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The Moisture Evaporation Rate of Walls Revisited and Predicting Temperature Profile of Moisture Containing Walls Exposed to Fire

  • Tensei MizukamiEmail author
  • Takeyoshi Tanaka
Conference paper

Abstract

Most building materials more or less contain moisture. It is often observed at temperature measurements at fire resistance tests and also at numerical calculations of heat conduction in walls containing moisture that the temperature rises stagnate around 100 °C for some time periods. This temperature stagnation significantly contributes to the high fire resistance performance of some types of wall, e.g., gypsum board. In this paper, the existing moisture evaporation rate formula has been revisited and re-examined the heat continuity equation from the standpoint of the existence of heat loss not only for moisture evaporation but also by raising the temperature of the wall. It reduces the number of uncertainties in the heat continuity equation and allows us to skip the step of regression fits to numerical simulation. The new formula is compared to the numerical calculation, and the range of application is validated.

Keywords

Moisture evaporation rate Moisture containing wall Semi-infinite body theory 

Nomenclature

C0

Specific heat of wall material (kJ/kg K)

Cw

Specific heat of water (kJ/kg K)

F

Fourier number (–)

\( F_{\phi } \)

Fourier number corresponding to drying front (–)

C

Proportionality in ISO 834-11 (–)

D

Proportionality constant (–)

Dp

Temperature stagnation time in ISO 834-11 (min)

\( \Delta t_{\text{v}} \)

Temperature stagnation time (s)

Lv

Latent heat of water evaporation (kJ/kg)

\( \dot{q}^{{\prime \prime }} \)

Conductive heat flux to drying front (kW/m2 s)

T

Temperature (°C)

T

Temperature rise (K)

t

Time (s)

dp

Fire protection material thickness in ISO 834 (mm)

x

Distance from exposed surface (m)

\( {\text{erfc}}\left( {} \right) \)

Complementary error function

Greek symbols

α

Thermal diffusivity of wall material (m2/s)

ϕ

Mass ratio of moisture content to wall material (kg/kg)

λ

Thermal conductivity of wall material (kW/m K)

ρ

Density of wall material (kg/m3)

Subscripts

c

Insulation criterion

\( \phi \)

At drying front

(x, t)

At a given point in time and place

f

Fire

0

Initial

v

Water evaporation

References

  1. 1.
    ISO 834. (1999). Fire resistance tests-elements of building construction. Geneva, Switzerland: ISO.Google Scholar
  2. 2.
    Mizukami, T., & Tanaka, T. (2012). Simple equations for predicting thermal resistance of mud-plastered wall. In The 9th Asia-Oceania Symposium on Fire Science and Technology (pp. 432–442).Google Scholar
  3. 3.
    Carslaw, H. S., & Jeager, J. G. (1959). Conduction of heat in solid (2nd ed.). Oxford: Oxford University Press.Google Scholar

Copyright information

© Springer Nature Singapore Pte Ltd. 2020

Authors and Affiliations

  1. 1.National Institute of Land and Infrastructure ManagementTsukubaJapan
  2. 2.Kyoto UniversityGokasyo, Uji, KyotoJapan

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