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

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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
Page 6 and 7: Table 2. Values of the various para
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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