3D Numerical Simulation of Thawing Frozen Wood Using Microwave Energy: Frequency Effect on the Applicability of the Beer–Lambert Law

Abstract

In this article, the frequency effect on the applicability of Beer–Lambert's law for thawing frozen wood using the microwave energy was analyzed. To this end, we use Maxwell's equations to determine the absorbed power and characterize the critical slab thickness L _crit of three Canadian eastern wood species: trembling aspen (Populus tremuloides Michx), yellow birch (Betula alleghaniensis), and sugar maple (Acer saccharum). The critical thickness L _crit above which the Beer–Lambert law is valid is estimated as a hyperbolic function in the frequency domain: L _crit = m/f ⁿ (f is the frequency of microwave radiation; m and n are adjustment constants). The nonlinear heat conduction problem involving phase changes such as wood freezing is solved by a three-dimensional volumetric specific enthalpy-based finite element method. The dielectric and thermophysical properties are functions of temperature and moisture content. The specific volumetric enthalpy approach is validated by experimental testing. For instance, we studied the frequency effect on the thawing of frozen trembling aspen wood.

Keywords:

• Beer–Lambert's law
• Critical thickness
• Frozen wood
• Maxwell's equation
• Microwave heating
• Sugar maple
• Trembling aspen
• Yellow birch

ACKNOWLEDGMENT

We fully acknowledge the Natural Sciences and Engineering Research Council of Canada (NSERC) for their financial support of this project.