The study is focused on convective heat transfer in the processing of solid foods, specifically with the scope
to develop simple analytical calculation tools that can be incorporated into spreadsheet solutions. In areas of
food engineering such as equipment manufacture the use of predictive calculations, modelling activities and
simulations for improved design is employed to a high degree.
In food manufacture the use process calculations are seldom applied. Even though, the calculation of thermal
processes is not a challenging task in academia; this is not the case for food manufacture. However; the
calculations need fundamental validation and a generality that ensures a wide application, thus also the
development of simplified approximations and engineering equations have to be conducted in academia. The
focus group for the utilization of the presented work is; food manufacture, authorities ensuring food safety
standards and students pursuing a food engineering career but lacks full engineering training.
The approach in this study is to identify possible simplifications to the complete Fourier series expansion
[Fo-exp]. This is done through; a new method to non-iteratively find the Fourier exponents and lag factors
needed in a 1st term approximation, expanding the use of the 1st term approximation to also cover low
Fourier numbers [Fo], and investigating the input in the series expansion in terms of the determination of
convective heat transfer coefficients. For the investigation it was crucial to establish a thorough
understanding of the origin of both the standard [Fo-exp] solution and the criteria coupled with standard
A new description of the internal and external resistance to heat transfer has been suggested in form of a
normalization of the Biot number [Bi]. The normalized Biot number [Binorm] enables a simple, monotonically
increasing expression, used to determine the Fourier exponents and lag factors needed in the [Fo-exp]
solution to the heat equation. The proposed method has a low prediction error and can be used as an
alternative to iterative methods or the use of charts. Additionally, [Binorm] provides a rational investigation of
the sensitivity of important parameters such as the thermal conductivity and the heat transfer coefficients [h].
For the calculation of the thermal history during convective heating and cooling of solids, a solution is
proposed that can also handle the initial heating/cooling period (Fo<0.2). In the construction of the new
procedure the residual between a 1st term [Fo-exp] and the complete [Fo-exp] was modelled without
introducing new parameters, except one experimental constant.
The combined procedure of the determination of Fourier exponents and lag factors have been used in excel
calculations for the calculation of finite bodies. The developed method is validated with numerical solutions
with comparable accuracy in two representative cases; cooling of packaged cream cheese and a three step
processing of ham.
In the study, three investigations into the measurement methods for convective heat transfer coefficients [hc]
have been conducted.
The [hc] for separate boundaries have been measured for a cooling operation, where also the influence of a
present headspace was investigated. The contribution of the phenomena of boiling in the overall [h] to
suspended particles was investigated in a new experimental setup. Experiments conducted at a comparison
level emphasize that process control of vessel cooking should also include boiling rate instead of only using
A study in fluid to particle heat transfer coefficients [hfp] have been conducted, where it is shown that
potatoes can be used as a model food device for temperature measurements, in otherwise challenging
environments. The method utilizes an observed gelatinization front in potatoes and inverse calculations of
the thermal curve.
Based on a literature search it has been experienced that the common rules acknowledged in all textbooks
and papers on the subject have not been properly investigated in terms of induced uncertainties coupled with
the common rules. This includes the use of the lumped capacitance method for [Bi<0.1], and the criteria that
a 1st term approximation is adequate for [Fo>0.2].
Whereas it was possible to trace the origin of the [Fo>0.2] criterion, the [Bi<0.1] criterion for the lumped
capacitance method were unsuccessful. However, the error accompanied by this assumption is now
documented and I believe it should be stated along with the criteria in future textbooks. The analysis shows
that for elementary geometries the criteria [Fo>0.2], in worst case, generate calculation errors of up to 1.8%.
The most troubling is that the worst case is for infinite slabs, which are used in the construction of general
geometries, such as the shape of a box, increasing the induced error to almost 6%. The highest errors were
observed at [Bi] around 2. For food manufacture [Bi] around 2 are extremely common.
The thesis presents an analysis and description of the [Fo-exp] to the heat equation, and also presents
solutions to common challenges when calculations are conducted in food manufacture. The study provides a
method where traditional processes can be calculated with a high precision by using an expanded 1st term
approximation to the series expansion. This is an advantageous in terms of application in the industry where
the solution can be incorporated into spreadsheet solutions. This feature is important in conducting process
planning and scheduling, handling changes in products and processes and it is valuable in debottlenecking
It is wished that the proposed work could help facilitate that the use of rational engineering calculations are
performed in food manufacture. It is also hoped that the solutions provided and the insight to the [Fo-exp]
will become a part of the engineering training for food science students. And most important, that the study
will find application in the food industry.