Abstract
This paper presents a theoretical solution to the heating of logs, frozen or not, having any length-to-diameter ratio. The solution is based on the enthalpy method and makes use of an explicit finite-difference scheme. The model has been verified for nonfrozen logs, assuming a longitudinal vs. radial thermal diffusivity ratio of two. The diffusivity of frozen logs still needs to be experimentally determined before the model can be computerized for the whole range of interest.
Zusammenfassung
Dieser Artikel beschreibt eine Lösung zur Theorie der Bestimmung der Aufheizzeit für gefrorene und nichtgefrorene Stämme im Wasseroder Dampfbad, für beliebige Verhältnisse der Stammlänge zum Stammdurchmesser. Die Lösung basiert auf der Enthalpiemethode und verwendet explizite finite Differenzen. Das Modell ist für nichtgefrorene Stämme unter Annahme eines Verhältnisses von 2∶1 für die Wärmedurchgangszahl in Längsrichtung zur Wärmedurchgangszahl in Radialrichtung verifiziert worden. Für gefrorene Stämme muß das Verhältnis der Wärmedurchgangszahl längs der Faser zur radialen Wärmedurchgangszahl noch experimentell ermittelt werden, bevor das Modell für den Elektronenrechner über den gesamten interessierenden Bereich programmiert werden kann.
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Abbreviations
- Cp:
-
specific heat at constant pressure (J/kg.°C)
- D :
-
distance between mesh points (m)
- d :
-
differential operator
- F :
-
latent heat (J/kg)
- H :
-
enthalpy (J/kg)
- k :
-
thermal conductivity (W/m.°C)
- L :
-
length (m)
- MC:
-
moisture content based on dry mass (percent)
- R :
-
radial coordinate (m)
- SG:
-
specific gravity based on dry mass and green volume (−)
- T :
-
temperature (°C)
- Z :
-
longitudinal coordinate (m)
- Δ:
-
interval (−)
- ∇:
-
del operator
- δ:
-
derivation operator
- 2ε:
-
thawing temperature range (°C)
- θ:
-
time (s)
- φ:
-
density (kg/m3)
- avg:
-
average
- e :
-
exterior
- l :
-
nonfrozen
- m :
-
nodal point 0, 1, 2, 3,... in radial direction
- n :
-
nodal point 0, 1, 2, 3,... in longitudinal direction
- o :
-
initial
- r :
-
radial direction
- s :
-
frozen
- th :
-
thawing
- w :
-
melting
- z :
-
longitudinal direction
- ∞:
-
ambient
- p :
-
time level 0, 1, 2, 3,...
References
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Khattabi, A., Steinhagen, H.P. Numerical solution to two-dimensional heating of logs. Holz als Roh-und Werkstoff 50, 308–312 (1992). https://doi.org/10.1007/BF02615359
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DOI: https://doi.org/10.1007/BF02615359