“No.” She turned to Chapter 7 (External Flow) and Chapter 8 (Internal Flow). “We don’t just heat the bearing. We cool the shaft. Simultaneously. We need a temperature difference of at least 120°C across the interface—hot bearing, cold shaft—to break the seizure.”
The penstock was a ten-foot-diameter steel pipe that once fed water to the turbine at 15°C. Marco argued for an hour that it was impossible. Elara countered with Reynolds numbers, Nusselt correlations, and the log-mean temperature difference equation from Chapter 11 (Heat Exchangers). She calculated the convective heat transfer coefficient for water flowing through the shaft’s hollow core. She estimated the Biot number to justify lumped-capacitance analysis for the thin bearing shell. --- Fundamentals Of Heat And Mass Transfer 8th Edition
Marco crossed his arms. “So we’re stuck.” Simultaneously
“If we run cold river water through the shaft at 20 m³/s,” she said, tapping a page of hand-scrawled calculations, “the shaft’s surface temperature will drop 80°C in forty minutes. Then we hit the bearing with induction heaters—180°C outer surface. The differential strain will crack the oxide bond. It will move .” Elara stood on the turbine deck
Outside, the river fell. The dam held. And the 8th edition—with all its tables, equations, and Nusselt numbers—rested quietly on the desk, still warm from the fight.
He pulled the hydraulic puller. For one second, nothing. Then a sound like a gunshot—the crack of a thousand frozen micro-welds shattering. The bearing slid three millimeters.
“Then thermal shock cracks the shaft. And we walk home.” Forty-three minutes later, Elara stood on the turbine deck, sweat freezing on her brow despite the cavern’s chill. The induction coils glowed cherry red around the bearing. Infrared thermometers danced: bearing outer race, 176°C. Shaft surface (monitored through a small access port), 4°C. ΔT = 172 K. More than enough.