F. Nimmo et D. Mckenzie, CONVECTIVE THERMAL EVOLUTION OF THE UPPER MANTLES OF EARTH AND VENUS, Geophysical research letters, 24(12), 1997, pp. 1539-1542
On Earth the present-day rate of heat loss is about twice the heat gen
eration rate; on Venus it is about half. Though this rough balance may
be due to a feedback mechanism between mantle temperature and heat lo
ss, it is difficult to see how such a mechanism can occur on timescale
s of 1 Ga or less when the upper mantle of the Earth is thought to be
cooling at about 40 degrees C Ga-1. On Venus a decrease in surface hea
t flux presumably occurred at the end of the catastrophic resurfacing
event at similar to 500 Ma. Parameterized convection models relate hea
t flux to Rayleigh number by the exponent beta. Such models using a ra
nge of viscosities and values of beta from 0.2 to 0.3 show that the ef
fect of a sudden decrease in surface heat flux is to cause an independ
ently convecting upper mantle to increase in temperature by 100 - 500
degrees C over 1 Ga, whereas, if whole mantle convection occurs, the t
emperature change is less than 60 degrees C. An increase in mantle tem
perature of 200 degrees C or more will affect mantle viscosity, lithos
pheric thickness and melt generation rate, all of which may affect the
feedback mechanism.