Counter-Current Heat Exchanger
Simulating the startup transient of a counter-current shell-and-tube heat exchanger, showing how temperature profiles develop along the exchanger length.
The exchanger is discretized into MATHINLINE2ENDMATH cells along its length. In each cell, the hot and cold streams exchange heat proportional to the local temperature difference:
MATHDISPLAY0ENDMATH
MATHDISPLAY1ENDMATH
The hot stream flows from cell 1 to MATHINLINE3ENDMATH, the cold stream flows counter-currently from cell MATHINLINE4ENDMATH to 1.
Configure a heat exchanger with 10 cells. Both sides start at 300 K (cold), then hot fluid at 370 K enters. This lets us watch the temperature profile build up from the initial uniform state. The high MATHINLINE0ENDMATH relative to the flow rate ensures significant heat transfer.
Feed hot water at 370 K and cold water at 290 K. Record the outlet temperatures over time.
18:18:16 - INFO - LOGGING (log: True) 18:18:16 - INFO - BLOCKS (total: 4, dynamic: 1, static: 3, eventful: 0) 18:18:16 - INFO - GRAPH (nodes: 4, edges: 4, alg. depth: 1, loop depth: 0, runtime: 0.174ms) 18:18:16 - INFO - STARTING -> TRANSIENT (Duration: 200.00s) 18:18:17 - INFO - -------------------- 1% | 0.0s<1.2s | 8259.1 it/s 18:18:17 - INFO - ####---------------- 20% | 0.3s<1.0s | 8070.1 it/s 18:18:17 - INFO - ########------------ 40% | 0.6s<0.8s | 7989.9 it/s 18:18:17 - INFO - ############-------- 60% | 0.8s<0.5s | 8277.9 it/s 18:18:18 - INFO - ################---- 80% | 1.1s<0.3s | 7985.9 it/s 18:18:18 - INFO - #################### 100% | 1.3s<--:-- | 10878.7 it/s 18:18:18 - INFO - FINISHED -> TRANSIENT (total steps: 10000, successful: 10000, runtime: 1258.22 ms)
At startup, both sides are cold. The hot fluid quickly warms the exchanger from the inlet side while the cold fluid absorbs heat. At steady state, the counter-current arrangement creates the characteristic temperature cross — the cold outlet approaches the hot inlet and vice versa, achieving high thermal efficiency.