4. Modelling technique

The dynamic behaviour of the thermal processes is generally described by the nonlinear differential equations. Their formulation and resolution by the classic numerical methods are limited [20]. These equations are really associated with the physical phenomena such as storage and energy dissipation. The bond graph approach allows by their graphical description to show these energy exchanges in the system.

The bond graph modelling approach is a unified and causal approach applied to all types of dynamical systems; it allows the modellers to obtain the mathematical model in the form of a state equation easier than the classical modelling methods.

Figure 3. Flow diagram of drying process in a tunnel dryer.

Dynamic Modelling by Bond Graph Approach of Convective Drying Phenomena DOI: http://dx.doi.org/10.5772/intechopen.91276

Moreover, to provide information on the structural properties of the studied system.

The first modelling step is to divide the global system into subsystems that exchange power with each other; this is the word-pseudo bond graph (Figure 4). The effort and flow variables are marked at the input and output of each subsystem. Depending on the physical phenomena that occur during drying and using the properties of the bond graph approach, the words are replaced by their corresponding elements, which lead to the complete models shown in Figure 5.

The pseudo-bond graph model of the studied tunnel dryer was developed based on the equations derived from the energy balances of the system.

The variables of effort and flux are respectively temperature (T) and heat flux (Q\_ ), moreover, the pseudo bond graph model of Figure 4 is constructed by five elements which are Se, R, C, 0 and 1.

Figure 4. Word pseudo bond graph model of the tunnel dryer.

Figure 5. Pseudo bond graph model of the tunnel dryer.

## 4.1 Effort sources

The two sources of effort used in this pseudo-bond graph model are Se1 and Se2 which respectively model the average temperature of the air drying Tha and the ambient air temperature Tam.

$$T\_{ha} = \frac{T\_{a\text{aux}} + T\_{so}}{2} \tag{7}$$
