A parameterized internally heated convection model for the Earth has been developed. The mantle viscosity is temperature and volatile-content dependent. A heat flow/Rayleigh number relationship appropriate for an internally heated mantle is assumed. For each model an initial homologous temperature and bulk water content are assumed and the initial radiogenic heat production is constrained to give a present day heat flow of 0.07 W m-2. The model is run for 4.6 Gyr, and temperature, heat flow, degassing and regassing rates, stress, and viscosity are calculated. A nominal case is established which shows good agreement with accepted mantle values. The effects of changing various parameters have also been tested. All cases show rapid cooling early in the planet's history and strong self-regulation of viscosity due to the temperature and volatile-content dependence. The values chosen for initial temperature and volatile content have negligible effects on the results, while assumptions about present-day heat flow, viscosity, and mantle volatile content can have important consequences. The effects of weakly stress dependent viscosity are examined within the bounds of this model and are found to be small. Mantle water is typically outgassed rapidly to reach an equilibrium concentration on a time scale of less than 200 m.y. for almost all models, the main exception being for models which start out with temperatures well below the melting temperature. For some cases the degassing efficiency is allowed to decrease with time as the mantle cools which, combined with the rapid early loss of volatiles, leads to a net regassing of the mantle to the present day and loss of water from the surface. ¿ American Geophysical Union 1992