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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
Page 4 and 5: Fig. 3. Sources of heat losses/gain
Page 8 and 9: (a) Conventional reactor(b) Coil re
Page 10 and 11: (a) Heat output rate(b) Volumetric
Page 12: Van Osdell, D. and K. Foarde. 2002.

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