4.2 C-fields

The energy storage phenomena are modelled by the C elements, the effort or flux variable is determined according to the attributed causality using the following relation:

$$e = \rho\_c^{-1} \left[ f dt \right] \tag{8}$$

On the surface of the product modelled by the element Cpr, the corresponding temperature is expressed by:

$$T\_{pr} = \frac{1}{C\_{pr}} \int \dot{Q}\_{pr} dt \tag{9}$$

Q\_ pr is the thermal heat flow accumulated on the surface of the product and Cpr is thermal capacity of products.

$$\mathbf{C}\_{pr} = m\_{pr}\mathbf{C}\_{p,pr} \tag{10}$$

with mpr being the mass and Cp,pr being the specific heat of the product.

Cma represents the accumulation of energy inside the drying chamber, the moist air temperature in the chamber is given by:

$$T\_{ma} = \frac{1}{C\_{ma}} \int \dot{Q}\_{ma} dt \tag{11}$$

Q\_ ma is the thermal heat flow accumulated in the chamber and Cma is the thermal capacity of the moist air.

$$\mathbf{C}\_{ma} = \rho\_{ma} \ \mathbf{V}\_{ma} \ \mathbf{C}\_{p,ma} \tag{12}$$

ρma, Vma and Cp,ma are respectively the density of the moist air, the volume of the chamber and the specific heat of the moist air.

The accumulation of energy on the inner wall of the chamber is modelled by the Cwa element; the temperature of the inner wall is expressed by:

$$T\_{uu} = \frac{1}{C\_{uu}} \int \dot{Q}\_{uu} dt \tag{13}$$

Q\_ wa and Cwa are the thermal heat flow and the thermal capacity of the inner wall.

$$\mathbf{C}\_{uu} = \rho\_{uu}\mathbf{V}\_{uu}\mathbf{C}\_{p,uu} \tag{14}$$

ρwa, Vwa and Cp,wa are respectively the density, the volume and the specific heat of inner walls.

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