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Ultra-high-temperature (UHT) processing of milk. Process lethality, chemical effects and use of temperature-time-integrators (TTIs) to predict heat treatment and over-processing


This article investigates how to calculate the lethal effects of UHT treatment and the usefulness of TTIs for differentiating sterilised, direct and indirectly processed UHT-treated milk. The importance of accessing accurate temperature time-data and knowing holding tube dimensions, flow rate, average and minimum holding time and the flow characteristics (Reynolds number) are discussed. The reliability of a model developed by Claeys et al. (2003) to predict the effects of UHT-processing on hydroxymethylfurfural, lactulose and furosine concentrations in milk is discussed. Free On Line calculators for calculating holding time, average flow rate, holding tube length in UHT and HTST plants are provided. A free On Line calculator programmed using the thermal constants calculated by Claeys et al. (2003) is provided to calculate hydroxymethylfurfural, lactulose and furosine concentrations following heat treatment in skim, semi fat and full fat milks. This calculator also calculates F0, B*, C* and % destruction of thiamine. Two methods of numerical integration are used to measure the cumulative lethal and chemical effects of UHT treatment, namely the Trapezoid and Simpson's rules.


Typical UHT treatments involve heating milk to 137 to 150 in a continuous-flow process and holding at that temperature for one or more seconds before cooling rapidly to room temperature. The milk is then aseptically packaged to give a product that is stable for several months at ambient temperature.

In Europe, UHT treatment is defined as heating milk in a continuous flow of heat at a high temperature for a short time (not less than 135 °C in combination with a suitable holding time, not less than a second) such that there are no viable microorganisms or spores capable of growing in the treated product when kept in an aseptic closed container at ambient temperature (Reg EC 2074/2005).

Basic principles behind UHT treatment

It has been known for many decades that:

  • the lethal effects of heat increase as the temperature is raised,

  • as temperature increases the time required to obtain an equivalent lethal effect to that at a lower temperature decreases,

  • the longer the duration of heat treatment the greater the detrimental nutritional and organoleptic effects will be. See for example, the excellent textbook by Stumbo (1965).

This principle that the higher the temperature, the greater the antimicrobial effect, and the lower the holding time to give a specified lethality, coupled with the lower organoleptic, colour changes and nutritional effects due to the reduced duration of heating forms the basis of UHT processing.

The way in which the rate of reaction is influenced by temperature can be described by the Q10 value, this is the factor by which the rate of a reaction changes when the temperature is changed by 10. The Q10 values for the microbiological killing effect on thermophilic spores is in the range 10-20, however, the value for most of the chemical changes is much lower, about 3 (Burton, 1988). Deeth (2004) has succinctly demonstrated this temperature / time effect (Table 1).

Table 1: Chemical and bactericidal effects* with temperature


Time for equal bactericidal effect

Chemical change for same bactericidal effect













*Q10 values of 10 for spore destruction and 3 for chemical change were assumed. From: Deeth (2004).

It is apparent from Table 1 that by increasing the temperature from 115 to 145 an equivalent bactericidal effect can be obtained in one thousand of the time at 115 and for less than a 3% chemical change.

Because the heat treatments used in UHT processing typically yield minimum F0 values ranging from  5 – 6 (Bylund, 1995), design of UHT-processes is primarily concerned with reducing the numbers of thermoduric and thermophilic spore forming bacteria rather than pathogens such as Clostridium botulinum.

Types of UHT treatment

UHT processing is typically achieved using either indirect heating and cooling in heat exchangers,

or by direct heating using steam injection or infusion of milk into steam and cooling by expansion under vacuum. Because many modern UHT plants have a holding tube, or cell, it is important to also consider both lethal and chemical effects during heating from, and cooling to, 90. Note that in some jurisdictions only the minimum temperature and time achieved in the holding tube are considered in lethality calculations. It will be noted later that this considerably underestimates the heat treatment received by the milk.

 Milk is subjected to considerably more heat treatment in an indirect process, Figure 1.

 Figure 1. Typical temperature–time profiles of direct (A) and indirect UHT (B) plants


Figure 1. Typical temperature–time profiles of direct (A) and indirect UHT (B) plants

 Balancing the bacteriological and chemical indices of heat treatment

All UHT processes must produce a microbiologically safe product, this is generally referred to as a commercially sterile product. However, the antimicrobial effects of high temperature treatment must be balanced by minimising the detrimental effects of heat treatment on the nutritional quality, colour, and taste of the final product.  

Hence, in calculating the adequacy of UHT-processes it is not enough to calculate the lethal effects against microorganisms’ in particular thermophilic sporeformers, the extent of chemical changes must also be calculated.

The lethal effects are determined by calculating F0 and the bacteriological effect (B*), referred to as B star. The chemical effect (C*) designated C star, is as an indicator of adverse chemical effects. Additionally changes in protein functionality, loss of thiamine and the formation of heat induced compounds can be predicted and used as time temperature integrators (TTIs).

Effective holding time during UHT processes

Obtaining a precise and relevant value for holding time is difficult in any flow-based thermal process and can be particularly challenging for UHT-plants (Burton, 1988). It is easy to calculate the flow rate of a UHT or HTST plant. It can often be relatively easy to calculate the dimensions of the holding tube, if any, and from that to calculate the average holding time. A free On Line calculator for calculating average holding time is available on the DSFT website.

The average holding time should not be used without adjustment in calculations of F0 and B.* It is necessary to obtain an estimate of the fastest travelling particle and to use this in calculations. This requires calculated values for lethality to be reduced by an appropriate factor. Bylund (1995) refers to this as an efficiency factor.

The minimum holding time (the time the fastest particle takes to traverse the length of the holding tube or cell) depends not just on flow velocity but also on whether the flow pattern in the heat treatment unit is laminar or turbulent (Figure 2).


Figure 2. Differences between laminar and turbulent flow

This distinction between different flow types is recognized in heat treatment regulations e.g. in commercial HTST pasteurization:

“the holding tube must be such that the fastest flowing particle . . . will not traverse the holding tube in less than the required holding time” (U.S. Department of Health and Human Services, 2011).

Particles do not travel at uniform velocity in a pipe line. There is a range of particle velocity distributions. Even in an ideal stream line flow situation there is still a significant although greatly reduced range of particle velocities compared with laminar flow.

Particle velocity distributions can be reduced by either using high flow rates to create turbulent flow and/or by designing the plant to promote turbulent conditions.

The extent of turbulence can be calculated by determining Reynolds number (equation 1).

Equation 1. NRe = ρ x v x D


NRe = Reynolds number

ρ = density, kg/m3                                                 

v = velocity of flow, m/s                                      

D = diameter, m                                                     

µ= viscosity of product, Pa s.

Note the values above must be recorded at the same temperature as v, the velocity of flow. Flow velocity is not the same as flow rate which often expressed in Litres / minute or gallons / minutes and must be derived from the flow rate taking the dimensions of the holding tube into account.   

A free calculator for determining Reynolds number can be accessed on the DSFT website.

It is generally accepted that the flow pattern is laminar for NRe < 2,100 and turbulent flow exists when NRe exceeds 4,100. A value of 4100 is not particularly high and higher values are recommended. The higher the value, the less difference there will be between the average particle velocity and the highest particle velocity. Also there will be a more uniform particle velocity distribution. The IDF recommends a value of ≥ 12,000 for HTST pasteurizers (IDF, 1986).

The efficiency factor for plants with an NRe of < 2,100 is 0.5 and 0.8-0.9 for NRe of ≥ 4100 (Bylund, 1995).   This means that the calculated values of F0 and B* should be divided by 2 in a plant with an NRe of < 2,100 to allow for the variation in particle velocity and multiplied by 0.8-0.9 under turbulent flow conditions to ensure that the fastest moving particle was considered.

 This approach is fairly crude and can be improved by determining the minimum residence time by injecting a suitable tracer into the flow. This can be challenging to do in practice (Burton, 1988). Following this determination the length of the holding tube can be increased or the temperature raised, which is usually easier to do, if required.  A free calculator for calculating holding tube length is available on the DFST website.

 UHT-milk on sale in a Spanish supermarket

                                 UHT-milk on sale in a Spanish supermarket

Calculation of the lethality and chemical effects of UHT heat treatment

Fo values. Determination of Fo values has been described previously, particularly in relation to canning. While F0 calculation is less relevant in UHT processing since the target organisms are thermophilic sporeformers that are more heat resistant than Cl. botulinum, it is customary to also determine F0 values for UHT processes. As mentioned earlier there may also be a regulatory requirement to do this in some countries.

Fo is calculated by determining the lethality (L) at appropriate points from the time vs lethality curve and integrating the time and lethality values using numerical integration to obtain the area under the curve.

L is calculated using equation 2.

Equation 2. L = t x 10 ((T-Tr)/Z)

Note time is divided by 60 to bring seconds to minutes.


 t is the sterilization time in seconds at temperature T in

 T is the sterilization temperature in

Tr is the reference temperature and a value of 121.1° C is used in the determination of F0.

Z  is measured in °C, and is the reciprocal of the slope of the thermal death curve for the target organism; 10° C is the value frequently used in F0 calculations performed on low acid foods.  An alternative explanation of Z and perhaps one that is easier to understand is that Z is a value expressing the increase in temperature necessary to obtain the same lethal effect in 1/10 of the time.  

The minimum F0 value recommended for UHT treatment of good quality milk has been reported as 5 – 6 (Bylund, 1995).

Bacteriological index, B*.  This criterion was introduced by Horak and Kessler around 1980 (reviewed by Burton, 1988).  B* is defined the minimum heat treatment for UHT sterilisation as the minimal time / temperature required to give a 9-log cycle reduction of thermophilic spores. Kessler and Horak found that a heat treatment of 10.1 seconds at 135°C achieved this 9-log cycle reduction, this is equivalent to a  B*value of 1. The spores had a Z value of 10.5.

The B* value for a process is calculated similarly to the F0 . The lethal elements that make up B*, designated B below (equation 3), are integrated to obtain B*

Equation 3. B = 10 ((T - Tref) / Z) x t / 10.1

B* is calculated by determining the B-lethality at appropriate points from the time vs B-lethality curve and integrating the time and lethality values using numerical integration to obtain the area under the curve.

Tref = the reference temperature, (135

T = processing temperature (°C)

 t = processing time (seconds)Sterilised milk

Z = 10.5

While a B* of 1 (equivalent to an F0 = 3) is the minimal cumulative heat treatment required in UHT processing, higher B*values ranging from 2-20 have been reported in commercial plants in New Zealand (Tran et al., 2008).

Chemical index, C*. This well-known criterion is used to gauge the adverse effects of heat on milk. While it predicts the destruction of thiamine, it is used as a general measure of the cumulative detrimental effects of heat.

Horak and Kessler (reviewed by Burton, 1988) proposed that an acceptable limit of chemical change can be described by time-temperature combinations corresponding to the thermal destruction of 3% of thiamine.  This corresponds to a C* value of 1.                                

The C* value for a process is calculated similarly to the F0 and B* values, equation 4.

Equation 4. C = 10 ((T - Tref) / Z) x t / 30.5.


Tref = the reference temperature, (135)

T = processing temperature (°C)

t = processing time (seconds)

Z = 31.4

C* is calculated by determining the C values at appropriate points from the time vs C curve and integrating the time and C values using numerical integration to obtain the area under the curve. While C* does have utility its choice as an indicator of gross chemical changes following heat treatment has been questioned e.g. it has been known for many years that comparatively low heat treatments denature whey proteins while having relatively little effect on thiamine. Burton (1988) commenting on C* referred to work by Andrews and Morant (1987) that showed that the flavour acceptability  of UHT milk over a wide range of heat treatment processes was closely correlated with the concentration of lactulose.

Importance of monitoring temperature during UHT processing

It is the cumulative heat treatment that milk and other products receive during processing that determines the overall effectiveness of a heat treatment process. Lethal effects and chemical changes occur during any pre-processing or conditioning period used, come-up or heat-up time to the holding temperature, during holding and during cooling.

This is well known in canning where the lethal effects during heating and cooling are significant and are included in the calculation of F value.

Recent work by Tran et al. (2008) has revealed the significance of the lethal effects recorded during heating and cooling. For 22 commercial UHT plants (5 direct) the heat-up and cool-down sections of the indirect and direct plants contributed an average of 53% and 17%, respectively, to the overall B* of the plants, and 76 and 39%, respectively, to the overall C* values.

Using furosine, hydroxymethylfurfural and lactulose formation as Temperature Time Integrators (TTIs) in UHT-treated milk

The main chemical changes occurring upon UHT-processing of milk are protein denaturation, the Maillard reaction and lactose isomerization. While a range of compounds have been studied as potential TTIs to allow the discrimination of pasteurised, UHT-treated and sterilised milk and temperature-abused UHT-treated milk, furosine, hydroxymethylfurfural and lactulose have received particular attention.

The Maillard reaction is a chemical reaction between amino acids and reducing sugars that gives foods e.g. bread their brown colour and typical taste.  It is the reaction of reducing sugars with lysine residues in milk proteins that is mainly responsible for the reduction in nutritional value of proteins in severely heated milk products.

5-Hydroxymethylfurfural (HMF)

HMF is an end product of the Maillard reaction. The presence of high concentrations suggests that severe heating has occurred. Care needs to be taken when reviewing HMF concentrations in milk, since some authors report free HMF and others total HMF. Total HMF is the sum of the HMF precursors and free HMF and is a better indicator of cumulative damage.

Burton (1988) has suggested 10 µm/L as the upper limit for UHT-treatment. There are concerns that changes in the concentration of this compound during storage may complicate its use as a TTI.

Ireland produces UHT milk for a global marketLactulose

Lactulose, 4-0-β-galactopyranosyl-D-fructose, is not normally present in raw milk unless skim milk powder has been added. It is formed by a process called epimerization. Epimerization of lactose in milk is a heat-induced process that causes a molecular rearrangement of lactose into a compound with the same molecular weight. Lactulose is more soluble than lactose and significantly sweetener. The rate of formation is dependent on pH and the time and temperature of the heat process. More lactulose is formed as the pH increases.

It has been known for several decades that the concentration of lactulose in milk can be used as an indicator of severe heat treatment.

As discussed previously, Andrews and Morant (1987) found that the flavour acceptability of UHT milk over a wide range of heat treatment processes was closely correlated with the concentration of lactulose

The IDF (IDF, 1986) has proposed that the lactulose content of UHT-treated milk can be used to differentiate it from sterilised milk. They have proposed that the lactulose concentration in UHT milk should be between 100-600mg/L and 850-2000 mg/L in container sterilised milk.

There have been many studies of the levels of lactulose in market milk. The partial results of a Belgium study are shown in Table 2. These results indicate the differences between direct and indirect-UHT treatment and sterilisation. As expected the data for high pasteurization and thermisation show only low concentrations of lactulose. Interesting the average concentration of lactulose in both studies of indirect-UHT milk show lactulose concentrations close to or slightly in excess of 600 mg / L in some samples clearly indicating potential challenges for processors if the IDF proposals for lactulose (IDF, 1986) were adopted.

While some workers have reported a small increase in lactulose concentration during storage of UHT milk, this increase is normally small and in many cases it is insignificant.


Furosine, ε-N-2-furoylmethylL-lysine, is an early reactant during the Maillard reaction. The formation of furosine is known to be significantly dependant on protein concentration.

Claeys et al. (2004) have suggested an upper limit of 250 mg/100 g protein for furosine in UHT milk.

The furosine content of UHT-milk has been widely studied particularly in Europe. These studies were able to differentiate direct-UHT, indirect-UHT and sterilised milk (Table 2).

As with HMF, furosine has been found to increase in concentration in stored UHT milk potentially also complicating its use as a TTI.

Table 2. Concentration of lactulose and fursosine in market milk in Belgium


Heat treatment

Study 1

Study 2

Lactulose (mg/L)


7.75 (n=4)

10.82 (n=5)

(High) pasteurisation

6.52 (n=21)

19.59 (n=14)


245.67 (n=6)

414.22 (n=8)


569.25 (n=8)

620.13 (n=5)


1062.00 (n=6)

1064.37 (n=7)

Furosine (mg/100 mg protein)


7.00 (n=4)

6.60 (n=5)

(High) pasteurisation

8.32 (n=21)

9.61 (n=14)


95.28 (n=6)

116.18 (n=8)


217.34 (n=8)

196.38 (n=5)


367.77 (n=6)

336.94 (n=7)

 Data from Mortier et al. (2000)

Modelling furosine, hydroxymethylfurfural and lactulose formation in UHT-treated milk

The formation of HMF, lactulose and furosine in heated milk has been widely studied.   Claeys et al. (2001) found that that their formation reached a plateau upon prolonged heating, and could be described by a fractional conversion model. Later they simplified this model (Claeys et al., 2003) by taking only the first phase of the model into consideration and produced a pseudo-zero order model (equation 5):

Equation 5. C =C0+kref exp [Ea/R (1/Tref-1/T)] t


C0 is the initial concentration,

 C the concentration of the chemical compound formed at treatment time t,

 Ea (J/mol) the activation energy,

 R the universal gas constant and

Kref the reaction rate constant at reference temperature Tref.

Claeys et al. (2003) investigated the effect of fat content on the formation of these compounds to clarify the significance of milk composition on the potential use of these TTI indicators. While there were arithmetic differences in the kinetic factors for each of the compounds the formation kinetics of HMF and lactulose were not significantly affected by milk fat content. Although significant differences were observed between the kinetic parameters in the formation of furosine in whole, semi-skimmed and skimmed milk the authors concluded that the differences had little practical relevance.

The reaction rate constants, reference temperatures and activation energies for the formation of hydroxymethylfurfural, lactulose and furosine in heated milk determined by Claeys et al. (2003) are given in Table 3.

Table 3. Reaction rate constants, reference temperatures and activation energies for the formation of hydroxymethylfurfural, lactulose and furosine in heated milk*



Whole milk

Semi-skimmed milk

Skimmed milk


Hydroxymethylfurfural; T-domain: 90-120; Tref 105


kref, µmol/I per min


0.794 ±0.1

0.815 ±0022


Ea, kJ/mol


113.4 ±1.1



Lactulose; T-domain: 90-120; Tref 105


kref mg/l per min


31.2 ±1-0

28.2 ±0-8


Ea, kJ/mol

109.2 ±1-6


113.6± 1 -5


Furosine; T-domain: 90-130; Tref 110


kref, mg/100 g protein per min)

9.64 ±0-14


8.61 ±0-07


Ea, kJ/mol

88.4 ±0-9

92.8 ±0-8

91.3 ±0-5


*Data from Claeys et al. (2003)



 Calculating the cumulative effects of heating on bacteriological and chemical indices using numerical integration

Let’s assume we want to calculate F0 where time is expressed in minutes, equation 6 is used. Note the differences from equation 2.

equation for calculating F0
The ∫ sign is an integral. This means that the formula should be integrated. If we knew the equation that described the temperature versus lethal rate curve for the series of time versus temperature values that had been captured by a data recorder we could integrate the equation and obtain the area under the curve. This value would give F0 in minutes.

In reality we rarely know the equation describing the relationship between time and lethal rate although we could approximate it using a computer programme or using an Excel function.

To overcome this limitation the industry standard method is to use the Trapezoidal Rule to approximate the area under the curve.  

While the Trapezoidal Rule can give fairly accurate results, the use of Simpson’s rules (there are more than one!) gives a more accurate estimate of the area and is arguably more appropriate when working with UHT processes.  The main reason that it is not commonly used is because the mathematics are a little more complicated. However, it is relatively easy to write a Simpson’s rules macro in Excel to do these calculations.

The author has provided a free calculator which calculates the F0, B*, C*, HMF, lactulose, furosine and the % thiamine destroyed by UHT processing. HMF, lactulose, furosine are determined using equation 4 as derived by Claeys et al., 2003. Integration is undertaken using both the Trapezoid rule and the more accurate Simpson's rules. An Excel spreadsheet that performs these calculations using both Trapezoidal and Simpson’s Integration can also be downloaded.

The reliability of the Claeys et al. (2003) model in predicting the effects of UHT-processing on hydroxymethylfurfural, lactulose and furosine concentrations in milk

Firstly models give indicative values within the limits used to construct them e.g. temperature range. Using them outside these limits is likely to give erroneous results.

From limited work undertaken by the author with commercial plants the model appeared to work satisfactorily for predicting lactulose and furosine formation. I have not tested it with HMF.

The flow rates, temperatures, particle velocity distributions vary markedly between direct and indirect-UHT plants and between different plants of the same type. This means that it is technically challenging to obtain the data required to predict TTI formation using commercial plants, particularly direct-UHT plants.

For some TTIs the seasonal variation in milk composition, which is not factored into the model may influence the formation of the TTI indicator compounds.

Many workers have reported significant increases in HMF and furosine, and slight increases in lactulose during storage of UHT-treated milk. This obviously needs to be considered when using TTIs.

Literature cited

Andrews, G. R. and Morant, S. V. (1987). Lactulose content, colour and organoleptic assessment of UHT and sterilized milk. Journal Dairy Research. 54, 493–507.

Burton, H. (1988). Ultra-high temperature processing of milk and milk products. New York. Elsevier Science Publishing Co., Inc. New York

Bylund, G. (1995) Dairy Processing Handbook. Tetra Pak (Processing System Division) A/B, Lund, Sweden.

Claeys, W., Ludikhuyze L. and Hendrickx, M. (2001). Formation kinetics of hydroxymethylfurfural, lactulose and furosine under isothermal and non-isothermal conditions. Journal of Dairy Research. 68, 287–301.

Claeys, W., Van Loey, A., and Hendrickx, M. (2003). Kinetics of hydroxymethylfurfural, lactulose and furosine formation in milk with different fat content. Journal of Dairy Research. 70, 85-90.

Claeys, W.L., Smout, C., Van Loey, A.M., Hendrickx, M.E. (2004). From time temperature integrator kinetics to time temperature integrator tolerance levels: heat-treated milk. Biotechnol Prog. 20, 1–12.

Deeth, H.C. (2004). The Challenges of UHT Milk Processing: Heat Treatment, Raw Material Quality and Handling. SIFST Annual 2004, 16-23.

Deeth, H.C. and Lewis, M.J. (2017). High Temperature Processing of Milk and Milk Products. Wiley-Blackwell. Hoboken, New Jersey.

Goff, H.D. and Davidson, V.J. (1990). Analysing fluid flow of mixes in HTST pasteurizers. Modern Dairy. 69. 13-14.

Kessler, H.G., Horak, P. (1981). Objective evaluation of UHT-milk heating by standardization of bacteriological and chemical effects. Milchwissenschaft. 36,12933.

International Dairy Federation. (1986). Monograph on pasteurized milk. Bull. 200. International Dairy Federation, Brussels.

Mortier, L, Braekman, A, Cartuyvels, D, Van Renterghem, R. and De Block, J. (2000). Intrinsic indicators for monitoring heat damage of consumption milk. Biotechnol. Agron. Soc. Environ. 4 (4), 221–225.

Reg EC 2074/2005, “Official Journal of the European Union L 338/27.

Stumbo, C. R. (1973). Thermobacteriology in food processing, 2nd ed. Academic Press, New York.

Tran, H., Datta, N., Lewis M.J. & Deeth H.C. (2008) Processing parameters and predicted product properties of industrial UHT milk processing plants in Australia. International Dairy Journal, 18, 939–944.

U.S. Department of Health and Human Services. (2011). Grade A Pasteurized Milk Ordinance. Food and Drug Administration, College Park, MD. Available from:
Regulation/GuidanceDocumentsRegulatoryInformation/Milk/ucm2007966.htm. Accessed 21th December, 2015.

How to cite this article

Mullan, W.M.A. (2018). [On-line]. Available from: https://www.dairyscience.info/index.php/thermal-processing/325-uht-processing.html . Accessed: 23 March, 2018.  

Google Translations of Summary


本文研究如何計算UHT處理的致死效應和TTI用於區分滅菌,直接和間接處理UHT處理奶的有用性。討論獲取準確溫度時間數據和了解保持管尺寸,流速,平均和最小保溫時間以及流動特性(雷諾數)的重要性。由Claeys等開發的模型的可靠性。 (2003)預測UHT處理對牛奶中羥甲基糠醛,乳果糖和糠酸濃度的影響。提供免費在線計算器,用於計算UHT和HTST工廠的保溫時間,平均流速,保溫管長度。使用由Claeys等人計算的熱常數編程的免費在線計算器。 (2003)用於計算脫脂,半脂肪和全脂奶中熱處理後的羥甲基糠醛,乳果糖和糠酸濃度。該計算器還計算F0,B *,C *和硫胺素的%破壞。使用兩種數值積分方法來測量UHT處理的累積致死和化學效應,即梯形和辛普森規則。


В статье рассматривается, как рассчитать смертельные последствия лечения и полезность ППИ для дифференциации стерилизованного, прямого и опосредованно обработанного молока. Обсуждаются важность получения точных температурных данных и знание размеров трубок, расхода, среднего и минимального времени удержания и характеристик потока (число Рейнольдса). Обсуждается надежность модели, разработанной клаэйс et al. (2003) для прогнозирования воздействия обработки хидроксимесилфурфурал, лактулоза и фуросине концентраций в молоке. Предоставляются бесплатные онлайн калькуляторы для расчета времени удержания, среднего расхода, удержания длины трубки в HTST и на заводах. Для расчета хидроксимесилфурфурал, лактулоза и фуросине концентраций после термической обработки в обезжиренном, полу-жировом и полном жире молоке предусмотрен бесплатный калькулятор на линии, запрограммированный с использованием тепловых констант, рассчитанных клаэйс et al. (2003). Этот калькулятор также вычисляет F0, B *, C * и% разрушение тиамина. Для измерения кумулятивного смертоносного и химического воздействия лечения, а именно трапеции и правила Симпсонов, используются два метода численной интеграции.



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