### Abstract

An effect of melting on the thermal history of the Earth is considered in a numerical experiment, the basis of which is an inhomogeneous quasilinear equation of heat conductivity. This implies the introduction of two new ideas into the computation process: 1) the latent heat of melting on the boundary of the melting layer, and 2) an increased rate of heat transfer within that layer. The first idea was treated by solving the problem for two moving interfaces; the difference method was applied. The second required the consideration of an effective heat conductivity coefficient. Both ideas lead to new aspects of the Earth's thermal history, principally due to the movement of melt from the interior to the surface of the Earth. The numerical experiment, performed by an electronic computer, has shown that the evolution of the partially melting zone and the velocity of its rising from the interior to the Mohorovičić discontinuity depends mainly on the value of the heat transfer coefficient in the melted layer. At certain values of the coefficient, several melted layers follow each other at successive periods of time. The closeness of the upper boundary of the melted layer to the Mohorovičić discontinuity depends on the heat transfer parameters for the solid part outside the melted layer, e.g. on the opacity coefficient for the radiative component of the termal conduction. When the latter grows from 10 to 100 cm^{-1}, the depths of the upper boundary of the melt increases from 30 to 100 km, and the effect of melting on the terrestrial heat flow decreases. The lower boundary of the level is quite stable and situated at the 400 to 500 km level, if the melting curve is presented by the Uffen (1952) curve. This paper gives a new mathematical treatment of the so-called theory of thermal cycles by Joly (1930).

Original language | English |
---|---|

Pages (from-to) | 326-331 |

Number of pages | 6 |

Journal | Physics of the Earth and Planetary Interiors |

Volume | 2 |

Issue number | 5 |

Publication status | Published - Dec 1969 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Astronomy and Astrophysics
- Physics and Astronomy (miscellaneous)
- Space and Planetary Science
- Geophysics

### Cite this

*Physics of the Earth and Planetary Interiors*,

*2*(5), 326-331.

**On the evolution of melting zones in the thermal history of the earth.** / Tikhonov, A. N.; Lubimova, E. A.; Vlasov, V. K.

Research output: Contribution to journal › Article

*Physics of the Earth and Planetary Interiors*, vol. 2, no. 5, pp. 326-331.

}

TY - JOUR

T1 - On the evolution of melting zones in the thermal history of the earth

AU - Tikhonov, A. N.

AU - Lubimova, E. A.

AU - Vlasov, V. K.

PY - 1969/12

Y1 - 1969/12

N2 - An effect of melting on the thermal history of the Earth is considered in a numerical experiment, the basis of which is an inhomogeneous quasilinear equation of heat conductivity. This implies the introduction of two new ideas into the computation process: 1) the latent heat of melting on the boundary of the melting layer, and 2) an increased rate of heat transfer within that layer. The first idea was treated by solving the problem for two moving interfaces; the difference method was applied. The second required the consideration of an effective heat conductivity coefficient. Both ideas lead to new aspects of the Earth's thermal history, principally due to the movement of melt from the interior to the surface of the Earth. The numerical experiment, performed by an electronic computer, has shown that the evolution of the partially melting zone and the velocity of its rising from the interior to the Mohorovičić discontinuity depends mainly on the value of the heat transfer coefficient in the melted layer. At certain values of the coefficient, several melted layers follow each other at successive periods of time. The closeness of the upper boundary of the melted layer to the Mohorovičić discontinuity depends on the heat transfer parameters for the solid part outside the melted layer, e.g. on the opacity coefficient for the radiative component of the termal conduction. When the latter grows from 10 to 100 cm-1, the depths of the upper boundary of the melt increases from 30 to 100 km, and the effect of melting on the terrestrial heat flow decreases. The lower boundary of the level is quite stable and situated at the 400 to 500 km level, if the melting curve is presented by the Uffen (1952) curve. This paper gives a new mathematical treatment of the so-called theory of thermal cycles by Joly (1930).

AB - An effect of melting on the thermal history of the Earth is considered in a numerical experiment, the basis of which is an inhomogeneous quasilinear equation of heat conductivity. This implies the introduction of two new ideas into the computation process: 1) the latent heat of melting on the boundary of the melting layer, and 2) an increased rate of heat transfer within that layer. The first idea was treated by solving the problem for two moving interfaces; the difference method was applied. The second required the consideration of an effective heat conductivity coefficient. Both ideas lead to new aspects of the Earth's thermal history, principally due to the movement of melt from the interior to the surface of the Earth. The numerical experiment, performed by an electronic computer, has shown that the evolution of the partially melting zone and the velocity of its rising from the interior to the Mohorovičić discontinuity depends mainly on the value of the heat transfer coefficient in the melted layer. At certain values of the coefficient, several melted layers follow each other at successive periods of time. The closeness of the upper boundary of the melted layer to the Mohorovičić discontinuity depends on the heat transfer parameters for the solid part outside the melted layer, e.g. on the opacity coefficient for the radiative component of the termal conduction. When the latter grows from 10 to 100 cm-1, the depths of the upper boundary of the melt increases from 30 to 100 km, and the effect of melting on the terrestrial heat flow decreases. The lower boundary of the level is quite stable and situated at the 400 to 500 km level, if the melting curve is presented by the Uffen (1952) curve. This paper gives a new mathematical treatment of the so-called theory of thermal cycles by Joly (1930).

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M3 - Article

VL - 2

SP - 326

EP - 331

JO - Physics of the Earth and Planetary Interiors

JF - Physics of the Earth and Planetary Interiors

SN - 0031-9201

IS - 5

ER -