A Heat Transfer Model for the Upper Respiratory Tract of Livestock under Tropical Conditions

To determine the heat and mass transport in the respiratory tract it is necessary to obtain estimatives of the expired air temperature and its water vapor contents, but the measurement of these variables require a lot of expensive equipments. A way to estimate the temperature and the water vapor concentration in upper animals' airway is by solving the energy balance for the mass and heat transport in the trachea considering it as a horizontal cylinder. The aim of this work was to discuss the development of a mathematical model to the upper airway of trachea to predict the expired air temperature and the water vapor concentration in sheep, goats and beef cattle.

The model considered the trachea a circular tube with 0.014 m of diameter and 0.256 m of length for sheep; 0.015 m of diameter and 0.385 m of length for goats and 0.036 m of diameter and 0.526 m of length for beef cattle measuring using a digital caliper. The model was considered a one-dimensional steady-state condition, only the axial direction, and no includes the heat generation by the metabolism and assumes a constant core temperature to be the same of the trachea wall. The model will be validated against experimental data collected using a database of tree experiments for sheep, goats and beef cattle, developed under the environmental conditions of Jaboticabal, SP, Brazil (21o08' South latitude, 595 m high), at the São Paulo State University – UNESP. All environmental conditions were continuously monitored by a datalogger (Hobo, Onset). The Exercise Physiological System used to the continuous measurement of respiratory flow ( , L seg-1), respiratory rate (RR, breaths min-1) and Tidal Volume (VT, L breaths-1); and body temperatures (rectal and expired air), while the Metabolic System measures the water vapor (PExp, kPa).

The results showed that the respiratory rate of sheep was higher than of goats and beef cattle (P<0.001) and we observed average values of 154±26 breaths min-1, 17± 3 breaths min-1 and 19± 1 breaths min-1 respectively. For sheep averages for tidal volume and respiratory flow of 0.257±0.047 L breaths-1 and 0.653±0.109 l min-1 were observed, respectively. Goats and beef cattle presented a lower RR and showed a tidal volume of approximately 0.740±0.135 L breaths-1 and 7.8±0.3 L breaths-1, respectively, and an average value for respiratory flow of 0.213±0.047 l min-1 for goats and 2.47±0.030 l min-1 for beef cattle. Expired air temperature was an average of 31.12±1.6 °C, 34±0.8 °C and 32.8±0.18 °C for sheep, goats and beef cattle, respectively.

These results will be compared with values estimated by the model.