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Heat and Mass Transfer

, Volume 53, Issue 6, pp 2143–2154 | Cite as

Modelling and simulation of a moving interface problem: freeze drying of black tea extract

  • Ebubekir Sıddık AydinEmail author
  • Ozgun Yucel
  • Hasan Sadikoglu
Original

Abstract

The moving interface separates the material that is subjected to the freeze drying process as dried and frozen. Therefore, the accurate modeling the moving interface reduces the process time and energy consumption by improving the heat and mass transfer predictions during the process. To describe the dynamic behavior of the drying stages of the freeze-drying, a case study of brewed black tea extract in storage trays including moving interface was modeled that the heat and mass transfer equations were solved using orthogonal collocation method based on Jacobian polynomial approximation. Transport parameters and physical properties describing the freeze drying of black tea extract were evaluated by fitting the experimental data using Levenberg–Marquardt algorithm. Experimental results showed good agreement with the theoretical predictions.

Keywords

Collocation Point Freeze Dryer Knudsen Diffusivity Orthogonal Collocation Total Mass Flux 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

List of symbols

C01

Constant dependent only upon the structure of the porous medium and giving relative Darcy flow permeability (m2)

C1

Constant dependent only upon the structure of the porous medium and giving relative Knudsen flow permeability (m)

C2

Constant dependent only upon the structure of the porous medium and giving the ratio of bulk diffusivity (dimensionless)

Cp

Heat capacity (kJ/kg K)

Csw

Concentration of bound (sorbed) water (kg water/kg solid)

\({\rm D}^{o}_{{w,{\text{in}}}}\)

Dw,inP (N/s)

Dw,in

Free gas mutual diffusivity in a binary mixture of water vapor and inert gas

f(TX)

Water vapor pressure–temperature functional form

k

Thermal conductivity

k1

Bulk diffusivity constant, C2 \({\rm D}^{o}_{{w,{\text{in}}}}\) Kw/(C2 \({\rm D}^{o}_{{w,{\text{in}}}}\) + KmxP)

k2,k4

Self-diffusivity constant, (Kw Kin/(C2 \({\rm D}^{o}_{{w,{\text{in}}}}\) + KmxP)) + (C01/µ)

k3

Bulk diffusivity constant, C2 \({\rm D}^{o}_{{w,{\text{in}}}}\) Kin/(C2 \({\rm D}^{o}_{{w,{\text{in}}}}\) + KmxP)

kd

Desorption rate constant of bound water

kf

Film thermal conductivity (kW/m K)

Kin

Inert gas Knudsen diffusivity, Kin = C1(RT1/Min)0.5

Kmx

Mean Knudsen diffusivity for binary gas mixture, Kmx = (ywKw + yin Kin)

Kw

Water vapor Knudsen diffusivity, Kw = C1(RT1/Mw)0.5

L

Thickness of being dried material (m)

M

Molecular weight (kg)

N

Mass flux (Nw + Nin)

P

Total pressure in dried layer (Pa)

q

Energy flux

R

Universal gas constant

t

Time

T

Temperature

V

Velocity of interface

X

Position of frozen interface

x

Space coordinate of distance along the height of the material in the tray

Y

Mole fraction

Greek letters

∆Hs

Enthalpy of sublimation of frozen water

∆Hv

Enthalpy of vaporization of sorbed water

µ

Viscosity

α

Thermal diffusivity

ɛp

Voidage fraction

ɛ

Emissivity constant

ρ

Density

σ

Stefan–Boltzman constant

Superscripts

o

Initial value at t = 0

Subscripts

e

Effective value

exp

Experimental

f

Film

I

Dried layer

II

Frozen layer

in

Inert

L

Value at x = L

LP

Lower plate

m

Melting

mx

Mixture

o

Surface value

scor

Scorch

t

total

UP

Upper plate

w

Water vapor

x

Interfacial value

Notes

Acknowledgements

This research did not receive any specific Grant from funding agencies in the public, commercial, or not-for-profit sectors.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  1. 1.Department of Chemical EngineeringGebze Technical UniversityGebzeTurkey
  2. 2.Department of Chemical EngineeringYildiz Technical UniversityDavutpaşa, EsenlerTurkey

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