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High intensive microwave pretreatment is a new method to modify wood for the fabrication of wood-based nanocomposites. Based on the physical law on heat transfer, a mathematical model to describe the temperature profiles within wood heated by high intensive microwave was established and simulated in this research. The results showed that the temperature profiles within wood were related to microwave heating methods; The temperature inside wood firstly increased and then gradually decreased along the direction of microwave transmission when the unilateral microwave heating was applied, and the temperature difference along the thickness direction of wood was very significant; The temperature with wood firstly increased and then gradually decreased from the wood surface to interior when the bilateral microwave heating was applied. Compared with the unilateral microwave heating, bilateral microwave heating is a better microwave heating method for the more uniform wood microwave pretreatment.

Microwave pretreatment is a technique in the forest product industry to improve process efficiency and product performance. Intensive microwave energy usually generates high internal steam pressure that could rupture weaker elements of wood structure and create the microvoids in the radial-longitudinal planes of wood [

The heat within wood during microwave heating can result from two aspects. One part is the absorption of microwave by wood, which can be described by absorption power of microwave, and the other is the heat transfer through wood. Thus, the temperature profile of wood during microwave heating can be simulated if the heat transfer model of microwave heating and its corresponding initial and boundary conditions were established within wood. Wood is regarded as a homogeneous material in this study in order to make analysis and simulate more effectively.

When wood was vertically and evenly radiated by the unilateral and bilateral microwave source (Figure ^{3};

The microwave heating method during wood pretreatment.

Unilateral microwave heating

Bilateral microwave heating

When microwave got into the wood, the energy on wood surface was the most intensive. With the microwave penetrating inside the wood, energy attenuated in an exponential form, while microwave field released energy to the wood. As the energy of microwave field weakened with increased depth of microwave getting into the wood, the wood thickness was limited when microwave heating was applied for wood drying. During microwave heating, the depth of microwave penetrating the wood can be described by Lambert’s law. For one-dimensional unilateral microwave source radiation, if the direction of the microwave transmission is

Here,

If the temperature of wood distribution is

While the heat obtained by absorbing the microwave directly is

Based on the heat balance principle:
^{3°}C.

Based on (

Partial differential equations (

The initial condition of heat transfer model is relatively simple, because a heat balance existed between the wood and the surrounding environment before heating, so the wood temperature is the same as the ambient temperature, when the room temperature is

The initial condition for bilateral microwave source heating is

In order to solve the mathematical model, the boundary equations of heat transfer within wood during microwave heating should be developed.

When the unilateral microwave source was applied for heating, the boundary equations for heat transfer on ^{2°}C).

In summary, a heat conduction model to describe the temperature distribution within wood was established as follows:

Based on the mathematical model of heat conduction and the given parameters mentioned above, using the MATLAB Software, the temperature profile of wood during microwave heating can be simulated. In the mathematical simulation, the thickness of sawn timber was ^{2} (unilateral microwave source). When using bilateral microwave sources, the radiation power of each microwave source was ^{2}, which means the total microwave radiation intensity of bilateral microwave sources is the same as that of the unilateral microwave source. According to the references [

Figures

Temperature profile of wood microwave heating (unilateral microwave heating; 3D).

Temperature profile of wood microwave heating (unilateral microwave heating; gray).

The temperature profiles within wood heated by the bilateral microwave source were shown in Figures

Temperature profile of wood microwave heating (bilateral microwave heating, 3D).

Temperature profile of wood microwave heating (bilateral microwave heating, gray).

Based on the simulation results above, without considering the differences in microwave absorption within wood, the temperature profiles within wood were related to the methods of microwave heating directly. Compared with the unilateral microwave source heating, the temperature distribution is more uniform for the bilateral microwave source heating. Here, It must be stressed that wood is the nonhomogeneous material, and the difference of dielectric properties of wood are significant within the different areas of wood, which results in a difference on the microwave absorption ability. Therefore, the temperature distribution within wood heated by microwave may be in fact more complex.

Based on the physical law on heat transfer, a mathematical model to describe the temperature profiles within wood microwave heated with deferent methods was established and simulated in this research. The results showed that the temperature profiles inside wood were related to the methods of microwave heating during modification pretreatment. the temperature within wood firstly increased and then gradually decreased along the direction of microwave transmission when the unilateral microwave source was applied for wood microwave pretreatment. The temperature inside wood firstly increased and then gradually decreased from wood surface to interior when the bilateral microwave source were applied for wood microwave pretreatment. Compared with the unilateral microwave source heating, the temperature distribution is more uniform for the bilateral microwave sources heating. Therefore, the effects of the number of microwave source and microwave transmission direction on uniformity of microwave heating should be taken into account during the design of wood microwave heating device.

Thanks for the support of the R&D Special Fund for National Forestry Public Welfare Industry (Grant no. 201204708), New Century Training Program Foundation for the Talents by the Ministry of Education of China.

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