Abstract: Mantle convection with temperature-dependent heat conductivity, specific heat, and thermal expansion coefficient

Abstract

Mantle convection with temperature-dependent heat conductivity, specific heat, and thermal expansion coefficient

The hydrodynamic problem of stability of a plane, horizontal fluid layer is solved both for the free-free and the rigid-rigid case of the boundary conditions. A Newtonian fluid with spatial heat sources is assumed. The present study differs from previous inquiries in that it takes into account, in the problem of convection considered, the following quantities and their temperature dependencies in a way adapted to the conditions in the earth's mantle: radiative and lattice heat conductivity, specific heat, and thermal expansion coefficient. It was possible to determine, with only insignificant neglects, the analytical solutions as well as all the respective constants and the secular equations.

Keywords: CONDUCTIVE HEAT TRANSFER, CONVECTIVE HEAT TRANSFER, EARTH MANTLE, MAGNETOHYDRODYNAMIC STABILITY, SPECIFIC HEAT, THERMAL EXPANSION, BOUNDARY CONDITIONS, BOUNDARY VALUE PROBLEMS, DIFFERENTIAL EQUATIONS, FREE BOUNDARIES, HEAT SOURCES, LINEAR EQUATIONS, NEWTONIAN FLUIDS, RADIATIVE HEAT TRANSFER, TEMPERATURE EFFECTS, TWO DIMENSIONAL FLOW, VISCOUS FLUIDS