Two-phase flow and heat transfer, such as boiling and condensing flows, are complicated physical phenomena that generally prohibit an exact solution and even pose severe challenges for numerical approaches. If numerical solution time is also an issue the challenge increases even further. We present here a numerical implementation and novel study of a fully distributed dynamic one-dimensional model of two-phase flow in a tube, including pressure drop, heat transfer, and variations in tube cross-section. The model is based on a homogeneous formulation of the governing equations, discretized by a high resolution finite difference scheme due to Kurganov and Tadmore.

The homogeneous formulation requires a set of thermodynamic relations to cover the entire range from liquid to gas state. This leads a number of numerical challenges since these relations introduce discontinuities in the derivative of the variables and are usually very slow to evaluate. To overcome these challenges, we use an interpolation scheme with local refinement.

The simulations show that the method handles crossing of the saturation lines for both liquid to two-phase and two-phase to gas regions. Furthermore, a novel result obtained in this work, the method is stable towards dynamic transitions of the inlet/outlet boundaries across the saturation lines. Results for these cases are presented along with a numerical demonstration of conservation of mass under dynamically varying boundary conditions. Finally we present results for the stability of the code in a case of a tube with a narrow section.

The effects of short-term exposure to high ambient temperatures on gas exchange, heat production (HE), respiration rate (RR) and rectal temperature were evaluated individually with boars of approximately 100 kg live weight. The boars were of different breeds with four of Yorkshire (YS), eight of Danish Landrace (DL), out of which three were found stress susceptible by the halothane test (DLH+), eight of Duroc (DR) and eight of Hampshire (HS) breeds. After 1 h rest in the respiration chamber at 17·0°C the gas exchange measurements started with al-h basal period at 17 °C, followed by 2h of heating during which temperature increased to 35·0 °C (period I) and then further to 39·7X1 (period II). Then cooling of the chamber started, and after 1 h (period III) temperature had decreased to 21·8°C, and after the 2nd h of cooling (period IV) temperature was 18·2 °C. The gas exchange was measured for each hour from 09.00 h (basal period) until 14.00 h (period IV). RR was recorded every 15 min. Rectal temperatures were measured when the animals were removed from the chamber. The gas exchange and HE increased slowly during period I but rapidly in period II, followed by decreasing values in the cooling periods. HS and DLH+ had considerably higher gas exchange and HE than other breeds in these two periods and the values remained high during period III. In period IV all breeds had gas exchange rates and HE below those of the basal period. RR increased slightly in period I and then a sharp increase followed during period II. Maximum RR was recorded in period III with an average of 183 breaths per min for all breeds. RR increased earlier and more steeply in HS and reached the highest mean value of 236 breaths per min. Four HS boars salivated heavily during heat stress and rectal temperatures of these animals were 39·7 °C when removed from the chamber compared with close to 39·0 °C for all other breeds. It was concluded that there were considerable breed differences in response to heat stress and that DLH+ and HS were more severely stressed than boars ofYS, DL and DR.