10-10-2012, 02:10 PM
USING A QUASI-HEAT-PULSE METHOD TO DETERMINE HEAT AND
MOISTURE TRANSFER PROPERTIES FOR POROUS ORTHOTROPIC
WOOD PRODUCTS OR CELLULAR SOLID MATERIALS
USING A QUASI-HEAT-PULSE.pdf (Size: 300.95 KB / Downloads: 25)
ABSTRACT
Understanding heat and moisture transfer in a wood specimen as used in the K-tester has led to an unconventional numerical solution
and intriguing protocol to deriving the transfer properties. Laplace transform solutions of Luikov’s differential equations are
derived for one-dimensional heat and moisture transfer in porous hygroscopic orthotropic materials and for a gradual finite heat
pulse applied to both surfaces of a flat slab. The K-tester 637 (Lasercomp) supplies a quasi-heat-pulse to both sides of a 2-ft-square
specimen and records precise signals as function of time from surface thermocouples and heat flux thermopiles. We obtained transfer
properties for moist and oven-dried redwood lumber flooring.
Introduction
With wood being orthotropic, a practical test method
must be limited to high-aspect-ratio flat slab geometry,
which eliminates many short-pulse heat methods
provided in the literature [1–3]. Methods using sustained
heat pulse or steady-state conditions [4, 5] are
subject to strong moisture migration effects, which
can lead to confusion or inconsistencies in the derived
heat and moisture transfer properties. Difficulties in
measuring moisture and temperature profiles within a
solid wood specimen, for deriving moisture- and temperature-
dependent properties, preclude methods developed
for soft organic matter. In this method we derived
an analytical Laplace transform solution to the
Luikov’s differential equations for one-dimensional
heat and moisture transfer [6–9] and for a gradual finite
heat pulse applied to both surfaces of a flat slab.
The result is a rapid moisture wave being thermally
driven into the slab and then a gradual settling back to
the original uniform moisture upon heat pulse removal.
This moisture movement also involves the latent
heat of wate.
Homogeneous solutions of three relevant
boundary conditions
In solving the transient heat and mass transfer problem
for the K-tester, it is required to proceed in a
three-step process, as shown schematically in Table 1.
When the K-tester applies a heat pulse across the upper
and lower FR4 layers, the responses in these layers
are recorded with the thermocouple and thermopile
data. Therefore, temperatures as functions of time
are known at the surfaces of the FR4 material, for
which in applying a transient heat transfer solution we
derived the transient heat flux at the surface of the
copper cladding. This in turn allows us to solve for
transient heat transfers in the copper cladding and aluminum
plate covering the specimen. These solutions
provide the actual time-delayed heat fluxes that will
be experienced by both surfaces of the test specimen.
Calibration with extruded polystyrene foam
and measurement for redwood
In calibrating the K-tester we quasi-pulse heated
1-in.-thick aged, extruded-polystyrene foam (a decade-
old Dow’s blue board) in temperature jumps of
8°C from equilibrium states. We obtained from National
Institute of Standards and Technology (NIST)
material databank on-line the values and formula for
heat capacities and densities of pure polystyrene
(SRM-705a) and air as functions of temperature. By
using the measured foam’s density, the parallel-
mass-weighted values for the foam’s heat capacity
were then calculated to a fairly high degree of accuracy
(within three digits precision) and were within
measurement errors of Graves et al. [4] for similarly
aged Dow’s blue board. The thermopile substrate is a
thermoset laminate (FR4) with a copper cladding
(their thicknesses were provided by Lasercomp company),
so their nominal thermal properties of heat capacities,
thermal conductivity, and density were
adopted from Eveloy and others [13].
Conclusions
Our efforts to understand heat and moisture transfer
in a wood specimen as used in the K-tester has led to
an unconventional numerical solution and intriguing
protocol to deriving heat and moisture transfer properties.
Exact analytical solution to the Luikov’s equations
for one-dimensional flow in a porous hygroscopic
orthotropic material as described in this paper
has the following features. The solution was given for
three types of stepping boundary conditions: (1) stepping
functions of surface temperature and moisture
and their surface gradients on just one side of the material,
(2) stepping functions of surface temperature
and moisture on both sides of the material, and (3)
stepping functions of the surface gradients of temperature
and moisture on both sides of the material