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Heat and Mass Transfer

, Volume 53, Issue 12, pp 3571–3580 | Cite as

Influence of stationary and non-stationary conditions on drying time and mechanical properties of a porcelain slab

  • Imen HammoudaEmail author
  • Daoued Mihoubi
Original

Abstract

This work deals with a numerical study of the response of a porcelain slab when subjected to convective drying in stationary and non-stationary conditions. The used model describes heat, mass, and momentum transfers is applied to an unsaturated viscoelastic medium described by a Maxwell model. The numerical code allows us to determine the effect of the surrounding air temperature on drying kinetics and on mechanical stress intensities. Von Mises stresses are analysed in order to foresee an eventual damage that may occur during drying. Simulation results for several temperatures in the range of [30 °C, 90 °C] shows that for the temperature from 30 °C to 60 °C, Von Mises stresses are always lower than the yield strength. But above 70 °C, Von Mises stresses are higher than the ultimate strength, and consequently there is a risk of crack at the end of the constant drying rate period. The idea proposed in this work is to integrate a reducing temperature phase when the predicted Von Mises stress intensity exceeds the admissible stress. Simulation results shows that a non-stationary convective drying (90–60 °C) allows us to optimize costs and quality by reducing the drying time and maintaining Von Mises stress values under the admissible stress.

Nomenclature

aw

Water activity

Cps

Heat capacity of the solid phase (J.kg−1.K−1)

Cpl

Heat capacity of the liquid moisture (J.kg−1.K-1)

Cpa

Heat capacity of the dry gas (J.kg−1.K−1)

Cpv

Heat capacity of moisture vapour (J.kg−1.K−1)

Cp

Effective heat capacity (J.kg−1.K−1)

D

Diffusion coefficient (m2.s−1)

E(t,w)

Relaxation function (Pa)

Ei

Elastic modulus of branch i (Pa)

\( \overset{=}{\boldsymbol{e}} \)

Mechanical deviatory strain

G

Shear modulus (Pa)

H

Convective heat transfer coefficient (W.m−2.K−1)

hv

Latent heat of water evaporation (J.kg−1)

hm

Mass transfer coefficient (m.s−1)

I

Rate of Moisture vaporization (kg.m−2.s−1)

J

Diffusion flux (kg m−2 s−1)

Λ

Bulk modulus (MPa)

K

Intrinsic permeability (m2)

kr

Relative permeability

Mv

Molecular weight of water (kg.kmol−1)

P

Pressure (Pa)

R

Universal gas constant (J.kmol−1.K−1)

RH

Relative Humidity (%)

S

Saturation

T

Temperature (°C, K)

T

Time (s)

tc

Time of the changing of temperature signal (s)

v

Velocity (m.s−1)

V

Volume (m3)

w

Moisture content (kg.kg−1d.b.)

\( {\boldsymbol{\rho}}_{\boldsymbol{i}}^{\boldsymbol{i}} \)

Intrinsic density of i phase i = l, s, g (kg.m−3)

ρ

Apparent density (kg.m−3)

λeff

Thermal conductivity (W.m−1.K−1)

\( \overset{=}{\boldsymbol{\phi}} \)

Mechanical volumetric strain

\( \overset{=}{\boldsymbol{\sigma}} \)

Stress (Pa)

ρ

Density (kg.m−3)

Subscripts

ambient

0

Initial

A

Air

v

Vapour

s

Solid

l

Liquid

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Copyright information

© Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  1. 1.Thermal Processes LaboratoryResearch and Technology Center of EnergyHammam-lifTunisia

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