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Numerical investigation of heat and mass transfer behavior of freeze drying of milk in vial

  • G. Srinivasan
  • M. Muneeshwaran
  • B. RajaEmail author
Article
  • 60 Downloads

Abstract

The transient heat and mass transfer characteristics of the freeze-drying process of milk in a vial is numerically investigated. The paper reports the influence of semi- stoppered vial on mass transfer resistance and the relative importance of the bottom curvature of the vial on the drying time. Moreover, the variation of product temperature and mass transfer resistance as a function of time is predicted. The study revealed that the vial heat transfer coefficient strongly depends on chamber pressure; however, the effect of shelf temperature is minimal. The analysis is conducted for two fill heights (8.25 and 16.5 mm.) It is observed that the presence of curvature at the bottom of the vial increases the primary drying time but decreases the product temperature. Based on the simulation, it is observed that 16.5 mm product fill height provided higher mass transfer resistance than 8.25 mm fill height.

Nomenclature

Ac

Contact area between vial and shelf, mm2

cp

Specific heat capacity, J kg−1 K−1

C1

Empirical constant

h

Heat transfer coefficient, W m−2 K−1

I(t)

Sublimation interface position

k

Thermal conductivity, W m−1 K−1

kc

Direct conduction heat transfer coefficient, W m−2 K−1

kg

Gas conduction heat transfer coefficient, W m−2 K−1

kv

Vial heat transfer coefficient, W m−2 K−1

l

Effective curvature depth, mm

L

Product height, mm

m

Sublimation rate, kg s−1

pc

Chamber pressure, Pa

peq

Equilibrium vapor pressure of ice, Pa

pv

Total pressure in the vial, Pa

q

Heat flux, W m−2

Rd

Dry layer resistance, KPa s m−2 kg−1

Rs

Semi-stoppered vial resistance, KPa s m−2 kg−1

T

Temperature, K

t

Time, s

vn

Normal velocity of sublimation interface, m s−1

z

Spatial coordinate

Greek symbols

ΔHs

Sublimation enthalpy of ice, KJ kg−1

ρ

Density, kg m−3

α

Thermal diffusivity, m2 s−1

α

Accommodation coefficient

λamb

Heat conductivity of water vapor at ambient pressure, W m−1 K−1

Λ

Free molecular heat conductivity of water vapor at 0 °C, W Pa−1 K−1 m-2

Subscripts

f

Sublimation interface/front

g

Gas

s

Shelf

1

Dry layer

2

Frozen layer

Notes

Acknowledgements

The authors would like to thank Department of Science and Technology (DST-SERC), India (Ref no: SR/S3/MMER/0005/2014) for their financial aid to carry out the work and Dr. Joseph Daniel of VIT Chennai for extending COMSOL license.

Compliance with ethical standards

Conflict of interest

We have no potential conflict of interest to declare.

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Indian Institute of Information Technology, Design and Manufacturing (IIITDM) KancheepuramChennaiIndia

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