Food Biophysics

, Volume 5, Issue 3, pp 161–176 | Cite as

An Innovative Micro-Modelling of Simultaneous Heat and Moisture Transfer during Bread Baking Using the Lattice Boltzmann Method



A considerable fraction of the energy consumed in bread manufacturing is used for the baking process. A thorough understanding of internal moisture transfer mechanisms are important to optimise both the quality of the product and the economics of the process. From a transport phenomena point of view, bread baking has been considered as a simultaneous heat and mass transfer problem in a porous medium. Nevertheless, most efforts previously made have avoided modelling the phenomenon occurring in the microscale, although the mechanism occurs primarily in the microscale. In this work heat and moisture transfer models were developed to accomplish the mechanisms included, both in the microscale and the macroscale by means of Boltzmann’s equation. Modelling and predictions of moisture transfer, heat transfer, modelling of effective moisture diffusivity, thermal conductivity and diffusivity have been investigated in this work. The microstructure in the dough samples was obtained using micro-computer tomography images from the samples prior to baking. The models were quantified and validated with measurements from the literature in order to assess the predictive models. The simulated crust development has shown a crust thickness of 0.8 cm, which is slightly higher than similar experimental results in which a dehydrated thickness of 0.5–0.6 cm was reported. The crust over-estimation in this work fits to the overheating occurring in the model. Additionally, investigations were made on the influence of different porosities (11–16%) of the bread; the boundary layer temperature at a porosity of 11% was reached after 25 min and after 17.5 min at a porosity of 16%. Therewith, the results showed that, with increasing porosity, the heat transfer rate towards the centre was higher, which matches the knowledge of experienced bakers.


Heat transfer Moisture transfer Bread baking Dough microstructure Modelling LBM 



Water activity


Moisture content, kilogrammes per kilogramme


Heat capacity at constant pressure (mass-based), Joules per·kilogramme Kelvin


Diffusion coefficient, square metres per second


Effective diffusion coefficient, square metres per second

\( {\hat{e}_i} \)

Unit vector in the ith lattice direction


Particle distribution function


Heat transfer coefficient, watts per square metre kelvin


Moisture flux, kilogrammes metre per kilogramme second


Thermal conductivity, watts per metre kelvin


Mass transfer coefficient, per Pascal metre second


Characteristic length, metre


The 2nd norm error


Water partial pressure in dough, Pascal

\( {P_\infty } \)

Water partial pressure in the surrounding environment, Pascal


Vapour pressure of the food, Pascal


Vapour pressure of water, Pascal


Saturation pressure, Pascal


Heat flux, watts per square metre


Relative humidity, percent


Water temperature in dough, kelvin

\( {T_\infty } \)

Temperature in oven environment, kelvin


Particle velocity in Lattice units


Water content, kilogrammes per kilogramme


Weighting factor

Greek symbols


Thermal diffusivity, square metres per second



Average pore diameter, metres




Density, kilogrammes per cubic metre




Relaxation time


Concentration relaxation time


Temperature relaxation time


Local physical property at current position, r


Relaxation frequency

Volume, cubic metre


Collision term


Curve length, metres


Chord length, metres





Conversion factor


Lattice units


Counter number in Lattice directions

Free stream, oven environment




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© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.Group of (Bio-) Process Technology and Process Analysis, Faculty of Life Science EngineeringTechnische Universität MünchenFreisingGermany

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