A homogeneous macrostructured material sweet potato (Ipomoea batatas) is used to minimize the effects of macrostructure and component composition [18] on the evaluation of transfers during convective drying. Thereby, the sweet potato tubers were used as an experiment for this present work.

The tubers that served as samples for our experiments were purchased in a local market in the same heap in batches in order to reduce the differences in

material properties [13]. The potato is therefore transported to the University Nazi BONI of Bobo-Dioulasso, Burkina Faso. The tubers are washed, peeled and cut manually into the desired shape (Figure 2) and size using a stainless steel knife. the use of the stainless steel knife prevents the oxidation of surfaces in contact with the oxygen in the air. The cut samples are quickly immersed in water to prevent oxidation and to evacuate excess starch from the surface which forms a film that slows down transfers.

Washed and wiped with blotting paper, the samples are placed in the oven, the temperature of which is suitably adjusted for drying. We used an AIR concept, temperature varying from 40˚C to 250˚C, with PID regulation, with digital display. The samples are regularly withdrawn for the determination of the mass during the drying time and reintroduced into the oven. The mass is determined by a balance (SARTORIUS, 0.001 g precision, France). The measurement time is fast so as not to disturb the thermodynamic equilibrium. Given the regular withdrawal of samples, we consider that the transfers take place on all sides. The samples are placed directly on the racks. We calculate the initial areas as the total area of the sample from the dimensions measured with a Mitutoyo (Japan) precision 2.10 - 5 mm micrometer. Note that we were unable to measure air speed and relative humidity which are important parameters in the evaluation of drying. To do this, we compare the results of experiments which were carried out simultaneously and in the same oven to circumvent the influence of these two parameters.

The determination of the dry mass is made after a stay of 24 hours in an oven at 70˚C [20] (AOAC, 1990).

The initial water content of the product is the quotient of the total mass of water contained in the freshly cut product m_e divided by the mass of solid matter m_s.

X 0 = m e m s = m 0 − m s m s (1)

where m₀ is the initial mass of the sample and ms is the dry mass of the sample.

The curves of the water contents as a function of the drying time were drawn from the experimental data. From the mass of the sample at time t, we deduce the water content according to:

X ( t ) = m ( t ) − m s m s (2)

where m(t) is the mass of the sample at time t of drying.

From the value of the mass m(t) and the dry mass m_s of the sample we calculate the water content X(t) according to the equation Eq-2. The relation X(t)-t gives us the kinetics of the variation of the water content of the product. To have the same basis for comparison, we normalize the water content at time t by the initial water content X₀ of the product determined according to the Equation (1), which gives us the X/X₀-t curves.

Figure 3 contains the results of the tests on the parallelepiped shape samples. The same thickness e = 1 cm is set for all the samples while the lengths and the widths L × l vary for the purposes of experiments. The L × l × e dimensions of 3 cm × 2 cm × 1 cm, 4 cm × 2 cm × 1 cm, 4 cm × 3 cm × 1 cm and 5 cm × 3 cm ×1 cm are used. We denote them respectively P_L = 3 − l = 2 − e = 1, P_L = 4 − l

= 2 − e = 1, P_L = 4 − l = 3 − e = 1 and P_L = 5 − l = 3 − e = 1. For each type of sample, three measurements are used to ensure the reliability of the experiments. The results show that the differences between the curves are minimal, going close to zero (0) kg_e/kg_ms for the most repetitive ones to 0.109 obtained, as the worst case, for samples 1 and 2 of the parallelepipedal samples P_L = 4 − l = 2 − e = 1 at the 161^st minute of drying. These small differences can be attributed to imperfect measurements, but also to the complex nature of agrifood products.

Figure 4 gathers the results of the experiment on the cylindrical samples, of the same radius R = 1 cm. Heights H vary from experiment to experiment. The heights H of 2 cm, 3 cm, 4 cm and 5 cm are used. For each type of sample, three are used to ensure the reliability of the experiments. The results show that the differences between the curves are ranging from almost zero (0 kg_e/kg_ms) for the most repetitive to 0.114 kg_e/kg_ms −0.079 kg_e/kg_ms = 0.035 kg_e/kg_ms obtained for samples 1 and 2 of the cylinders C_H = 2 − R = 1 at the 175^th minute of drying. These insignificant differences can be attributed to imperfect measurements, but also to the complex nature of agrifood products.

In this paragraph we seek to verify if the thickness e of the samples in parallelepiped

shape is the characteristic dimension of drying. Indeed, according to Ouoba, 2013 [1] the smallest path for the migration of water from the inside of the product to the outside in this case would be the thickness. This is the smallest dimension compared to the length and width of the samples.

To do this, we have set a thickness e = 1 cm facing lengths of 3 cm, 4 cm, 5 cm and widths of 2 cm, 3 cm. the sample is denoted here P_L-l-e according to the dimensions length L, width l, thickness e used for these parallelepipedic shapes P.

Figure 5 contains the results from the convective drying of these different samples. The average of the normalized water contents X/X₀ of the three tests by type of sample is plotted as a function of the drying time. This average makes it possible to reduce the differences in handling errors and difficulties linked to the nature of the product. As we can see, the results are very superposable.

The maximum standard water content deviation is 0.223 kg_e/kg_ms − 0.144 kg_e/kg_ms = 0.079 kg_e/kg_ms between P_L = 3 − l = 2 − e = 1 and P_L = 5 − l = 4 − e = 1 at the 140^th minute of drying. this difference is negligible and occurs when the material undergoes visible deformations of its structure which can also interfere with the transfer path.

The search for the characteristic dimension continues here with the cylindrical samples. We look for it in the radial direction, fixing the radius R = 1 cm as the smallest dimension. This corroborates the idea of Ouoba, 2013 [1], as a smaller

path for the migration of water from the inside to the outside of the product. This is the smallest dimension compared to the height of the samples.

To do this, we have set a radius R = 1 cm facing heights of 2 cm, 3 cm, 4 cm and 5 cm. The sample is denoted here c_H-R according to the dimensions height H, radius R used for these cylindrical shapes c.

Figure 6 contains the results from the convective drying of these different samples. The average of the normalized water contents X/X₀ of the three tests by type of sample is plotted as a function of the drying time. The goal is to reduce the effects of handling and difficulties linked to the nature of the product.

Here also, it can be seen, according to Figure 6, that the results are indeed superposable.

The maximum standard water content deviation is 0.302 kg_e/kg_ms − 0.217 kg_e/kg_ms = 0.085 kg_e/kg_ms between c_H = 2 − R = 1 and c_H = 5 − R = 1 at the 119^th minute of drying. This difference is also negligible and occurs when the material undergoes visible deformations of its structure as well.

From the foregoing, the thickness of the parallelepiped samples turns out to be the dimension which best governs the transfers versus its length and its width. Likewise, with regard to cylindrical samples, the fixed radius smaller than the height is the characteristic dimension of the transfers in the product during its convective drying.

In any case, the thickness and the radius in this present work are the smallest

dimensions. According to, Ouoba, 2013 [1], we can affirm that these dimensions of thickness and radius constitute the shortest path for the migration of heat to the most remote point of the drying environment. They are also the shortest path for the water furthest from the outside to be able to escape from the grip of matter.

For these samples of parallelepipedal and cylindrical shape, the notion of characteristic dimension, as being the shortest distance between the outside and the point most unfavorable for drying is verified.