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# Introduction

As previously discussed (Mullan, 2016), there will be occasions when a food manufacturer who has been using two different but equivalent thermal processes from a lethality perspective wishes to use a different, but equivalent lethal thermal process. This is straightforward if the z-value is known (Mullan, 2016). How does the processor calculate the equivalent lethal process if z is unknown?

This article explains how to calculate z using the time and temperature values of the two different, but equivalent lethal processes, and provides access to a free On Line calculator for checking your calculations.

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# Introduction

This article provides access to a calculator and an introduction to the mathematics derived by Dr Tomas Skoglund that enables the z-value, a term used in microbial thermal death time calculations, to be corrected to comply with Arrhenius calculations. This value can be defined in several ways, including that z is the number of degrees that the temperature must be increased to achieve a tenfold (i.e.,1 log10) reduction in the decimal reduction value (D-value)**. **The D-value is the time required to reduce the number of organisms by 1 log cycle and is an indication of the heat resistance of an organism.

## Bigelow and the Arrhenius models

There are two main approaches to calculating the bactericidal effectiveness of a heat process namely the Bigelow and Arrhenius methods. Both methods require the use of constants to allow for the temperature dependence of the kinetics of thermal destruction. The Bigelow method uses z-value (SI unit K or °C) and the Arrhenius model uses activation energy (E_{a}, SI unit J/ mol).

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**Introduction **

DSFT has an extensive range of free-On Line resources for undertaking a wide range of thermal process calculations including dry heat sterilisation (F_{H}) and depyrogenation (F_{D} or F_{P}). This page provides access to a range of Microsoft Excel spreadsheets that can be downloaded for a small donation and will work on a PC or Mac without access to the Internet. In general these spreadsheets are similar to their corresponding free applications on this website.

These donations are important. They contribute towards the running costs of the website and enable me to provide free access to the website rather than require a subscription.

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Technologists producing acidic foods such as pickles and sauces often find it difficult to get information on the processing conditions required to obtain commercial sterility or how to calculate the processing time at a higher temperature. Following the experience of working with processors experiencing technical issues, including spoilage problems and difficulties in exporting products, I have produced a concise Ebook (Thermal processing of acid fruit and vegetable products. Significant microorganisms, recommended processing time / temperatures, and public health significance of spoilage) that may be helpful. Currently the Ebook (figure 1):

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Many students have problems in understanding the mathematics describing the destruction of microorganisms by heat. Log reductions of pathogens and equivalent time-temperature treatments along with the associated lethalities account for a large part of the harder to understand topics. The quiz below is a simple test of of some of the basic concepts. Note Z value is not dealt with in this quiz. If there is sufficient interest I will provide the answers.

# Heat Processing Quiz

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# Introduction

There will be occasions when a food manufacturer wishes to use a different, but equivalent lethal thermal process. How does the processor calculate the equivalent process?

This article explains how to calculate an equivalent thermal or heat process at a higher or lower temperature and provides access to a free On Line calculator for checking your calculations.

Providing that the F value at T_{ref} and the z value are known then the F value at the required temperature, T, can be calculated using equation 1.

Equation 1.

Equation 1 has been derived from Stumbo (1973).

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**Summary**

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 F_{0, }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. A simpler calculator that enables the concentration of lactulose to be predicted after a single, defined heat treatment using 3-algorithms (Browning et at. (2001), Claeys et al. (2003), Rombaut et al. (2002)) has also been provided. All algorithms use the Arrhenius rate equation but use slightly different values for activation energy (E). This calculator enables readers to compare the accuracy of the three algorithms using experimental data.

# Introduction

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).

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- Calculator for determining the lethality (F, value) of a thermal process using the Trapezoid and Simpson's rules. This unique calculator works with thousands of pasted values e.g. from a data logger.
- Calculator for determining the lethality (F, B* values) and chemical changes (C* value, formation of HMF, Lactulose, Furosine, and destruction of thiamine) in heated milk integrated using the Trapezoid and Simpson's rules.
- Calculator for determining the lethality (F, B* values) and chemical changes (C* value) for generic high-temperature processes using the Trapezoid and Simpson's rules.
- Determine the accuracy of 3 algorithms for predicting the concentration of lactulose in milk after defined heat treatment.

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Can you destroy *Mycobacterium avium* subsp. *paratuberculosis (MAP)* by pasteurization? How important is holding time compared with holding temperature? Use the powerful free tools in this section to answer these questions.

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# MICROSOFT EXCEL LETHAL RATE CALCULATORS AND TEMPERATURE TIME INTEGRATORS FOR THERMAL PROCESSES

**Introduction**

This section provides the context to using Excel to calculate the cumulative lethal effects (at all stages during processing) of heat on microorganisms and provides an explanation of how the Excel spreadsheets and On Line calculators available for download from the Dairy Science and Food Technology (DSFT) work.

Here we provide an overview of the background, including a summary of the underlying mathematics, required to produce an Excel spreadsheet for performing basic thermal processing calculations. Note I am not providing a guide to using spreadsheets but basic information that a competent Excel user should be able to use to make their own thermal processing spreadsheet.

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An article on thermal process modelling has been added. This article calculates the effect of HTST treatment on the number of log reductions of major milk pathogens and discusses the temperature milk should be pasteurized if *Mycobacterium* *avium* subsp. *paratuberculosis* (MAP) was designated as a human pathogen. The log reductions refer to log10 or decimal (10 fold) reductions in the concentration of viable bacteria.

Effect of HTST treatment on the number of log reductions of major milk pathogens.

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Dr Michael Mullan has been retired for several years but still continues to provide consultancy services on a pro bono basis if you have an interesting problem or project. These include:

- Independent validation of the antimicrobial effectiveness of the heat treatments used in processing.
- Calculation of the average holding time used in processing HTST and HHST products.
- Determination of the flow type and calculation of the minimum holding or residence time of the fastest flowing particles in HTST and HHST products.
- Determination of the F values and the number of logarithmic (log10) reductions of designated microorganisms following heat treatment.
- Advice on equivalent heat processes to meet legislative and other requirements.
- Benchmarking of company processes against statutory and international best practice.
- Advice on alternative methods to microbiological examination for providing additional assurance of adequate heat treatment e.g. the phosphatase test is of no value in providing assurance that a temperature >80°C was used in milk processing. Additional tests that confirm higher temperatures than e.g. normal milk-pasteurization temperatures can be provided. The merits of incorporating these into routine quality assurance testing will be explained.

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** Dry heat sterilisation** is widely used for glassware and materials that are not suitable for sterilisation using saturated steam. A range of temperatures and times are used. Currently a temperature of at least 170°C for 30-60 minutes is widely used. The term is not particularly precise since variable concentrations of water may be present in the oven used (Sandle, 2013).