Pasteurization Modelling

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Journal of Food Engineering 77 (2006) 500–513

Modeling, simulation and optimization of abeer pasteurization tunnel

E. Dilay a, J.V.C. Vargas a,*, S.C. Amico a, J.C. Ordonez b

a Department of Mechanical Engineering, Federal University of Parana, CP 19011, 81531-990, Curitiba/PR, Brazilb Department of Mechanical Engineering and Center for Advanced Power Systems, Florida State University, Tallahassee, FL 32310-6046, USA

Received 28 June 2005Available online 22 August 2005

Abstract

This paper introduces a general computational model for beer pasteurization tunnels, which could be applied for any pasteur-ization tunnel in the food industry. A simplified physical model, which combines fundamental and empirical correlations, and prin-ciples of classical thermodynamics, and heat transfer, is developed and the resulting three-dimensional differential equations arediscretized in space using a three-dimensional cell centered finite volume scheme. Therefore, the combination of the proposed sim-plified physical model with the adopted finite volume scheme for the numerical discretization of the differential equations is called avolume element model, VEM [Vargas, J. V. C., Stanescu, G., Florea, R., & Campos, M. C. (2001). A numerical model to predict thethermal and psychrometric response of electronic packages. ASME Journal of Electronic Packaging 123(3), 200–210]. The numericalresults of the model were validated by direct comparison with actual temperature experimental data, measured with a mobile tem-perature recorder traveling within such a tunnel at a brewery company. Next, an optimization study was conducted with the exper-imentally validated and adjusted mathematical model, determining the optimal geometry for minimum energy consumption by thetunnel, identifying, as a physical constraint, the total tunnel volume (or mass of material). A parametric analysis investigated theoptimized system response to the variation of total tunnel volume, inlet water temperature, production rate, pipe diameter and insu-lation layer thickness, from the energetic point of view. It was shown that the optimum tunnel length found is �robust� with respect tothe variation of total tunnel volume, combining quality of the final product with minimum energy consumption. The proposedmethodology is shown to allow a coarse converged mesh through the experimental validation of numerical results, therefore com-bining numerical accuracy with low computational time. As a result, the model is expected to be a useful tool for simulation, design,and optimization of pasteurization tunnels.� 2005 Elsevier Ltd. All rights reserved.

Keywords: Pasteurization; Mathematical modeling; Volume element model; Optimization

1. Introduction

Through the past decades, the economic and environ-mental cost of energy has been steadily increasing. Suchgrowth makes fuel usage and energy efficiency important

0260-8774/$ - see front matter � 2005 Elsevier Ltd. All rights reserved.doi:10.1016/j.jfoodeng.2005.07.001

* Corresponding author. Tel.: +55 41 361 3307; fax: +55 41 3613129.

E-mail addresses: [email protected], [email protected](J.V.C. Vargas).

factors to be taken into account in the building of newfactories.

In a brewery company, the cost of electric energy andfuels comprises 20–30% of production costs in the twostages of bottled beer production, namely: (i) Grainprocessing, i.e., unit operations such as clarification,milling, fermentation and filtration and (ii) Beer packag-ing, which includes all operations undergone by the glassbottle, from its receiving, washing, filling up and pas-teurization to its secondary packaging and transporta-tion. Among all the equipments, the pasteurization

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Nomenclature

A area, m2

c specific heat, J/(kg K)cp specific heat at constant pressure, J/(kg K)cv specific heat at constant volume, J/(kg K)Dpd pipe diameter, mE energy, Jf friction factorg gravity, m/s2

h convection heat transfer coefficient, W/m2 �C�h wall-averaged heat transfer coefficient, W/

m2 �C, Eq. (11)H tunnel height, mK curve pressure drop coefficientk thermal conductivity, W/m �CL tunnel length, mLb bottle height, mm mass, kg_m mass flow rate, kg/sn number of volume elements in one tunnel

zonenb number of bottles in one volume elementnc number of curvesnve total number of volume elements in the

tunnelNu average Nusselt numberPb bottle production rate, bottle/hPr Prandt number, m/a_Q heat transfer rate, WRe Reynolds numberT temperature, �C~T temperature vector, �Ct time, stx residence time in a VE, su horizontal velocity, m/sU global heat transfer coefficient, W/m2 �CUp aggregated pasteurization unit, PU_Up pasteurization unit aggregation rate, PU/min

v vertical velocity, m/sV total tunnel volume, m3

V pipe cross section average velocity, m/sW tunnel width, m

_W power, Wx horizontal coordinate, mX fitting parameter in Eq. (11)y vertical coordinate, m

Greek symbols

a thermal diffusivity, m2/sd insulation layer thickness, mdw wall thickness, mDp pressure drop, PaDx volume element length, me tolerance value, Eq. (28)m kinematic viscosity, m2/sq density, kg/m3

Subscripts

1 external ambienta airb bottlebe beerc consumptionf air/water fogg glassi volume element numberin input valueins insulation materialint internalmin minimumout output valuep water piper water sprayrt total water sprays tunnel cross-sectiont water inside the tanktot totalve volume elementw wallwa waterwt water tank wallz zone number

E. Dilay et al. / Journal of Food Engineering 77 (2006) 500–513 501

tunnel deserves most attention since it consists of a greatnumber of electric pumps, with high steam consumptionin a complex heat regeneration system.

The pasteurization process was invented by theFrench scientist Louis Pasteur in 1864, when he demon-strated that wine diseases are caused by micro-organ-isms that can be killed by heating the wine to 55 �Cfor several minutes. The process therefore consists of asubtle heating of a food product to around 60 �C andmaintenance of this temperature for a few minutes in

order to inactivate or eliminate potentially harmfulmicro-organisms. The process stabilizes the productfor a certain period of time, without severe variationof its organoleptic characteristics.

Pasteurization has been used by the beer industrysince the nineteenth century, remaining practicallyunaltered, being carried out on the already bottledproduct (in-package pasteurization). Since the 60�s,however, with the introduction of pasteurization tun-nels, this activity has reached high production levels.

502 E. Dilay et al. / Journal of Food Engineering 77 (2006) 500–513

The continuous pasteurization of the product occurs bymeans of the traveling of the bottle through the tunnel,which consists of progressive hotter zones, holdingzones and progressively cooler zones (Engelman & Sani,1983). The process temperature is controlled by the tem-perature of the water spray on the bottles inside the tun-nel. The tunnel may have as many as eight heating zoneswith a system of shell and tube heat exchangers, regen-eration and steam water heating.

Factors such as bottle size, shape and material influ-ence the specific processing conditions, such as residencetime within the tunnel, to achieve appropriate results. Inorder to monitor the pasteurization process, i.e., to mea-sure the lethal effect of the heat treatment on the micro-organisms, the concept of Pasteurization Unit [PU] wasintroduced. It was defined that 1 PU is aggregated to theproduct when it is exposed to the temperature of 60 �Cfor one minute. Additionally, the rate of pasteurizationunits aggregated per unit of time (min), _UpðT Þ, was tab-ulated as a function of the temperature, T, the product isexposed to, which in turn is a function of time, t, in apasteurization tunnel (Broderick, 1977). The total num-ber of pasteurization units aggregated to the product inthe pasteurization process is therefore evaluated byBroderick (1977)

U p ¼Z ttot

0

_UpðT bÞdt ð1Þ

where ttot is the total processing time and Tb is the tem-perature at the center of the bottle, and _UpðT bÞ is ob-tained in this work from an exponential curve fit oftabulated data (Broderick, 1977) for the range45 �C 6 Tb 6 65 �C, as follows:

_U p ¼ 2.82� 10�9e0.32811T b ð2ÞIt is a common practice to aggregate 19 PU to the

product, although 13.7 PU are known to ensure productstability (Broderick, 1977). Due to operational difficul-ties related to discontinuities of other equipments inthe production line, the number of PU is considered ade-quate if kept in the 15–30 PU range. Further heat treat-ment may cause undesirable side reactions in theproduct, altering beer flavor and foam formation (Zufall& Wackerbauer, 2000).

The modeling of a pasteurization tunnel may be usedto predict the operation status of the pasteurization pro-cess, in order to suggest changes to the design, opera-tion, or even for process optimization. The heatingprocess inside a beer bottle traveling through a pasteur-ization tunnel was modeled previously by Brandon,Gardner, Huling, and Staack (1984) who found a con-siderable axial thermal gradient during the initial heat-ing, and a uniform temperature distribution after that.

Horn, Franke, Blakemore, and Stannek (1997) de-scribed a model for the unsteady convective heat trans-fer inside a bottle, taking into account the influence of

the convective flow on pasteurization and staling effectsand showed that the traditional procedure for determin-ing pasteurization units (PU) can considerably overesti-mate the actual effect if the reference point is not chosenaccurately regarding bottle size and shape. The authoralso suggested that convective transport of micro-organ-isms and staling effects have to be taken into accountduring the design of a tunnel pasteurization plant ifincreasing demands on product quality are to be met.

Kumar and Bhattacharya (1991) simulated naturalconvection heating of a canned liquid food during ster-ilization by solving the governing equations of mass,momentum and energy conservation, using a finite ele-ment code. It was found that the can coldest portionfluctuates in a region around 10–12% of the can heightfrom its bottom, at a radial distance approximatelyhalf-way between the center of the can and its inner wall.Tattiyakul, Rao, and Datta (2001), on the other hand,found a non-uniform temperature distribution with dif-ferent slowest heating points when modeling heat trans-fer to a canned corn starch dispersion, where a finiteelement based simulation software (FIDAP) was usedto solve the governing mass, momentum and energytransport equations.

Ghani, Farid, and Chen (2002) carried out a three-dimensional analysis of a soup can being heated fromall sides up to 121 �C, where the temperature transient,the velocity field and the slowest heating zone (SHZ)during natural convection heating were calculated. Inthis case, the partial differential equations describingmass, momentum and energy were numerically solvedusing a commercial software called Phoenics (2005),which is based on a finite volume method of analysis.Horizontally laid cans showed slower heating than ver-tically laid ones due to the enhancement of natural con-vection caused by the greater height of the latter.

Zheng and Amano (1999) adopted two different ap-proaches to model the pasteurization tunnel: (i) TheLumped Parameter Method (LPM), which was used tomodel the whole pasteurization system, including pipes,zones and heat exchangers and (ii) The ComputationalFluid Dynamics (CFD) technology to calculate the heattransfer and fluid flow rates in the heat exchanger tank.The temperatures of the spray water and the products inthe pasteurization process were calculated and com-pared reasonably well with the experimental data.

Beck and Watkins (2003) presented a heat and masstransfer model of sprays of several fluids, includingwater, which was based upon an assumed distributionof the number of drops. With that information, thedrops size distribution was obtained from the solutionof the mass and momentum conservation equations.Collisions and drag force were accounted for. The heattransfer problem was solved by applying the energyequation to the liquid and surrounding air, togetherwith the ideal gas model. All equations were solved


numerically by the finite volume method. The modelalso captured the conic sprays behavior and evaporatingsprays.

Rosen and Dincer (2003) reported that the industryusually conducts energetic analyses, at a macroscopic le-vel, by pinpointing the largest energy consumer compo-nent in the plant for a more detailed analysis. Forexample, in the case of breweries, the beer pasteurizationtunnel would be selected for a more detailed analysis.Following that path, the authors developed a methodol-ogy for the exergetic and cost analysis of processes andsystems. The analysis was based on the amounts of ex-ergy, cost, energy and mass (EXCEM) involved in theparticular process or system. The work presented a ser-ies of applications in engineering processes, such aspower and hydrogen generation, and investigated therelations between exergy loss and capital cost, andbetween exergy and environmental impact.

Sarimveis, Angelou, Retsina, Rutherford, and Bafas(2003) investigated the utilization of mathematical pro-gramming tools to optimize the energy management ofa power generation plant for the paper industry. Theobjective was to reach self-sufficiency in electrical powerand steam with the lowest possible cost. The proposedmethodology was based on the development of a de-tailed mathematical model of the power generationplant, using balances of mass and energy, and a mathe-matical formulation from the energy demand contract,what could be translated into a linear optimization pro-gramming problem. The results showed that the methodcould be a useful tool for production cost reduction be-cause it minimizes the fuels and electric energy costs.

In sum, the literature review showed that severalstudies developed mathematical models for pasteuriza-tion processes and specific parts of the process (e.g.,sprays) ranging from simple to complex. The literaturealso shows that energy or exergy based models havebeen applied to the analysis and optimization of severalindustrial processes and systems. However, no optimiza-tion studies were found in the literature for pasteuriza-tion tunnels. In that context, the objective of thisstudy is to develop a simplified mathematical model toobtain the energetic behavior of a pasteurization tunnelused for bottled beer production, that is capable of per-forming a geometric optimization of typical pasteuriza-tion tunnels. The energetic analysis comprises the energysupplied to the equipment via steam and electric energy.Steam is used for water heating, whereas the pumps thatpromote water circulation use electric energy.

2. Mathematical model

Although there are several detailed (and complex)models to apply for isolated processes within a pasteur-ization tunnel, two or three dimensional models are usu-

ally not suitable for the analysis of the whole system,because they require the solving of partial differentialequations for the flow simulation for many different flowconfigurations and operating parameters. Such modelslead to high cost and computational time even for thesimulation of a few selected cases, what practically dis-cards the possibility of an optimization study.

In an earlier work presented by Vargas, Stanescu,Florea, and Campos (2001), a general computationalmodel combining principles of classical thermodynamicsand heat transfer was developed for electronic packagesand the resulting three-dimensional differential equa-tions were discretized in space using a three-dimensionalcell centered finite volume scheme. The combination ofthe proposed physical model with the finite volumescheme was called a volume element model (VEM). Thismethodology showed to be accurate enough to capturethe thermal response of the system, and at the same timerequiring low computational time. Therefore, the vol-ume element model methodology was selected to model,simulate, and optimize the beer pasteurization tunnel inthe present work.

Fig. 1 shows schematically the interactions (mass andenergy flow) between volume elements in a beer pasteur-ization tunnel. The tunnel zones are divided into n vol-ume elements, each containing three systems: (1) air/water fog system generated by the spray, (2) mass ofbottles system, and (3) water system, which defines theportion of the water tank within the specific volume ele-ment (VE). System 3 is not shown in Fig. 1, but it is rightbelow each volume element shown in Fig. 1. For clarity,system 3 is shown in Fig. 2, which shows how the waterrecirculates in each volume element, being collected inthe bottom part of the volume element, in the water tankand pumped up to the appropriate spray on the top ofeach volume element in a predefined zone of the tunnel,according to the distribution shown in Fig. 3. To eachsystem, mass and energy conservation equations areapplied, as follows:

2.1. Air/water fog system

Applying the first law of thermodynamics to the air/water fog system, it follows:

_Qw;i þ _Qi þ _mr;icwaðT in;wa � T iÞ þ _mi�1cp;f T i�1

� _micp;f T i þ _miþ1cp;fT iþ1 � _micp;fT i

¼ mfcv;fdT i

dtð3Þ

where _Qw;i and _Qi are the heat transfer rate between sys-tem 1 and the external environment and between system1 and the mass of bottles (system 2) within the volumeelement Vi, respectively; _mr;i; _mi�1 and _miþ1 are the watermass flow rate entering the VE through the spray, theair/water fog mass flow rate from the preceding VE

Fig. 1. Schematic diagram of system 1 (air/water fog) and system 2 (mass of bottles), and mass flow rates in each volume element.

Fig. 2. Schematic diagram of system 3 (water).

Fig. 3. Schematic diagram of the water circulation in the entire pasteurization tunnel.


and from the successive one, respectively; _mi is the air/water fog mass flow rate exiting the VE to the next,which is taken by the model as approximately equal tothe air/water fog mass flow rate exiting the VE to theprevious one; cwa, cp,f, and cv,f are the specific heat of

the water, of the air/water fog at constant pressureand of the air/water fog at constant volume, respec-tively; mf is the mass of air/water fog in the volume ele-ment; Tin,wa is the inlet water temperature; Ti, Ti+1 andTi�1 are the temperatures of the air/water fog inside the


VE ‘‘i’’, inside the next element, and the previous one,respectively.

The heat transfer rate lost by the VE to the surround-ings through the walls is calculated by

_Qw;i ¼ U w;iAw;iðT1 � T iÞ ð4Þ

where Uw,i is the global heat transfer coefficient betweenthe air/water fog system and the surroundings throughthe walls and T1 is the external ambient temperature.

The calculation of Uw,i is carried out by

U w;i ¼1

h1þ dw

kw

þ dkins

þ 1

hint

� ��1

ð5Þ

where kw is the thermal conductivity of the wall mate-rial, dw is the wall thickness, kins is the thermal conduc-tivity of the insulation material, d is the insulationmaterial thickness; h1 the convection heat transfer coef-ficient outside the tunnel walls, and hint the convectionheat transfer coefficient between the air/water fog andthe walls. Such variables are assumed as input parame-ters of the model.

The mass flow rates are evaluated by

_mi�1 þ _miþ1 ¼ 2 _mi ð6Þ

_mi ¼ qfuiAs

2ð7Þ

where qf is the density of the air/water fog and As is thevertical cross-section area of the tunnel, defined by thevolume occupied by the air/water fog. For i ¼ 1;_mi�1 ¼ _mn (from the previous zone) and for i ¼ n;_miþ1 ¼ _m1 (from the next zone).

The horizontal velocity of the air/water fog flow be-tween the volume elements, ui, is estimated by a scaleanalysis using the continuity equation for a two-dimen-sional domain, according to Fig. 1:

ouoxþ ov

oy¼ 0 ð8Þ

where v represents the air/water fog velocity in the ver-tical direction, i.e., the direction of the height.

Since oy � H and ox � Dx, one may write

ui

Dx� v

H) ui �

vDxH

ð9Þ

with v being calculated from _mr;i, for v ffi _mr;i=ðqwaDxW Þ.In zone 1, _m0 ¼ qau1

As

2represents the surrounding air

entering the tunnel (following the direction of bottlemovement entering the tunnel) calculated from u1 ob-tained with Eq. (9), whereas in zone 8, _mnþ1 ¼ qaun

As

2

represents the surrounding air entering the tunnel (inthe opposite direction of bottle exiting the tunnel), alsocalculated from un obtained with Eq. (9).

The heat transfer rate between systems 1 and 2 isgiven by

_Qi ¼ hiAbðT b;i � T iÞ ð10Þ

where Ab is the total external surface area of the mass ofbottles within a VE, and Tb,i is the internal bottletemperature.

In Eq. (10), the convection heat transfer between theair/water fog and the mass of bottles, hi, was estimatedas the average convection heat transfer coefficient for aturbulent boundary layer over a plane wall, �h. There-fore, hi is calculated based on a formula presented byBejan (1993, Chapter 5) for the calculation of the wall-averaged Nusselt number NuLb

¼ �hLb

kwa, for 5� 105

6

ReLb6 108, and Pr P 0.5, as follows:

hi ¼ �h ¼ XNuLb

kwa

Lb

¼ X0.037Pr1=3ðRe4=5

Lb� 23; 550Þkwa

Lb

ð11Þ

where Pr = 7.0 for water and ReLb¼ vLb=mwa, with Lb

being the height of the bottle for an isothermal wall con-dition. As hi is directly related to the heat transfer of thewhole tunnel system and the beer bottle, a fitting X fac-tor was included in the correlation, initially set to 1, andcalibrated in the present work, based on experimentalmeasurements, by a trial-and-error numericalprocedure.

2.2. Mass of bottles system

The first law of thermodynamics states that

� _Qi ¼ mb;icb

dT b;i

dtð12Þ

for

cb ¼mg;icg þ mbe;icbe

mb;ið13Þ

where cb is the bottle specific heat as a function of theweight average of the specific heat of the casing material(glass), cg, and of the liquid (beer) inside the bottle, cbe,considering their respective masses, mg,i and mbe,i, for acertain VE, in which mb,i = mg,i + mbe,i is the total massof the set of bottles in the VE.

2.3. Water system

Applying the first law of thermodynamics to thewater inside the water tank in the volume element, asshown in Fig. 2, it follows:

_Qwt;i þ _mr;icwaT i � _mwa;icwaT t;i þ _mwa;iþ1cwaT t;iþ1

¼ mt;icwa

dT t;i

dtð14Þ

where Tt,i and Tt,i+1 are the temperatures of the waterinside the tank, in the VE and in the next one, respec-tively; mt,i is the mass of water inside the tank, in theVE; _mwa;iþ1 is the mass flow rate exiting the next VE

Table 1Modeling parameters of the energetic interactions between tunnelzones

Zone Tin,wa (input watertemperature)

_Qin;z (input heat transferrate in zone z)

1 Tin,wa,z=1 = Tt,i=1,z=8_Qin;1 ¼ 0

2 Input parameterTin,wa,z=2 = 45 �C

_Qin;2 ¼ _mrt;z¼2cwa

ðT in;wa;z¼2 � T t;i¼1;z¼7Þ3 Input parameter

Tin,wa,z=3 = 55 �C



Tin,wa,z=4 = 60 �C



Tin,wa,z=5 = 62 �C


ðT in;wa;z¼5 � T t;i¼1;z¼5Þ6 Tin,wa,z=6 = Tt,i=1,z=3

_Qin;6 ¼ 07 Tin,wa,z=7 = Tt,i=1,z=2

_Qin;7 ¼ 08 Tin,wa,z=8 = Tt,i=1,z=1

_Qin;8 ¼ 0


and entering the VE. The mass flow rate exiting the VE,and entering the previous VE, is defined by _mwa;i ¼_mwa;iþ1 þ _mr;i, with _mwa;iþ1 ¼ 0 for i = n, i.e., in the lastVE of the zone.

The heat transfer rate between the water inside thetank, within the boundaries of the VE, and the sur-roundings, _Qwt;i, is given by

_Qwt;i ¼ U wt;iAwt;iðT1 � T t;iÞ ð15Þ

where Awt is the wall area bathed by the water inside thetank, in the VE, in contact with the external ambient(which is at T1) and Uwt,i is the global heat transfercoefficient between the water system and the surround-ings through the walls, as follows:

U wt;i ¼1

h1þ dw

kw

þ dkins

þ 1

ht;int

� ��1

ð16Þ

where ht,int is the convection heat transfer coefficient be-tween the water inside the tank and the walls. As in Eq.(5), all variables in Eq. (16) are assumed as input param-eters of the model.

For each zone of the tunnel, the mathematical modelis composed by 3n ordinary differential equations de-fined by Eqs. (3), (12), and (14), with the unknownsTi, Tb,i, and Tt,i. That system of equations models theflow and energy interactions between the systems of aparticular zone of the tunnel. The tunnel is composedby eight zones, which only differ by the origin of thespray water. Zones 1, 2, and 3 use the water from thetanks of zones 8, 7, and 6, respectively; zones 4 and 5use the water from their own tanks; zones 6, 7, and 8use the water from tanks 3, 2, and 1, respectively, asshown in Fig. 3.

Inside a particular VE there is a certain number ofbottles, nb, which is transported through the tunnel bya step-by-step mechanism, thus nb and Pb, the beer bot-tle production rate—an operating parameter—are re-lated to the time the bottles remain in a particular VE,tx, i.e., the residence time in a VE. In an actual beer pas-teurization tunnel, the mass of bottles inside a particulari-VE, after tx has passed, is transferred by means of thetransportation mechanism to the i + 1-VE, and so on,therefore, the residence time in a VE for a desired bottleproduction rate and the total bottle (or set of bottles inthe VE) traveling time in the tunnel are given by

tx ¼ nb=P b and ttot ¼ tx � nve ð17Þwhere nve ¼

P8z¼1nz is the total number of volume ele-

ments within the tunnel.The mass of bottles enters each VE with an ini-

tial temperature Tb,in,i = Tb,i�1, remaining inside theVE for a time tx, then leaving it with a temperatureTb,out,i = Tb,i. This way, the transient evolution of thebottles temperature is calculated during its entire travel-ing time through the pasteurization tunnel.

2.4. Heat transfer rate input

Table 1 shows the controlled inlet water temperaturesfor all zones and the calculation of the heat transfer ratesupplied to each zone z, _Qin;z. The water that comes outof the water tanks in zones 1, 6, 7 and 8 are not heatedby steam.

In Table 1, the total spray water mass flow rate for azone z, _mrt;z, is also a design parameter which is given by

_mrt;z ¼Xn

i¼1

ð _mr;iÞz ð18Þ

The total heat transfer rate _Qin;tot supplied to the tun-nel is given by

_Qin;tot ¼X5

z¼4

½ _mrtcwaðT in;wa � T t;i¼1Þ�z

þ _mrt;z¼2cwaðT in;wa;z¼2 � T t;i¼1;z¼7Þþ _mrt;z¼3cwaðT in;wa;z¼3 � T t;i¼1;z¼6Þ ð19Þ

The heat transfer rate to the bottles that travelthrough the tunnel, _Qout;b, is given by

_Qout;b ¼ mbcbðT b;out � T b;inÞ

ttot

ð20Þ

where mb is the mass of the set of bottles in one VE, Tb,in

and Tb,out are the set of bottles temperature when enter-ing and exiting the tunnel, respectively, and ttot is the to-tal travel time of one bottle (or set of bottles) in aparticular VE through the whole tunnel.

The energy balance for the entire tunnel states that

_Qin;tot ¼ _Qout;b þ _Q1 ¼ _Qout;tot ð21Þ

and by combining Eqs. (4) and (15), _Q1 (total heattransfer rate lost by the tunnel to the external ambient)is given by

_Q1 ¼X8

z¼1

Xn

i¼1

ð _Qw;i þ _Qwt;iÞz ð22Þ


2.5. Water pumps power

The computation of the power necessary for the eightcirculation pumps is calculated based on the pressuredrop within the set of pipes. The pressure drop withinthe water spray feeding pipes was calculated for eachtunnel zone by the pressure drop formula (e.g., Bejan,1995)

Dpz ¼ f2Lp

Dp

þ ncK2

� �qwaV

2 ð23Þ

where f is the friction factor within the pipes, Dp the pipediameter, Lp the total pipe length, nc the number ofcurves, K the pressure drop coefficient of each curve,qwa is the water density, V ¼ _mrt;z=ðqwaApÞ is the wateraverage velocity in the pipes cross section, and Ap isthe cross section area of the pipes.

The friction factor f is calculated from the Reynoldsnumber, ReDp , for turbulent flow through smooth ducts,as follows (e.g., Bejan, 1995):

f ¼ 0.0791

Re1=4Dp

for 2� 103 < ReDp < 2� 104 ð24Þ

ReDp ¼DpVmwa

ð25Þ

where mwa is the water kinematic viscosity.The necessary power to pump all spray water for a

particular zone, _W z, and the total pumping power re-quired by the tunnel to operate, _W tot, are calculated by(e.g., Fox & McDonald, 1992)

_W z ¼ _mrt;zDpz

qwa

ð26Þ

_W tot ¼X8

z¼1

_W z ð27Þ

3. Numerical method

In order to solve the system of ordinary differentialequations comprising Eqs. (3), (12), and (14), a classical4th/5th order adaptive time step vectorial Runge–Kuttamethod (Kincaid & Cheney, 1991, Chapter 8) wasimplemented computationally in Fortran language.The temperatures Ti, Tb,i, and Tt,i, and the quantitiesUp, Tb,max, _Qin, _Qout, and _W tot were the program outputs.

The initial objective of the study was to validate thenumerical results with the tunnel operating at steadystate, and sequentially to use the experimentally vali-dated model to optimize the tunnel configuration. Thenumerically computed temperatures Ti, Tb,i, and Tt,i

on steady state were then used to compute _Qin and_Qout through Eqs. (18)–(22). The adopted criterion toverify that steady state operation was reached, was de-

fined by comparing the three systems temperatures (Ti,Tb,i, and Tt,i) in all volume elements at times t + Dt

and t, where Dt is an appropriate simulation time inter-val (e.g., Dt = tx). In the model, each system tempera-ture forms a vector with nve positions, to account forthe temperatures of the three systems in a total of nve

volume elements. To accomplish that task, the Euclid-ean norm of each nve-dimensional temperature vectorwas utilized as follows:

k~T ðt þ DtÞ �~T ðtÞk=k~T ðtÞk < e ð28Þwhere ~T represents any of the three systems temperaturevector and e is a tolerance value, which was set to 0.001in the present work.

4. Results and discussion

4.1. Model experimental validation

The first part of the results consisted of the experi-mental validation of the numerical results obtained withthe model for an existing beer pasteurization tunnel. Thereal-time experimental temperature data were obtainedwith a mobile temperature recorder in a Ziemann Liesspasteurization tunnel (model PII 45/330).

The traveling thermograph is a portable equipmentused to evaluate the temperature profile within the bot-tles. The temperature sensor, a PT100 thermoresistor, isinstalled inside an actual beer bottle, which then travelsthrough the tunnel as a common bottle, recording tem-perature variation data, later acquired, by a computer.

The geometric characteristics of the modeled pasteur-ization tunnel where bottle transportation occurs are:H = 2 m, W = 4 m and L = 33 m. The bottle naturalhoneycomb arrangement in the transport belt in eachVE follows the geometry shown in Fig. 4, and the num-ber of bottles in each VE is calculated by

nb ¼WDb� 1

� �cos p

6

� � 4LDbnve

ð29Þ

where Db is the bottle diameter.The pipe parameters used in Eqs. (23)–(27) were ob-

tained from the characteristics of the pasteurization tun-nel as given by the supplier. The air/water fog propertieswere evaluated for humid air, considering a relativehumidity of 100%. Physical properties of interest ofthe fluids and the materials (e.g., glass, steel), and otherinput data for the program, were obtained from the lit-erature (Atkins, 1998; Bird, Stewart, & Lightfoot, 2002;Bejan, 1995; Burmeister, 1993).

The numerical results were obtained for a bottleexternal diameter Db = 0.082 m. The tunnel was dividedin volume elements distributed along the 8 zones. Zones1, 2, 3, 6, and 8 were divided in 8 VE each, zones 4, 5,

Fig. 4. Upper view of the geometric distribution of the bottles inside avolume element.

0

10

20

30

40

50

60

70

0 5 10 15 20 25 30 35

0 20 40 60 80

Zon

e 1

Zon

e 2

Zon

e 3

Zon

e 4

Zon

e 5

Zon

e 6

Zon

e 7

Zon

e 8

TTt ≡

bT]C[

To

x [m]

t [min]

95

Fig. 5. Numerical results for the temperatures of the three systems of avolume element, T, Tt (coincident with T) and Tb, in time and alongthe pasteurization tunnel.

30

35

40

45

50

55

60

65

70

0 20 40 60 80 90

0 4 8 12 16 20 24 28 32

Experimental Adjusted Model (X = 0.2)Model (X = 1)

x [m]

t [min]

]C[

To

b

Fig. 6. Variation of bottle temperature throughout the tunnel asmeasured in an actual experiment and as predicted by the model beforeand after parameter adjustment.


and 7 were divided in 14, 21, and 7 VE, respectively. Alarger number of volume elements was allocated in themesh where the input heat transfer rate is larger. There-fore, the mesh had a total of 82 VE, i.e., nve = 82. Oncethe geometry of the tunnel is established (L,W), and adesired bottle production rate Pb is selected, nb is deter-mined through Eq. (29) and tx, ttot through Eq. (17).

Fig. 5 shows the numerical results obtained with thecomputer simulation for the temperatures of the threesystems, i.e., mass of bottles, Tb, air/water fog, T, andwater inside the tank, Tt, as functions of the x positionfrom the entrance of the pasteurization tunnel. The T

and Tt curves, which are practically coincident, showthe existence of temperature plateaus in each tunnelzone. On the other hand, the Tb curve, shows that thebottles temperature increase monotonically up to zone5, and decrease from zones 6–8, i.e., the model qualita-tively captures the actual tunnel behavior.

The integration of Eq. (1), using the temperaturenumerical simulation results to obtain the _U p value fromEq. (2), produced Up = 45.0 which was not representa-tive of the actual value calculated with the experimen-tally measured temperatures in the tunnel. Therefore,the model was adjusted by calibrating the value of thefitting parameter X in Eq. (11), by a trial-and-error pro-cedure, bringing the numerically obtained Up closer tothe experimental value (Up = 23.5). The result of theprocedure was X = 0.2, such that the numerically com-puted value of the total number of pasteurization unitsaggregated in the beer pasteurization process wasUp = 23.8.

Fig. 6 shows the mass of bottles temperature data ob-tained with the traveling thermograph, Tb, as a functionof the x position from the entrance of the pasteurizationtunnel. In the same figure it is also shown the mass of

bottles temperature data obtained with the numericalsimulation before and after model adjustment. It is seenthat the adjusted curve shows an excellent agreementwith the experimental one. In fact, the largest observeddifference between the experimental and calibratedmodel curves is of about 4 �C in the 30–40 �C tempera-ture range, being even lower (�2 �C) in the range ofmost interest to the pasteurization process, 50–60 �C.Therefore, from this point on, all numerical results areobtained from the mesh with nve = 82, which is a coarseconverged mesh, mainly considering the size of a pas-teurization tunnel.

285

290

295

300

305

310

315

320

0 5 10 15 20 25

65000

58500

L [m]

h/bottle71500Pb =]kW[

Ec

264 m3V =

Fig. 7. Length optimization for a fixed volume of V = 264 m3, forthree different production rates Pb.


4.2. Optimization

An optimization study was carried out to seek thetunnel optimal configuration for minimum energy con-sumption. The tunnel total consumed power is evaluatedby the sum of water pumping power, _W tot, and total heattransfer rate consumed for water heating, _Qin;tot

_Ec ¼ _Qin;tot þ _W tot ð30Þ

The design constraint used in the optimization proce-dure was a fixed mass of material (or fixed volume—V)for tunnel construction. The tunnel dimensions L and W

in the optimization were varied, whereas, H was keptconstant since it is related to the bottle height. As the to-tal volume, V, and height, H, of the tunnel are fixed,tunnel dimensions, W and L have a one-to-one relation-ship given by

W ¼ VLH

ð31Þ

From the point of view of heat transfer, the larger thetunnel external surface, the larger the heat loss to theexternal ambient, i.e., _Q1 is proportional to surfacearea. The total water pumping power is proportionalto the pressure drop in the water pipes, which is propor-tional to L and W, i.e., DP = f(L,W). As there is watercirculation between the zones, the longer the distancebetween the zones (larger L), the higher the pressuredrop. Following Eq. (31) the increase in L also impliesa decrease in W. On the other hand, for a larger W, asmaller L will result. So, there must be an optimal setof tunnel geometric parameters (L,W)opt, such that thetunnel total consumed power, _Ec, is minimum.

The pasteurization tunnel total volume is V = 264m3, with water mass flow rates of _mrt;z ¼ 83.3 kg/s, forzones z = 1, 2, 3, 6, 7 and 8, _mrt;z ¼ 288.9 kg/s for zonez = 4, and _mrt;z ¼ 233.3 kg/s for zone z = 5, all beingthe actual existing tunnel process parameters. The opti-mum (L, W) pair for minimum _Ec is shown in Fig. 7,where the tunnel total consumed power is noted forLopt � 12 m, which corresponds to Wopt � 11 m, i.e., ageometric configuration slightly rectangular is expectedto result in minimum power consumption. For the opti-mization procedure, in which the total tunnel length wasvaried, the zone length versus total tunnel length ratioswere kept as the same as the existing tunnel tested in thisstudy.

It is also seen in Fig. 7 that the shape of the curves arenot parabolic. Although the pipe distribution within thetunnel leads to a symmetrical _W tot curve, the heat lossthrough the walls increases with external surface, pro-portional to L. The combination of these two trendsleads to a slight deformation of curve shape to the rightfor all numerically tested production rates, namely,71,500, 65,000, and 58,500 bottles/h, which is the actualexisting tunnel bottle production rate. Although it is not

shown in Fig. 7, the total power consumption of theexisting tunnel tested in this study (L = 33 m,W = 4 m) was evaluated with Eq. (30) and the resultwas _Ec ¼ 328.6 kW. An inspection of Fig. 7 shows forthe optimized configuration (L,W)opt = (12 m, 11 m)that _Ec;min ¼ 287.6 kW. Therefore, the optimized tunneloperating with a bottle production rate of 58,500 bot-tles/h is expected to consume �12% less power thanthe existing tunnel tested in this study.

In Figs. 8 and 9, in which the water mass flow ratesdistribution, _mrt;z, is kept constant and the tunnel vol-ume is, respectively, 10% and 20% lower than the actualtunnel, a similar trend to Fig. 7 is observed, with a min-imum near L � 12 m. As the total tunnel volume wasreduced, two other bottle production rates were tested,namely, 52,000 and 45,500 bottles/h. From the engineer-ing point of view, the most important conclusion of theanalysis of Figs. 7–9 is that the optimum tunnel lengthLopt � 12 m is shown to be �robust� with respect tochanges in total tunnel volume and bottle productionrate, for 211 m3

6 V 6 264 m3 and 45,500 bottles/h 6 Pb 6 72,000 bottles/h.

Fig. 10 compiles the results presented in Figs. 7–9, fora production rate of 58,500 bottles/h, showing theresulting minimum tunnel total energy consumption,the pumping power, the supplied heat transfer rate,and the number of pasteurization unities aggregated tothe product, therefore allowing tunnel optimizationanalysis regarding pasteurization unities aggregated tothe product in the bottles. It can be seen that for higherV values, _Ec;min increases since _Qin;tot and _W tot also in-crease. Most importantly, Fig. 10 also shows that to ob-tain a value of 22.5 PU, as it is expected from the beerpasteurization process (Broderick, 1977), a tunnel vol-ume of only 224 m3 is necessary, instead of the current264 m3 of the existing tunnel analyzed in this study.Thus, the optimized tunnel could still pasteurize the beer

h/bottle65000Pb =

275

280

285

290

295

300

305

310

0 5 10 15 20 25

58500

52000

L [m]

]kW[

Ec

3m237V =


h/bottle58500Pb =

265

270

275

280

285

290

295

300

0 5 10 15 20 25

52000

45500

L [m]

3m211V =

[kW]

Ec


50

100

150

200

250

300

15

20

25

30

35

210 220 230 240 250 260 270

]m[V 3

pU

]PU[

Up

bottle/h58500P

m12L

b

opt

=

≈

min,cE

tot,inQ

]kw[

E

Q

W

min,c

tot,in

tot

totW

Fig. 10. Variation of minimum power consumption, _Ec;min, andaggregated pasteurization units, Up with respect to total tunnelvolume, V, for a bottle production rate of Pb = 58500 bottle/h.

285

290

295

300

305

310

20

22

24

26

28

30

32

34

58000 60000 62000 64000 66000 68000 70000 72000

pU

]h/bottle[Pb

)m11,m12()W,L( opt =

]kW[

E min,c

]PU[

Up

min,cE

3m264V =

mm150Dp =

Fig. 11. Variation of Ec,min and the corresponding Up with respect tobottle production rate, Pg, for Dp = 150 mm.


according to the recommended value of 22.5 PU, with a15% smaller volume configuration and a total power

consumption reduction of �12%, compared to the exist-ing tunnel tested in this study.

4.3. Parametric analysis

The parametric analysis described in this section wascarried out using the optimum pair (L,W)opt = (12 m,11 m) found for V = 264 m3, a fixed spray water massflow rates distribution, _mrt;z, and water pipe diameterDp = 150 mm, the latter two taken as the same as inthe actual existing tunnel. The selected parameters werewater pipe diameter, insulation thickness, bottle produc-tion rate and inlet spray water temperature of zone 2;the former two are design parameters whereas the lattertwo are operating parameters.

The bottle production rate, Pb, has a direct influenceon the necessary heat transfer rate to produce the de-sired thermal treatment. Fig. 11 shows the variation ofUp and _Ec;min with respect to Pb. The increase on trans-port velocity for higher bottle production rates does notimply extra pumping power, however it causes an in-crease in the heat absorbed by the tunnel and a decreaseof bottles heat exposure time within the tunnel, leadingto lower values of Up. From Fig. 11, it is noticed that toachieve, for instance, 20 PU (within the range from 15 to30 PU) aggregated to the product, the bottle productionrate could be elevated to 72,000 bottles/h, far higherthan 58,500 bottles/h in use by the brewery companywith the existing tunnel tested in this work. However,such an increase in bottle production rate may not beachievable due to constraints imposed by other equip-ments down the production line. Anyway, it is an impor-tant finding of this work that the studied pasteurizationtunnel is over-designed for the specified bottle produc-tion rate.

The pumping power _W tot is a function of the waterflow rate _mrt;z, the pipe diameter and the total pipelength (considering pipes and valves), which is relatedto L and W. For a certain water flow rate, a decrease

48

49

50

51

52

53

54

55

56

260

265

270

275

280

285

290

295

300

0 200 400 600 800 1000

]mm[

h/bottle71500Pb =

)m11,m12()W,L( opt =

3m264V =

min,cE

]kW[

Q tot,in]kW[

E min,c

tot,inQ

Fig. 13. Variation of _Ec;min and _Qin;tot, with respect to thermalinsulation thickness, d, for a bottle production rate of Pb = 71,500bottle/h.


in pipe diameter is responsible for an increase in meanvelocity and ReDp value; this in turn results in an increasein pressure drop and pumping power. It is possible toobserve from Fig. 12 that _Qin;tot is practically unalteredwith the variation of Dp, since _Ec;minð _Ec;min ¼ _W totþ_Qin;totÞ and the _W tot curves remained almost equallyspaced for 120 mm 6 Dp 6 220 mm. The pipe diameteris also directly related to the pressure drop and the nec-essary pumping power for tunnel operation. WithDp = 150 mm, _Ec;min ¼ 292 kW is found from Fig. 12,whereas for Dp = 200 mm, _Ec;min ¼ 150 kW, a value�50% smaller than the former. Here, a thermoeconom-ics study is recommended to evaluate if power savingswould compensate the investment on larger diameterpipes, because there may be space constraints withinthe equipment that may discard the use of larger diam-eter pipes.

Since the tunnel operates in a temperature higherthan the room temperature, there is a heat transfer leakrate through the exterior walls of the tunnel, which maybe reduced with insulation. Therefore, the parameterwall insulation was studied by the introduction of aninsulation material (mineral wool) of a certain thickness,d. Fig. 13 shows that an increase in thickness causes anexpected reduction of heat loss to the external ambient,_Q1, and consequently, for the same inlet spray watertemperatures, a reduction of heat absorbed by the tun-nel _Qin;tot.

The existing tested tunnel in this study does not useany insulation (d = 0 mm), but if a 200-mm thick insula-tion layer is used, _Qin;tot may be reduced from 55.5 to50.1 kW. However, such power saving is not so highcompared to total tunnel power consumption _Ec;min ¼294.5 kW and, again, a thermoeconomics study mayconclude that investment on insulation material maynot be justified by the power saving of about 2% only.

0

100

200

300

400

500

600

700

800

120 140 160 180 200 220

)m11,m12()W,L( opt =

3m264V =

h/bottle65000Pb =

]kW[

E

W

min,c

tot

min,cE

totW

[mm]Dp

Fig. 12. Total water pumps required power, _W tot [kW], as a functionof the water pipes diameter, Dp [mm], for a bottle production rate ofPb = 65,000 bottle/h.

The inlet spray water temperatures of zones 2, 3, 4,and 5 are controlled by independent PID (propor-tional–integral–derivative) type meshes, and each tem-perature is set by a digital controller. The behavior ofzones 2 and 3 shows similar characteristics and regener-ate heat from zones 7 and 6, respectively. For this rea-son, it is sufficient to analyze the behavior of one ofthose zones with respect to the variation of inlet spraywater temperature. The variation of _Qin;tot with the inletspray water temperature is shown in Fig. 14. Heat regen-eration with zone 7 leads to a stabilization effect on_Qin;tot since the water of tank 7 returns with an increas-ingly higher temperature, therefore stabilizing theTin,wa,z=2 � Tt,i=1,z=7 term that defines _Qin;tot, as itwas shown previously in Table 1. The Up value increasesexponentially with the spray water temperature, as a re-sult of Eqs. (1) and (2), and depicted in Fig. 14. It is alsoimportant to notice that _Ec;min is equal to the heat trans-fer rate entering the tunnel plus the pumping power, thelatter being considered not affected by the temperature(neglecting density and viscosity variations in the

0

50

100

150

200

250

300

20

22

24

26

28

30

32

34

20 30 40 50 60 70 80

]C[T o2z,wa,in =

)m11,m12()W,L( opt =

3m264V =

h/bottle65000Pb =

min,cE

pU

tot,inQ

]PU[

Up

]kW[

Q

E

tot,in

min,c

Fig. 14. Variation Up and _Qin;tot with respect to the inlet watertemperature of zone 2, Tin,wa,z=2.


temperature range herein analyzed). Thus, _Ec;min shows abehavior similar to _Qin;tot with respect to the variation ofTin,wa,z = 2.

That analysis shows that spray water temperatures ofzones 2 and 3 have a small influence on the total powerconsumption of the tunnel. However they strongly affectpasteurization unities aggregated to the product. There-fore, the inlet spray water temperatures of zones 2 and 3are shown to be important operating parameters to con-trol the pasteurization units aggregated to the product.

5. Conclusions

A mathematical model was introduced in this studyto simulate computationally the energetic behavior ofa pasteurization tunnel used in a beer productionprocess. The numerically calculated bottle tempera-ture curves were compared to actually measured temper-atures. The numerical simulation results were thencalibrated by a model adjustment procedure. The exper-imentally validated model was then utilized to optimizethe geometric configuration of the tunnel and to per-form a parametric analysis to investigate the behaviorof the optima found, with respect to several designand operating parameters.

The total tunnel volume was fixed in the optimizationprocedure. This constraint accounts for the finiteness ofavailable space (or material) to build any pasteurizationtunnel. It was shown that a slightly rectangular tunnel isthe optimum geometric configuration considering totalpower consumption, i.e., the sum of heat transfer ratesupplied to the tunnel and water pumping power. Itwas also shown that the optimum tunnel length foundis �robust� with respect to the variation of total tunnelvolume, combining quality of the final product withminimum energy consumption.

A parametric analysis demonstrated that waterpumping power may be reduced in �50% (�150 kW)if pipe diameter is increased from 150 to 200 mm andheat transfer rate supplied to the tunnel may be reducedin 9.73% (5.4 kW) with the use of a mineral wool insula-tion layer 200-mm thick. However, a thermoeconomicsstudy is necessary to check the technical and economicalviability of introducing these design modifications onthe tunnel.

It was also found that the temperature of the zones 2and 3 have little influence on total power consumption.However they have a decisive role on beer pasteuriza-tion, i.e., the number of aggregated pasteurization uni-ties (PU) to the product.

In fact, it was shown in Fig. 10 that the optimized tun-nel which is 15% smaller in volume than the existingtested tunnel may deliver approximately the sameamount of PU to the product. Additionally, the opti-mized tunnel built with the same volume (or amount of

material), V = 264 m3, as the existing tested tunnel isable to reach a bottle production rate of 72,000 bottles/h, 23% higher than the bottle production rate currentlyobtained with the existing tested tunnel in this study, stillaggregating �20.5 PU to the product (Fig. 11).

The pasteurization tunnel numerical simulation andoptimization results provided several design improve-ment directions to be pursued. In all, if modificationssuch as thermal insulation of the tunnel, increase in pipediameter and optimization of the tunnel constructiongeometry are carried out, a very significant reductionin the expected total power (electricity and steam) con-sumption may be achieved with respect to the existingtunnel tested configuration of this study.

The model can be easily adapted for the analysis ofpasteurization tunnels with distinct characteristics, e.g.,geometrical configuration. The proposed methodologyis shown to allow a coarse converged mesh throughthe experimental validation of numerical results, there-fore combining numerical accuracy with low computa-tional time. As a result, the model is expected to be auseful tool for simulation, design, and optimization ofpasteurization tunnels. Furthermore, the results ob-tained in this study for a beer pasteurization tunnelare a good indication that the volume element method-ology could be applied efficiently to the simulation, de-sign and optimization of similar macro physicalsystems and industrial processes where diverse phenom-ena, several phases and different equipments are present.

References

Atkins, P. W. (1998). Physical chemistry (6th ed.). New York:Freeman.

Beck, J. C., & Watkins, A. P. (2003). The droplet number momentsapproach to spray modelling: the development of heat and masstransfer sub-models. International Journal of Heat and Fluid Flow,

24(2), 242–259.Bejan, A. (1993). Heat transfer. New York: John Wiley & Sons.Bejan, A. (1995). Convection heat transfer (2nd ed.). New York: John

Wiley & Sons.Bird, R. B., Stewart, W. E., & Lightfoot, E. N. (2002). Transport

phenomena (pp. 34–70) (2nd ed.). New York: John Wiley & Sons.Brandon, H., Gardner, R., Huling, J., & Staack, G. (1984). Time-

dependent modeling of in-package pasteurization. Technical

Quartely Master Brewers Association of the Americas, 21(4),153–159.

Broderick, H. M. (1977). The practical brewer, a manual for the brewing

industry (2nd ed.). Milwaukee, Wisconsin: Master Brewers Asso-ciation of the Americas.

Burmeister, L. C. (1993). Convective heat transfer (pp. 382–422) (2nded.). New York: John Wiley & Sons.

Engelman, M. S., & Sani, R. L. (1983). Finite-element simulation of anin-package pasteurization process. Numerical Heat Transfer, 6(1),41–54.

Fox, R. W., & McDonald, A. T. (1992). Introduction to fluid mechanics

(4th ed.). New York: John Wiley & Sons.Ghani, A. G. A., Farid, M. M., & Chen, X. D. (2002). Numerical

simulation of transient temperature and velocity profiles in a


horizontal can during sterilization using computational fluiddynamics. Journal of Food Engineering, 51(1), 77–83.

Horn, C. S., Franke, M., Blakemore, F. B., & Stannek, W. (1997).Modelling and simulation of pasteurization and staling effectsduring tunnel pasteurization of bottled beer. Food and Bioproducts

Processing, 75(C1), 23–33.Kincaid, D., & Cheney, W. (1991). Numerical analysis mathematics of

scientific computing (1st ed.). Belmont, CA: Wadsworth.Kumar, A., & Bhattacharya, M. (1991). Transient temperature and

velocity profiles in a canned non-newtonian liquid food duringsterilization in a still-cook retort. International Journal of Heat and

Mass Transfer, 34(4–5), 1083–1096.Phoenics (2005). Parabolic hyperbolic or elliptic numerical integration

code series. Available from http://www.cham.co.uk/phoenics/d_polis/d_info/phover.htm, internet page consulted on January 9.

Rosen, M. A., & Dincer, I. (2003). Exergy-cost-energy-mass analysis ofthermal systems and processes. Energy Conversion and Manage-

ment, 44(10), 1633–1651.

Sarimveis, H. K., Angelou, A. S., Retsina, T. R., Rutherford, S. R., &Bafas, G. V. (2003). Optimal energy management in pulp andpaper mills. Energy Conversion and Management, 44(10),1707–1718.

Tattiyakul, J., Rao, M. A., & Datta, A. K. (2001). Simulation of heattransfer to a canned corn starch dispersion subjected to axialrotation. Chemical Engineering and Processing, 40(4), 391–399.

Vargas, J. V. C., Stanescu, G., Florea, R., & Campos, M. C. (2001). Anumerical model to predict the thermal and psychrometric responseof electronic packages. ASME Journal of Electronic Packaging,

123(3), 200–210.Zheng, Y.H., Amano, R.S. (1999). Numerical modeling of turbulent

heat transfer and fluid flow in a tunnel pasteurization process. InProceedings of the ASME International Mechanical Engineering

Congress and Exposition, Nashville, vol. 364(4), pp. 219–227.Zufall, C., & Wackerbauer, K. (2000). The biological impact of flash

pasteurization over a wide temperature interval. Journal of the

Institute of Brewing, 106(3), 163–167.

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