5.1 Influence of the hot air temperature

In a first step, we consider that the speed of drying air is constant and we only vary its temperature.

Figures 6 and 7 show the evolution of the product temperature and the temperature of the humid air, they reach after a certain time the temperature of the drying air. With the same conditions, we also represent the evolution of the moisture content of the product (Figure 8). Increasing the drying air temperature from 55 to 75°C is accompanied by a reduction in drying time. This is due to a potential increase to water evaporation.

Experimentally, for a temperature of 75°C, an air velocity of 2 m/s is sufficient 125 minutes to dry tomatoes. A decrease in temperature of 10° results in an increase

Figure 6. Effect of the hot air temperature on the variation of the product temperature for Ua = 2 m/s and Tam = 30°C.

Figure 7. Effect of the hot air temperature on the variation of the moist air temperature for Ua = 2 m/s and Tam = 30°C.

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

#### Figure 8.

Effect of the hot air temperature on the variation of the moisture content for Ua = 2 m/s and Tam = 30°C.

in drying time of 150 minutes to reach this content. Still with a lower temperature of 55°C, the drying time increases up to 180 minutes.

These results clearly show the influence of drying air temperature on the drying of agro-food products and are in good agreement with previous work [25, 26].

#### 5.2 Influence of hot air velocity

For a constant drying air temperature 55°C and an increase in air velocity beyond 2 m/s does not show a good influence on the variation of the product temperatures and the humid air temperature in terms of reducing the drying time, this is clear in Figures 9 and 10.

The evolution of the moisture content is shown in Figure 11 we see that the influence of the drying air velocity is less important than the drying air temperature because an increase in the air velocity has brought a small decrease in drying time [27, 28].

Figure 9. Effect of the hot air velocity on the variation of the product temperature for Tha = 55°C and Tam = 30°C.

#### Figure 10.

Effect of the hot air velocity on the variation of the moist air temperature for Tha = 55°C and Tam = 30°C.

Figure 11. Effect of hot air velocity on the variation of the moisture content for Tha = 55°C and Tam = 30°C.

The predicted values of the different variables are in good agreement with the experimental values. The quality of the fit was determined using the Root Mean Square Errors (RMSE).


#### Table 2.

RMSE values for different variables studied.

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

$$RMSE = \left(\frac{1}{N} \sum\_{i=1}^{N} \left(X\_{cal} - X\_{mcs}\right)^2\right)^{1/2} \tag{37}$$

We present in Table 2 below the values of the mean squared error.

## 6. Conclusion

In this chapter, the bond-graph approach has been used for modelling a drying system with partially solar heating. This method provides reliable estimates of temperature distributions in the product and the moist air, also the moisture distributions in the product.

The geometry of the dryer, the physical properties of building materials, agricultural product and air are taken into account.

The influence of two aerothermal factors was studied to evaluate the performance of the dryer. The developed model can be adapted to other wet agricultural products as well as to other drying processes.

The challenge for the engineering designer is now to define optimal dryers, which provide a product of constant good quality. For this, the derived model of the tunnel dryer described by equations (1), (34), (35) and (36) will be used subsequently for the control of heat and mass transfer in drying process, which is important to enhance product quality such as colour and flavour.
