Heat transfer and convection currents

Abstract

‘Es gibt nichts praktischeres als die Theorie ’ (ludwig boltzmann—Vorlesungen 1895) The possible causes of convection in the Earth’s mantle are examined, and it is concluded that radiogenic heating together with thermal conduction is most likely to provide the driving force for any convection present at this stage of the Earth’s history. The theory of convection in a medium with internal heat generation is discussed semi-quantitatively. It is concluded that a mantle convection pattern based on calculations of marginal stability in an incompressible fluid is a gross oversimplification of the real situation. A more realistic theory indicates that thermal convection is probably confined to the outer mantle and is an unstable flow. There is evidence that it would have a character that would explain the narrowness and linearity of the pattern presented by the ocean ridges and some orogenic belts.

Whole planet cooling and the radiogenic heat source contents of the Earth and Moon

“…The single temperature T in the models is primarily determined by the rheological law, in accordance with the arguments of Tozer [1965]. This means that for each choice of A and ;;, Twill adjust so as to maintain the mantle viscosity required for transferring the specified heat flux.…”

“…More recently, the acceptance of the idea that there are plate and mantle convective motions with time scales much less than the age of the earth has led to the view that there is essentially a steady state in which heat production and heat loss through the surface are almost balanced (Tozer, 1965;Turcotte and Oxburgh, 1972]. This assumption has been made in discussions of the thermal state of the moon [Runcorn, 1962] and in attempts to estimate the abundances of uranium, thorium, and potassium in the earth and moon [Langseth et a/., 1976].…”

The Heat Flow from the Continents

“…Subsequent discoveries have rendered untenable Kelvin's approach to determining the age of the earth. The first nail in the coffin was the discovery of radioactivity in the late nineteenth century, and the quick recognition of its significance as a heat source that replenished to some degree the escaping primordial heat of the Earth.l A second difficulty arises from the more recent realization (Tozer 1965(Tozer , 1972 that temperature-dependent solid-state creep may be a very significant process within the Earth's mantle that leads to heat transfer principally by convection, rather than by conduction as Kelvin had assumed.…”

Controlling thermal chaos in the mantle by positive feedback from radiative thermal conductivity

“…On the one side, in the past thirty years, since the advent of plate tectonics much attention has been paid to the temperature-dependence of mantle viscosity because of the feedback on the thermal evolution of the mantle (Tozer, 1965(Tozer, , 1972, and the influence of the strong lithosphere on the style of planetary convection (Richter et al, 1983;Ogawa et al, 1991;Solomatov and Moresi, 2000;Monnereau and Quéré, 2001) and the development of fast narrow plumes (Yuen et al, 1976;Christensen, 1984;Olson et al, 1988;Larsen and Yuen, 1997;Thompson and Tackley, 1998). On the other side, not much attention has been devoted to thermal conductivity.…”