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Mathematics of Geothermal Energy

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Geothermal energy harnesses Earth's internal heat for heating and electricity. The geothermal gradient increases with depth, averaging 2.5–3°C per 100 meters, with extreme heat reaching 5000°C at 6000 km depth. Prime regions include the Ring of Fire.

Mathematical models—such as Lagrangian–Eulerian flow, stochastic, and geometric models—are used by scientists to study heat transport, reservoir engineering, and radioactive waste isolation. Applications extend to neurosurgery and industrial molding. Geothermal heating dates back to the 19th century, with Iceland emerging as a leader by the 1920s.

Heat pump systems transfer heat between ground and buildings seasonally. Large-scale water movement can cause subsidence, as seen in Venice, and affect reservoir pressure and seismic activity. Geothermal electricity generation began with early power plants, using steam from underground reservoirs to drive turbines.

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