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STUDIES OF THE DYNAMO ACTION OF THE LIQUID CORE OF THE EARTH.
Final rept. Jan 63-Aug 65,
WAYNE STATE UNIV DETROIT MICH DEPT OF CHEMISTRY
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The differential equations for the steady motion of a rotating conducting fluid interacting with a magnetic field, and driven by a volume distribution of thermal sources, have been set up. They contain two dimensionless parameters, one of which is proportional to the Joule heating and the other to the difference between the temperature gradient maintained by the thermal sources and the adiabatic temperature gradient. The problem is reduced to solving an infinite set of quadratic equations, and all necessary numerical calculations of the integrals involved have been carried out. The infinite set of equations can be approximated by finite sets, and properties of these sets have been investigated in detail. It has been shown that the two parameters of the problem must be related. Simple solutions of finite sets have been obtained, and a great deal of I.B.M. 7070 computer time has been devoted to attempts to generalize these solutions, but without success. The existence of a steady state dynamo has not been proved or disproved. The work reported should be of value to anyone undertaking similar calculations in the future. Author
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