**1. Introduction**

Microwave frequencies occupy portions of the electromagnetic spectrum between 300 MHz to 300 GHz. The full range of microwave frequencies is subdivided into various bands (Table 1). Because microwaves are also used in the communication, navigation and defence industries, their use in thermal heating is restricted to a small subset of the available frequency bands. In Australia, the commonly used frequencies include 434 ± 1 MHz, 922 ± 4 MHz, 2450 ± 50 MHz and 5800 ± 75 MHz [1]. These frequencies have been set aside for Industrial, Scientific and Medical (ISM) applications. All these frequencies interact to some degree with moist materials.


**Table 1.** Standard Radar Frequency Letter-Band Nomenclature (IEEE Standard 521-1984)

The major advantages of microwave heating are its short startup, precise control, and volumetric heating [2]. In industry, microwave heating is used for drying [2-5], oil extraction from tar sands, cross-linking of polymers, metal casting [2], medical applications [6], pest control [7], enhancing seed germination [8], and solvent free chemistry [9]. Microwave heating

© 2012 Brodie, licensee InTech. This is an open access chapter distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. © 2012 Brodie, licensee InTech. This is a paper distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

has been applied to various agricultural and forestry problems and products since the 1960's [10]. Studies have been undertaken to use microwave energy: to improve crop handling, storage and preservation; to provide pest and weed control for agricultural production, for food preservation and quarantine purposes; and for preconditioning of products for better quality and more energy efficient processing. This chapter is concerned with microwave heating applications in the agricultural and forestry industries for purposes other than human food processing and consists of a review, update, and discussion of some potential applications that may be of interest to the microwave power and agricultural industries.

#### **2. A brief review of microwave heating in moist materials**

Most agricultural and forest products are a heterogeneous mixture of various organic molecules and water, arranged in various geometries. There are some important features of microwave heating that will determine the final temperature and moisture distribution during microwave processing.

Any realistic study of microwave heating in moist materials must account for simultaneous heat and moisture diffusion through the material. The coupling between heat and moisture is well known but not very well understood [11]. Henry [12] first proposed the theory for simultaneous diffusion of heat and moisture in a textile package. Crank [13] later presented a more thorough development of Henry's work. Since then, this theory has been rewritten and used by many authors [11, 14-17]. Microwave heating can be described by a combined heat and moisture diffusion equation that includes a volumetric heating term associated with the dissipation of microwave energy in the material [17]:

$$\nabla^2 \left( pM\_v + nT \right) - \frac{\partial}{\partial t} \begin{bmatrix} 1 \\ \frac{\pi\_v D\_a}{c} \left( 1 + \frac{\left(1 - a\_v \right) \mathsf{op} \rho\_s}{a\_v} \right) - \frac{n \mathsf{p} \mathsf{o} L}{pk} \\\\ \left[ \frac{\mathsf{C} \mathsf{p}}{k} \left( 1 + \frac{\mathsf{o} L}{\mathsf{C}} \right) - \frac{p \left(1 - a\_v \right) \mathsf{e} \mathsf{o} \rho\_s}{n \mathsf{r}\_v D\_a a\_v} \right] nT \end{bmatrix} + \frac{n \mathsf{q}}{k} = 0 \tag{1}$$

This can be expressed in a simpler form if pMv + nT:

$$
\nabla^2 \Omega - \frac{1}{\chi} \frac{\partial \Omega}{\partial t} + \frac{nq}{k} = 0 \dots \tag{2}
$$

The constants of association, p and n, are calculated to satisfy:

$$\frac{1}{\gamma} = \left[ \frac{1}{\pi\_v D\_a} \left( 1 + \frac{(1 - a\_v) \sigma \rho\_s}{a\_v} \right) - \frac{n \rho \sigma L}{pk} \right] = \left[ \frac{C \rho}{k} \left( 1 + \frac{\alpha L}{C} \right) - \frac{p \left( 1 - a\_v \right) \alpha \rho\_s}{n \tau\_v D\_a a\_v} \right] \tag{3}$$

Essentially, the combined heat and moisture diffusion coefficient () has two independent values, implying that heating and moisture movement occurs in two independent waves. The slower wave of the coupled heat and moisture system is always slower than either the isothermal diffusion constant for moisture or the constant vapour concentration diffusion constant for heat diffusion, whichever is less, but never by more than one half [12, 13]. The faster wave is always many times faster than either of these independent diffusion constants.

46 The Development and Application of Microwave Heating

during microwave processing.

has been applied to various agricultural and forestry problems and products since the 1960's [10]. Studies have been undertaken to use microwave energy: to improve crop handling, storage and preservation; to provide pest and weed control for agricultural production, for food preservation and quarantine purposes; and for preconditioning of products for better quality and more energy efficient processing. This chapter is concerned with microwave heating applications in the agricultural and forestry industries for purposes other than human food processing and consists of a review, update, and discussion of some potential applications that may be of interest to the microwave power and agricultural industries.

Most agricultural and forest products are a heterogeneous mixture of various organic molecules and water, arranged in various geometries. There are some important features of microwave heating that will determine the final temperature and moisture distribution

Any realistic study of microwave heating in moist materials must account for simultaneous heat and moisture diffusion through the material. The coupling between heat and moisture is well known but not very well understood [11]. Henry [12] first proposed the theory for simultaneous diffusion of heat and moisture in a textile package. Crank [13] later presented a more thorough development of Henry's work. Since then, this theory has been rewritten and used by many authors [11, 14-17]. Microwave heating can be described by a combined heat and moisture diffusion equation that includes a volumetric heating term associated

*<sup>a</sup> n L pM D a pk nq pM nT t k C L p a nT*

*k C n Da*

<sup>2</sup> <sup>1</sup> <sup>0</sup> *nq t k* 

1 1 1 1 1 1 *v s v s v a v v av*

*D a pk k C n D a* 

Essentially, the combined heat and moisture diffusion coefficient () has two independent values, implying that heating and moisture movement occurs in two independent waves. The slower wave of the coupled heat and moisture system is always slower than either the isothermal diffusion constant for moisture or the constant vapour concentration diffusion

*a p nL C L a*

1 1 1

*v a v*

1

*v s v av*

1

 

*v s*

0

(1)

(3)

*v*

.. (2)

**2. A brief review of microwave heating in moist materials** 

with the dissipation of microwave energy in the material [17]:

This can be expressed in a simpler form if pMv + nT:

The constants of association, p and n, are calculated to satisfy:

*v*

2

Considerable evidence exists in literature for rapid heating and drying during microwave processing [5, 18]; therefore it is reasonable to assume that the faster diffusion wave dominates microwave heating in moist materials whereas the slower wave dominates conventional heating. A slow heat and moisture diffusion wave should also exist during microwave heating; however observing this slow wave during microwave heating experiments may be difficult and no evidence of its influence on microwave heating has been seen in literature so far.

The fast heat and moisture diffusion wave has a profound effect on biological materials during microwave heating. In particular, very rapid heat and moisture diffusion during microwave heating yields: faster heating compared to conventional heating; and localized steam explosions which may rupture plant and animal cells [18, 19].

Other important phenomena associated with microwave heating include: non-uniform heat and moisture distribution due to the geometry of the microwave applicator [20] and the geometry of the heated material [21]; and phenomenon such as thermal runaway which manifest itself as localised "hot spots" and very rapid rises in temperature [22]. The volumetric heating term (q) in equation (2) is strongly influenced by the geometry of the heated material. Ayappa et al. [2] demonstrate that the equation for electromagnetic power distribution generated in a slab of thickness (W) can be described by:

$$q = \frac{1}{2} \alpha \varepsilon\_o \kappa^n \left(\tau E\right)^2 \left(e^{-2\beta z} + \Gamma^2 e^{-2\beta(\mathcal{V} - z)} + 2\Gamma e^{-\beta(\mathcal{V} - 2z)} \cos(\delta + 2az)\right) \tag{4}$$

It has been shown elsewhere [21] that using this volumetric heating relationship, the solution for equation (2) is:

$$\cdots \,\,\Omega\left(t\right) = \frac{n\alpha\varepsilon\_o\kappa^{\prime\prime}\left(\tau E\right)^2}{8k\beta^2} \left| e^{4\gamma\beta^2 t} - 1 \right| \left| e^{-2\beta z} + \left(\frac{h}{k} + 2\beta\right) \overline{z} e^{\frac{-z^2}{4\gamma t}} \right| \left(1 + \Gamma^2 e^{-2\beta\beta\ell}\right) \tag{5}$$

From this it can be deduced that the temperature/moisture profiles in thick slabs and rectangular blocks usually result in subsurface heating where the maximum temperature is slightly below the material surface [23].

The microwave's electric field distribution in the radial dimension of a cylinder can be described by [21]:

$$E = \text{\textpi}E\_o \frac{I\_o \left(\text{\textdegree}r\right)}{I\_o \left(\text{\textdegree}r\_o\right)}\tag{6}$$

The resulting solution to equation (2) can ultimately be derived [21]:

$$\Omega(t) = \frac{m\alpha\_o \kappa^\* \pi^2 E\_o^2 \left( e^{4\eta^2 \eta t} - 1 \right)}{4k\beta^2 I\_o \left( 2\mathfrak{R}r\_o \right)} \left[ \frac{4\alpha \eta t}{\int I\_o \left( \alpha r\_o \right) I\_o \left( \mathfrak{R}r\_o \right)} e^{\frac{-r^2}{4\eta t}} + I\_o \left( 2\mathfrak{R}r \right) + \left\{ 2\mathfrak{R}I\_1 \left( 2\mathfrak{R}r\_o \right) + \frac{\hbar}{k} I\_o \left( 2\mathfrak{R}r\_o \right) \right\} \left( r\_o - r \right) e^{-\frac{\left( r\_o - r \right)^2}{4\eta t}} \right] \left( \nabla \right) \left( \left( \nabla \right) e^{\frac{-r^2}{4\eta t}} + \frac{\hbar}{k} I\_o \left( 2\mathfrak{R}r \right) \right)$$

The temperature/moisture profiles in small-diameter cylinders, such as a plant stem, usually exhibit pronounced core heating [23, 24]. On the other hand, temperature profiles in large cylinders exhibit subsurface heating, with the peak temperature occurring slightly below the surface [23].

Microwave heating in spheres is similar to that in cylinders. The microwave's electric field distribution in the radial dimension of a cylinder can be described by [21]:

$$E = \text{\textbullet}\_o \frac{j\_o(fr)}{j\_o(fr\_o)}\tag{8}$$

The resulting solution to equation (2) can ultimately be derived [21]:

$$\Omega(t) = \frac{m\alpha\_o \kappa^n \tau^2 E\_o^2 \left( e^{4\beta^2 \gamma t} - 1 \right)}{k\mathfrak{H} \cdot i\_o \left( 2\mathfrak{H} r\_o \right)} \left[ \frac{\alpha \gamma t}{\int j\_o \left( \alpha r\_o \right) i\_o \left( \mathfrak{H} r\_o \right)} e^{\frac{-r^2}{4 \gamma t}} + \frac{i\_o \left( 2\mathfrak{H} r \right)}{4 \mathfrak{H}} + \left\{ 2\mathfrak{H} \cdot i\_1 \left( 2\mathfrak{H} r\_o \right) + \frac{\hbar}{k} i\_o \left( 2\mathfrak{H} r\_o \right) \right\} \frac{\left( r\_o - r \right)^2}{4 \mathfrak{H}} e^{\frac{-\left( r\_o - r \right)^2}{4 \gamma t}} \right] \left( \mathfrak{H} \right)^2$$

This analysis can be used, in conjunction with experimental data, to better understand how microwave heating affects agricultural and forestry products.
