A generalised mathematical modelling methodology for the design of horticultural food packages exposed to refrigerated conditions Part 2. Heat transfer modelling and testing

Tanner, David J.; Cleland, A. C.; Robertson, Tom

doi:10.1016/s0140-7007(01)00018-4

Cited by 32 publications

(8 citation statements)

References 8 publications

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“…Tanner et al [79][80][81] developed a modeling system to predict produce cooling rate by assessment of the relative effect of different package configurations on produce heat and mass transfer. They used a ''zoned'' approach, in which each package was subdivided into a number of zones with defined dependencies between them.…”

Section: Models Available In the Literaturementioning

confidence: 99%

Mathematical Modeling Procedures for Airflow, Heat and Mass Transfer During Forced Convection Cooling of Produce: A Review

2010

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The aim of this review paper is to give comprehensive and detailed mathematical modeling procedures for the airflow, heat and mass transfer occurred during forced convection cooling of produce in order to optimize the cooling process. First, a brief explanation of forced-air precooling process and its importance in improving produce market quality will be given. Then, two main modeling procedures used during the process, namely porous medium approach and direct numerical simulation, will be explored. In addition, various related models available in the literature will be critically discussed together with their capabilities and drawbacks. Finally, a case study for optimizing the process using direct numerical simulation is shown. KeywordsMathematical modeling Á Direct numerical simulation Á Porous medium approach Á Forced-air precooling List of symbols A Surface area (m 2 ) A o Volumetric or specific surface area (1/m) A fs Interfacial area between fluid and solid phases (m 2 ) c Diffusivity in element Peclet number (Pa.s or W/m K) c art Coefficient of artificial diffusion (Pa.s or W/ m K) c p,a Air specific heat capacity (J/kg K) c p,p Produce specific heat capacity (J/kg K) d Hydraulic diameter (m) or pore-level linear length scale (m) d eff Effective produce diameter (m) D Diffusivity of water vapor in air (m 2 /s) or total diffusivity (m 2 /s) D d Dispersion coefficient (m 2 /s) f and g Respiration constants h Element size (m) h sf Interstitial convection heat transfer coefficient (W/m 2 K) I Second-order identity tensor k Mass transfer coefficient (kg/m 2 .s. Pa) k air Air film mass transfer coefficient (kg/m 2 .s. Pa) k 0 air Air film mass transfer coefficient (m/s) k skin Skin mass transfer coefficient (kg/m 2 .s. Pa) k a Air thermal conductivity (W/m K) k p Produce thermal conductivity (W/m K) K 1 and K 2 Constants in Darcy-Forchheimer equation K e Effective thermal conductivity (W/m K) ' Linear length scale for representative elementary volume (m) L Latent heat of evaporation (J/kg) or system dimension (m) _ m Rate of produce moisture loss (kg/s.m 2 ) Nu d Nusselt number (dimensionless) Nu d ¼ h sf d k a P Pressure (Pa)

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Section: Models Available In the Literaturementioning

confidence: 99%

Mathematical Modeling Procedures for Airflow, Heat and Mass Transfer During Forced Convection Cooling of Produce: A Review

2010

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“…Heat transfer coefficients for natural convection, are usually presented as Nusselt number versus Grashof number correlations for the specific geometry. In published literature these could be found for large containers (Tanner, Cleland, & Opara, 2002), for solar heating equipment (El-Sebaii, Aboul-Enein, Ramadan, & El-Gohary, 2002;Pangavhane, Sawhney, & Sarsavadia, 2002;Phoungchandang & Woods, 2000), and also for natural fruit dehydration, and more generally for plate transfer to an infinite environment. In the standard form [Nu = a(GrPr) b ] the coefficient is strongly dependent on geometry.…”

Section: Introductionmentioning

confidence: 99%

Heat and mass transfer coefficients for natural convection in fruit packages

Acevedo

Sánchez

Young

2007

Journal of Food Engineering

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“…For example, Schumann's model considers only convection in the fluid phase (no conduction or dispersion) and interface heat transfer depending on fluid velocity. Two-temperature models have been widely used in food process engineering, including heat generation (respiration of vegetables), mass transfer (dehydration) and packaging effects [14,21,22].…”

Section: Porous Medium /Packed Bed Approachesmentioning

confidence: 99%

Transient heat transfer by free convection in a packed bed of spheres: Comparison between two modelling approaches and experimental results

Laguerre

Amara

Álvarez

et al. 2008

Applied Thermal Engineering

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A generalised mathematical modelling methodology for the design of horticultural food packages exposed to refrigerated conditions Part 2. Heat transfer modelling and testing

Cited by 32 publications

References 8 publications

Mathematical Modeling Procedures for Airflow, Heat and Mass Transfer During Forced Convection Cooling of Produce: A Review

Mathematical Modeling Procedures for Airflow, Heat and Mass Transfer During Forced Convection Cooling of Produce: A Review

Heat and mass transfer coefficients for natural convection in fruit packages

Transient heat transfer by free convection in a packed bed of spheres: Comparison between two modelling approaches and experimental results

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