"""
Functions for wood properties.
"""
[docs]
def cp_wood(x, tk):
r"""
Wood heat capacity.
Heat capacity of wood based on moisture content and temperature
.. math::
c_{p,x} = \left(c_{p0} + c_{pw} \frac{x}{100}\right) / \left(1 + \frac{x}{100}\right) + A_c
where :math:`c_{p,x}` is heat capacity of wet wood [kJ/(kg K)],
:math:`c_{p0}` is heat capacity of dry wood [kJ/(kg K)], :math:`c_{pw}` is
heat capacity of water as 4.18 kJ/(kg K), :math:`x` is moisture content [%],
and :math:`Ac` is an adjustment factor that accounts for the additional
energy in the wood–water bond [1]_.
The :math:`c_{p0}` term is determined from
.. math:: c_{p0} = 0.1031 + 0.003867\,T
where :math:`T` is temperature in Kelvin. The :math:`A_c` term is calculated from
.. math:: A_c = x (b_1 + b_2 T + b_3 x)
with :math:`b_1 = -0.06191`, :math:`b_2 = 2.36e\times10^{-4}`,
and :math:`b_3 = -1.33\times10^{-4}`.
Parameters
----------
x : float
Moisture content as percent
tk : float
Temperature in Kelvin
Returns
-------
cp : float
Heat capacity of wood in kJ/(kg⋅K)
Example
-------
>>> cm.cp_wood(12, 340)
1.91...
References
----------
.. [1] Samuel V. Glass and Samuel L. Zelinka. Moisture Relations and
Physical Properties of Wood. Chapter 4 in Wood Handbook, pp. 1-19,
2010.
"""
cpw = 4.18 # heat capacity of water, kJ/(kg K)
# coefficients for adjustment factor Ac
b1 = -0.06191
b2 = 2.36e-4
b3 = -1.33e-4
# adjustment factor for additional energy in wood-water bond, Eq. 4-18
Ac = x * (b1 + b2 * tk + b3 * x)
# heat capacity of dry wood, Eq. 4-16a, kJ/(kg K)
cp_dry = 0.1031 + 0.003867 * tk
# heat capacity of wood that contains water, Eq. 4-17, kJ/(kg K)
cp_wet = (cp_dry + cpw * x / 100) / (1 + x / 100) + Ac
return cp_wet
[docs]
def k_wood(gb, so, x):
r"""
Wood thermal conductivity.
Thermal conductivity of wood based on moisture content, volumetric
shrinkage, and basic specific gravity
.. math:: k = G_x (B + C x) + A
where :math:`k` is thermal conductivity [W/(mK)] of wood, :math:`G_x` is
specific gravity [-] based on volume at moisture content :math:`x` [%] and
:math:`A, B, C` are constants.
The :math:`G_x` term is determined from
.. math:: G_x = \frac{G_b}{1 - S_x / 100}
where :math:`G_b` is basic specific gravity [-] and :math:`S_x` is
volumetric shrinkage [%] from green condition to moisture content :math:`x`.
The :math:`S_x` term is calculated from
.. math:: S_x = S_o \left(1 - \frac{x}{MC_{fs}} \right)
where :math:`S_o` is volumetric shrinkage [%] from Table 4-3 [2]_ and :math:`MC_{fs}`
is the fiber saturation point assumed to be 30% moisture content.
Parameters
----------
gb : float
Basic specific gravity
so : float
Volumetric shrinkage in percentage
x : float
Moisture content in percentage
Returns
-------
k : float
Thermal conductivity in W/(m⋅K)
Example
-------
>>> cm.k_wood(0.54, 12.3, 10)
0.1567...
References
----------
.. [2] Samuel V. Glass and Samuel L. Zelinka. Moisture Relations and
Physical Properties of Wood. Chapter 4 in Wood Handbook, pp. 1-19,
2010.
"""
mcfs = 30 # fiber staturation point estimate [%]
# shrinkage from green to final moisture content, Eq. 4-7 [%]
sx = so * (1 - x / mcfs)
# specific gravity based on volume at given moisture content, Eq. 4-9
gx = gb / (1 - sx / 100)
# thermal conductivity, Eq. 4-15 [W/(mK)]
a = 0.01864
b = 0.1941
c = 0.004064
k = gx * (b + c * x) + a
return k