41 (Nemeth and Bucsky 1997).0.5(38)(39)(40)hb = (41)2πwhere:a = tube diameter (m),b = a parameter (m),h = pitch of screw line (m),r = tube radius (m),r x = radius of circle having same surface as area of halfcross-section beside static element (m),Γ = radius of curvature of spherical line cut out by helicalelement from tubular housing (m), andδ = thickness of coil (m).The critical Dean number for the coil reactor was found tobe 1.09 at 5 mL/min and 15.41 at 70 mL/min. The L/d wasfound to be 1.01. These results indicate the existence ofsecondary flows due to the helical nature of the flow. Websterand Humphrey (1997) stated that the two counter-rotatingvortices (Dean vortices) will be present in helical pipes, even forthe most mildly curved pipe. The secondary flow started todevelop in the coil reactor at a Reynolds number of less than 20.The results also indicate that as the flow rate increases, themagnitude of the secondary flow increases resulting in anincrease of the critical Dean number.Low flow rates in the coil reactor did not produce asecondary flow and as a result the coil shielded themicroorganisms from the UV radiation. However, the microbialVolume 49 2007 CANADIAN BIOSYSTEMS ENGINEERING 3.7

(a) Conventional reactor(b) Coil reactorFig. 6. Effect of flow rate on the steady-state temperatures (locations ofthermocouples are shown in Fig. 2.)destruction efficiency of the coil reactor increased as a result ofthe development of the secondary flow which caused mixingthat increased the exposure of microorganisms to UV radiation.On the other hand, a flow rate greater than 39 mL/min resultedin a residence time that was too short for microbial destruction.TemperatureFigure 6 shows the variation of steady-state temperature withflow rate in the conventional and coil reactors. The temperaturesat all locations in the conventional and coil reactors decreasedwith increase in flow rate, except for the influent temperature(location 8), which remained constant. At steady state, thetemperatures measured near the bottom of the reactors were lessthan the temperatures measured at the top. This was because theliquid (which was kept at room temperature) entered the reactorat the bottom and picked up heat from the lamp as it traveledupward to the outlet. It was also noticed that the temperaturesmeasured at all the locations in the coil reactor were slightlyhigher than those measured at similarlocations in the conventional reactor. Thiscould be due to the mixing created byDean vortices.The steady state effluent temperature(location 7) decreased from 45.8EC at5 mL/min to 25.5EC at 70 mL/min in theconventional reactor and from 46.1EC at5 mL/min to 26.2EC at 70 mL/min in thecoil reactor. The outlet temperaturereported in the literature for various UVreactors varied from 10 to 62.8EC(Koutchma et al. 2004; Tran and Farid2004; Mahmoud and Ghaly 2004; Abu-Ghararah 1994). According to theenvironmental technology verificationprogram conducted by the EPA (USEPA2002) on UV reactors produced by TrojanTechnologies Incorporated (London,ON),the temperature of the effluent will varydepending on the flow rate and the reactorgeometry.Heat balanceThe heat losses from the bottom of thereactors were neglected because: (a) thearea of reactor bottom was very small and(b) the cheese whey inlet temperature wassimilar to the ambient air temperature. Theheat gained by the reactor components (q r )was also ignored as there was no otherexternal source of heat other than the lamp.Therefore, Eq. 1 was rewritten as:qu = qe + qr + qw(42)Since the temperature of the reactorhead space (T ia ) and the temperature of theinside surface of the reactor top (T it ) werealmost the same, the convective heattransfer coefficient between the innersurface of the top and the air entrappedinside the reactor (h it ) was ignored. Thecalculated Rayleigh number for the wall outer and inner surfaces(Eqs. 17 and 18) and the top (Eq. 29) for the reactors at the flowrates of 5-70 mL/min was less than 1 x 10 9 indicating that theflow was laminar. Equations 15, 28, 14, and 26 were used tocalculate h ot , h ow , U t , and U w , respectively. While Eqs. 2, 5, and3 were used to calculate q e , q w , and q 3 , respectively.Table 4 shows the calculated values of the various heattransfer coefficients during steady state in the reactors. Theresults show that the heat transfer coefficients of the coil reactorwere higher than those of the conventional reactor. Rane andTandale (2005) stated that the use of bends results inenhancement in heat transfer due to secondary flows induced inthe bends. Nemeth and Bucsky (1997) indicated that thesecondary flow present in curved-tube flow causes a markedvariation in local transfer coefficients around the periphery ofthe tube.Table 5 presents the calculated values of the various steadystate heat losses and the distribution of the total energy input in3.8LE GÉNIE DES BIOSYSTÈMES AU CANADA SINGH and GHALY

Table 4. Values of the heat transfer coefficients at the steady state conditions for the conventional and coil reactors.Coefficient(kL m -2 EC -1 h -1 )Reactor typeFlow rate (mL/min)5 10 15 20 25 30 35 40 50 60 70h otConventionalCoil0.330.340.320.320.300.310.280.310.260.270.250.290.250.270.250.260.240.250.220.250.210.23h owConventionalCoil0.190.210.180.190.170.180.150.160.140.150.140.150.130.140.130.130.130.130.130.120.050.07U tConventionalCoil0.330.340.310.320.300.310.280.300.260.280.250.270.250.260.250.260.240.250.220.240.210.23U wConventionalCoil0.190.210.180.190.170.180.160.170.140.150.130.150.130.140.130.140.130.130.120.130.050.07Table 5. Distribution of energy input during the steady state stage for the conventional and coil reactors.Energy(kJ/h)Reactor typeFlow rate (mL/min)5 10 15 20 25 30 35 40 50 60 70q eConventionalCoil25.4527.2240.2646.7152.3656.9555.9259.9463.5269.9468.6272.6870.4074.1672.8075.8975.1178.8677.3880.5081.4583.60q wConventionalCoil10.6312.268.468.557.667.906.196.543.784.503.263.812.893.102.382.562.302.301.482.001.201.80q tConventionalCoil1.101.320.710.870.570.690.340.470.210.330.160.270.070.240.070.200.050.180.030.110.020.09q l *ConventionalCoil37.1840.8049.4356.1360.5965.1462.4566.9567.5174.7772.0476.7673.3677.5075.2578.6577.4681.3478.8982.6182.6785.49UV**ConventionalCoil52.8249.2040.5733.8729.4124.4627.5523.0522.4915.2317.9613.2416.6412.5014.7511.3512.548.6611.117.397.334.51* Energy converted to heat q l = q e + q w + q t** UV radiation = total energy input (108 kJ/h) - total energy converted to heat (q l ) - total energy lost in ballast (18 kJ/h as stated bymanufacturer)the conventional and coil UV reactors. A major portion of heatwas lost with the cheese whey effluent (23.6-75.4% inconventional reactor and 25.2-77.4% in coil reactor) while somelosses were through the reactor wall (1.1-9.8% in conventionalreactor and 1.7-11.4% in coil reactor) and very small losseswere from the reactor top (0.2-1.0% in conventional reactor and0.1-1.2% in coil reactor) depending on the flow rate. The rate ofheat lost with the effluent increased with increased flow ratewhereas the rate of heat losses through the reactor walls and topdecreased with increases in flow rate for the conventional andcoil reactors. As the flow rate increased, both the averagetemperature of the cheese whey effluent and the temperature ofthe air entrapped in the head space of the reactor decreased (andconsequently the differences between the average cheese wheytemperature and ambient air and between the air inside the headspace and the ambient air decreased) leading to less heattransfer. Blatchley and Peel (2001) and Mahmoud and Ghaly(2004) stated that the greater the volume passed through the UVreactor, the greater the heat removed.The results also indicate that the heat losses through theeffluent, walls, and top of the coil reactor were more than thoseof the conventional reactor. Nemeth and Bucsky (1997) statedthat helical and spiral coils are often used for transferring heatin mixing, storage, and reactor vessels, as well as in process heatexchangers. The calculated values of the output heat per unitvolume of the flowing cheese whey in both reactors are shownin Fig. 7. The heat gain per unit volume in both the reactorsdecreased with increased flow rate. Greater flow rates in the coiland conventional reactors resulted in lesser contact time of thefluid with the UV lamp thus causing less heat gain per unitvolume.According to the manufacturer (Trojan Technologies,London, ON), approximately 18 kJ/h of the energy input is lostin the ballast. Part of the remaining 90 kJ/h is converted to UVradiation at a wavelength of 257.3 nm while the rest is radiatedat other wavelengths and ultimately ends up as heat. Some of theradiated UV radiation is consumed in photochemical reactionsand the rest is also converted to heat. The fraction of energyconverted to heat increases with increases in flow rate in bothreactors (Table 5). As a result, the effective radiation which isVolume 49 2007 CANADIAN BIOSYSTEMS ENGINEERING 3.9

(a) Heat output rate(b) Volumetric heat outputFig. 7. Output heat per unit volume of flowing cheese whey in conventional andcoil reactors.(a) Conventional reactor(b) Coil reactorFig. 8. Photographs showing fouling on UV lamps of photo-reactors.consumed in a photochemical reactiondecreased with increase in flow rate. Intheir study on heat generation and itsimpact on lamp fouling during cheesewhey sterilization using a conventionalUV reactor, Mahmoud and Ghaly (2004)found that the heat generated by a lowpressure mercury arc lamp decreasedwhile the effective radiation that isconsumed in the photochemical reactionincreased with decreasing flow.FoulingSuspended particles and high turbidity ofthe liquid medium have been found toreduce the penetration ability of the UVlight and thus reduce the efficiency of theUV conventional reactor (Mahmoud andGhaly 2004). Similarly, microorganismscan aggregate or clump together, formingparticles that potentially protectmicroorganisms within aggregates thatwould otherwise be inactivated (USEPA1999). Visual observation of the UVlamps revealed less fouling in the coilreactor compared to conventional reactor(Fig. 8). As a result of secondary flow inthe coil reactor, the hydraulics of the flowdiffered from that in the conventionalreactor and resulted in less fouling.CONCLUSIONThe coil reactor was found to be moreefficient than the conventional reactor asit resulted in higher microbial destructionin shorter retention time. The destructionefficiency of the conventional reactordecreased from 99.4% (at 5 mL/min) to31.58% (at 70 mL/min), whereas thedestruction efficiency in the coil reactorincreased from 60.77% (at 5 mL/min) to99.98% (at 30 mL/min) and thendecreased with further increases in flowrate reaching 46.2% (at 70 mL/min). Therate of microbial destruction was found tobe exponential in the conventional reactorand polynomial in the coil reactor. Theflow was laminar in both reactors (Re =1.4 - 20.1). Dean flow was observed inthe coil reactor (De = 1.09 - 15.41) andDean vortices resulted in higherdestruction efficiencies and increasedheat transfer as compared to theconventional reactor. The maximumeffluent temperatures in the conventionalreactor and coil reactor were 45.8 and46.1EC, respectively. The heat generationand thus effective radiation that wasconsumed in the photochemical reactionin the conventional and coil reactors was3.10LE GÉNIE DES BIOSYSTÈMES AU CANADA SINGH and GHALY

affected by flow rate. The portion of input energy that wasconverted to heat increased from 37.18 to 82.67 kJ/h in theconventional reactor and from 40.80 to 85.49 kJ/h in the coilreactor when flow rate was increased from 5 to 70 mL/min. Theheat gain per unit volume of the flowing cheese whey decreasedfrom 123.93 to 19.68 kJ/L in the conventional reactor and from136.0 to 20.35 kJ/Lin the coil reactor when the flow rate wasincreased from 5 to 70 mL/min. The effective UV radiationdecreased from 52.82 to 7.33 kJ/h in the conventional reactorand from 49.20 to 4.51 kJ/h in the coil reactor when the flowrate was increased from 5 to 70 mL/min. Fouling in the coilreactor was less compared to the conventional reactor.ACKNOWLEDGEMENTThis research was funded by the Natural Sciences andEngineering Research Council of Canada (NSERC).REFERENCESAbu-Ghararah, Z.H. 1994. Effect of temperature on the kineticsof wastewater disinfection using ultraviolet radiation.Journal of Environmental Science and Health A29 (3): 585-603.APHA. 1967. Standard Methods for the Examination of DairyProducts. Washington, DC: American Public HealthAssociation.Ben-Hassan, R.M., A.E. Ghaly and N. Ben-Abdallah. 1993.Heat generation during batch and continuous production ofsingle cell protein from cheese whey. Biomass andBioenergy 4(3): 213-225.Blatchley, E.R.K. 1997. Numerical modeling of UV intensity:Application to collimated-beam reactors and continuousflowsystems. Water Research 31(9): 2205-2218.Blatchley, E.R. and M.M. Peel. 2001. Disinfection byultraviolet irradiation. In Disinfection, Sterilization andPreservation, 5 th edition, ed. S.S. Block, 823 - 852.Philadelphia, PA: Lippincott Williams & Wilkins.Brewster, M.E., K.Y. Chung and G. Belfort. 1993. Deanvortices with wall flux in a curved channel membranesystem: A new approach to membrane module design.Journal of Membrane Science 81:127–137.Cengel, Y.A. 2003. Heat Transfer: A Practical Approach, 2 ndedition. Boston, MA: McGraw-Hill.Ghaly, A.E. and A.A. El-Taweel. 1995. Effect of lactoseconcentration on batch production of ethanol from cheesewhey using Candida Pseudotropicalis. Transactions of theASAE 38(4): 1113-1120.Ghogomu, J.N., C. Guigui, J.C. Rouch, M.J. Clifton and P.Aptel. 2001. Hollow-fibre membrane module design:Comparison of different curved geometries with Deanvortices. Journal of Membrane Science 181 (1): 71-80.Holman, J.P. 2002. Heat Transfer, 9 th edition. New York, NY:McGraw-Hill.Khomich, V.A., I.A. Soloshenko, V.V. Tsiolko and I.L Mikhno.1998. Investigation of principle factors of the sterilization byplasma DC glow discharge. In Proceedings of ICPP & 25 thEPS Conference on Controlled Fusion and Plasma Physics,ed. P. Pavlo, Vol. 22C: 2745-2748. European PhysicalSociety.Koch, A.L. 1995. Bacterial Growth and Form. New York, NY:Chapman & Hall.Koutchma, T., S.K. Stuart, C. Stuary and B. Parisi. 2004.Ultraviolet disinfection of juice products in laminar andturbulent flow reactors. Innovative Food Science andEmerging Technologies 5: 179-189.Mahmoud, N.S. and A.E. Ghaly. 2004. On-line sterilization ofcheese whey using ultraviolet radiations. BiotechnologyProgress 20: 550-560.Mallubhotla, H. and G. Belfort. 1997. Flux enhancement duringDean vortex microfiltration: 8. Further diagnostics. Journalof Membrane Science 125: 75-91.Marshall, K.R. and W.J. Harper. 1984. Treatment of wastesfrom the dairy industry. In Surveys in Industrial WastewaterTreatment, eds. D. Barnes, C.F. Forster and S.E. Hrudey,Vol. 1: 296-376. Boston, MA: Pitman Advanced PublishingProgram.McCandless, L. 1998. Cider pasteurization via ultraviolet light(UV). http://www.nysaes.cornell.edu/pubs/press/1998/cider_uv_past.html. (2004/07/08)Miller, R.V., W. Jeffrey, D. Mitchell and M. Elasri. 1999.Bacterial responses to ultraviolet light. ASM News 65(8):535-541.Mitscherlich, E. and E.H. Marth. 1984. Microbial Survival inthe Environment. Berlin, Germany: Springer Verlag.Nemeth, J. and G. Bucsky. 1997. Secondary flow generated incurved flow. Hungarian Journal of Industrial Chemistry 25:91.Qualls, R.G., M.P. Flynn and J.D. Johnson. 1983. The role ofsuspended particles in ultraviolet disinfection. Journal of theWater Pollution Control Federation 55(10): 1280-1285.Rane, M.V. and M.S. Tandale. 2005. Water-to-water heattransfer in tube-tube heat exchanger: Experimental andanalytical study. Applied Thermal Engineering 25 (17-18):2715-2729.Singh, R.K. and A.E. Ghaly. 1988. Cheese whey processingalternatives. ASAE Paper No. 88-6540. St. Joseph, MI:ASABE.Singh, J.P. and A.E. Ghaly. 2006. Reduced fouling andenhanced microbial inactivation during online sterilizationof cheese whey using UV coil reactors. Bioprocess andBiosystems Engineering 29(2): 269-281.Tran, M.T.T. and M. Farid. 2004. Ultraviolet treatment oforange juice. Innovative Food Science and EmergingTechnologies 5(4): 495-502.USEPA. 1999. Wastewater technology fact sheet. Ultravioletdisinfection. EPA 832-F-99-064. Office of Water.Environmental Protection Agency, Washington, DC.http://www.epa.gov/owm/mtb/uv.pdf. (2004/06/04)USEPA. 2002. The environmental technology verificationprogram. Inactivation of MS2 virus in drinking water.NSF02/03/EPADWCTR. National Science Foundation,Washington, DC. http://www.epa.gov/etv/pdfs/vrvs/02_vr_trojan.pdf. (2005/11/10)Volume 49 2007 CANADIAN BIOSYSTEMS ENGINEERING 3.11

Van Osdell, D. and K. Foarde. 2002. Defining the effectivenessof UV lamps installed in circulating air ductwork. ARTI-21CR/610-40030-01. Final Report, prepared for the Air-Conditioning and Refrigeration Technology Institute,Arlington,VA.Webster, D.R. and J.A.C. Humphrey. 1997. Traveling waveinstability in helical coil flow. Physics of Fluids 9(2): 407-418.LIST OF SYMBOLSβ volume coefficient of expansion (K -1 )Γ radius of curvature of spherical line cut out by helicalelement from tubular housing (m)δ thickness of coil (m)∆t time interval (h)ρ b density of material of reactor bottom (kg/m 3 )ρ t density of material of reactor top (kg/m 3 )ρ w density of the material of reactor walls (kg/m 3 )υ kinematic viscosity (m 2 /s)a tube diameter (m)A b surface area of the reactor bottom (m 2 )A c annular section area (m 2 )A dw cross-sectional area of cylinder (m 2 )A iw surface area of inside wall of reactor (m 2 )A ow surface area of outside wall of reactor (m 2 )A t surface area of the reactor top (m 2 )A w surface area of reactor outer walls (m 2 )b a parameter (m)C bt specific heat of bottom material of reactor(kJ kg -1 K -1 )C pe specific heat of effluent (kJ kg -1 K -1 )C pt specific heat of top material of reactor (kJ kg -1 K -1 )C w specific heat of wall material of reactor (kJ kg -1 K -1 )d b thickness of reactor bottom (m)De Dean numberd h hydraulic diameter (m)d i inner diameter (m)d o outer diameter (m)d t thickness of reactor top (m)g gravitational acceleration (m/s 2 )Gr f Grashof numberGr f Pr f Rayleigh numberh pitch of screw line (m)h ib convective heat transfer coefficient between innersurface of reactor bottom and cheese whey effluent(kJ m -2 h -1 K -1 )h it convective heat transfer coefficient between innersurface of reactor top and air in reactor(kJ m -2 h -1 K -1 )h iw convective heat transfer coefficient between cheesewhey and reactor inside wall (kJ m -2 h -1 K -1 )h ob convective heat transfer coefficient between outersurface of reactor bottom and ambient air(kJ m -2 h -1 K -1 )h ot convective heat transfer coefficient between outersurface of reactor top and ambient air (kJ m -2 h -1 K -1 )h ow convective heat transfer coefficient between reactoroutside wall and ambient air (kJ m -2 h -1 K -1 )k b thermal conductivity of bottom material(kJ m -1 h -1 K -1 )k t thermal conductivity of top material (kJ m -1 h -1 K -1 )k w thermal conductivity of cylindrical wall (kJ m -1 h -1 K -1 )L b characteristic length of reactor bottom diameter ofbottom (m)L t characteristic length diameter of the top (m)L w characteristic length height of reactor (m)M flow rate of effluent (kg/h)m b mass of bottom of reactor (kg)m t mass of top of reactor (kg)m w mass of walls of reactor (kg)N final number of microorganismsN o initial number of microorganismsq volumetric flow rate (m 3 /s)q b rate of heat lost through reactor bottom (kJ/h)q e rate of heat lost with cheese whey effluent (kJ/h)q gb rate of heat gained by reactor bottom (kJ/h)q gt rate of heat gained by reactor top (kJ/h)q gw rate of heat gained by reactor walls (kJ/h)q r rate of heat gained by reactor components (kJ/h)q t rate of heat lost through reactor top (kJ/h)q u rate of heat generated by UV lamp (kJ/h)q w rate of heat lost through reactor walls (kJ/h)r tube radius (m)Re Reynolds numberr i inner radius of reactor (m)r o outer radius of reactor (m)r x radius of circle having same surface as area of halfcross-section beside static element (m)T 1 initial temperature (K)T 2 final temperature (K)T a ambient air temperature (K)T f film temperatureT i inlet temperature of cheese whey (K)T ia temperature of air entrapped in head space of reactor(K)T ie inlet temperature of effluent (K)T it temperature of inside surface of reactor top (K)T m mean temperature of cheese whey (K)T ob temperature of the surface of the bottom (K)T oe outlet temperature of effluent (K)T ot temperature on outside surface of reactor top (K)T ow temperature of outer surface of reactor wall (K)U mean velocity (m/s)U b overall heat transfer coefficient of reactor bottom(kJ m -2 h -1 K -1 )U t overall heat transfer coefficient of reactor top(kJ m -2 h -1 K -1 )U w overall heat transfer coefficient of reactor walls(kJ m -2 h -1 K -1 )3.12LE GÉNIE DES BIOSYSTÈMES AU CANADA SINGH and GHALY