Simple thermal models based on the creation and cooling of the lithosphere can account for the observed subsidence of the ocean floor and the measured decreased in heat flow with age. In well‐sedimented areas, where there is little loss of heat due to hydrothermal circulation, the surface heat flow decays uniformly from values in excess of 6 µcal/cm² s (250 mW/m²), for crust younger than 4 Ma (4 m.y. B.P.), to close to 1.1 µcal/cm² s (46 mW/m²) through crust between 120 and 140 Ma. After 200 Ma the heat flow is predicted to reach an equilibrium value of 0.9 µcal/cm² s (38 mW/m²). The surface heat flow on continents is controlled by many phenomena. On the time scale of geological periods the most important of these are the last orogenic event, the distribution of heat‐producing elements, and erosion. To better understand the effects of age, each continent is separated into four provinces on the basis of radiometric dates. Reflecting the preponderance of Precambrian crust, two of these provinces cover the Archean to the middle Proterozoic, and the third covers the late Proterozoic to the Mesozoic. The mean heat flow decreases from a value of 1.84 µcal/cm² s (77 mW/m²) for the youngest province to a constant value of 1.1 µcal/cm² s (46 mW/m²) after 800 Ma. The nonradiogenic component of the surface heat flow decays to a constant value of between 0.65 and 0.5 µcal/cm² s (25 and 21 mW/m²) within 200–400 Ma. Using theoretical models, we compute the heat loss through the oceans to be 727 × 1010 cal/s (30.4 × 1012 W). The comparison between the theoretical and measured values allows an estimate of 241 × 1010 cal/s (10.1 × 1012 W) for the heat lost owing to hydrothermal circulation. We show that the heat flow through the marginal basins follows the same relation as that for crust created at a midocean spreading center. These basins have a corresponding heat loss of 71 × 1010 cal/s (3.0 × 1012 W). The heat loss through the continents is calculated from the observations and is 208 × 1010 cal/s (8.8 × 1012 W). Our estimate of the value for the shelves is 67 × 1010 cal/s (2.8 × 1012 W). The total heat loss of the earth is 1002 × 1010 cal/s (42.0 × 1012 W), of which 70% is through the deep oceans and marginal basins and 30% through the continents and continental shelves. The creation of lithosphere accounts for just under 90% of the heat lost through the oceans and hence about 60% of the worldwide heat loss. Convective processes, which include plate creation and orogeny on continents, dissipate two thirds of the heat lost by the earth. Conduction through the lithosphere is responsible for 20%, and the rest is lost by the radioactive decay of the continental and oceanic crust. We place bounds of between 0.6 and 0.9 µcal/cm² s (25 and 38 mW/m²) for the mantle heat flow beneath an ocean at equilibrium and between 0.40 and 0.75 µcal/cm² s (17 and 31 mW/m²) for the heat flow beneath an old stable continent. The computed range of geotherms for an equilibrium ocean overlaps the range of stable continental geotherms below a depth of 1...

The characteristics of thermal convection in a fluid whose viscosity varies strongly with temperature are studied in the laboratory. At the start of an experiment, the upper boundary of an isothermal layer of Golden Syrup is cooled rapidly and maintained at a fixed temperature. The fluid layer is insulated at the bottom and cools continuously. Rayleigh numbers calculated with the viscosity of the well-mixed interior are between 106 and 108 and viscosity contrasts are up to 106. Thermal convection develops only in the lower part of the thermal boundary layer, and the upper part remains stagnant. Vertical profiles of temperature are measured with precision, allowing deduction of the thickness of the stagnant lid and the convective heat flux. At the onset of convection, the viscosity contrast across the unstable boundary layer has a value of about 3. In fully developed convection, this viscosity contrast is higher, with a typical value of 10. The heat flux through the top of the layer depends solely on local conditions in the unstable boundary layer and may be written \[Q_{\rm s} = - CK_{\rm m} (\alpha g/\kappa \nu_{\rm m})^{\frac{1}{3}} \Delta T^{\frac{4}{3}}_{\rm v}\], where km and νm are thermal conductivity and kinematic viscosity at the temperature of the well-mixed interior, κ thermal diffusivity, α the coefficient of thermal expansion, g the acceleration due to gravity. ΔTv, is the ‘viscous’ temperature scale defined by \[\Delta T_{\rm v} = - \frac{\mu (T_{\rm m})}{({\rm d}\mu /{\rm d}T)(T_{\rm m})}\] where μ(T) is the fluid viscosity and Tm the temperature of the well-mixed interior. Constant C takes a value of 0.47 ± 0.03. Using these relations, the magnitude of temperature fluctuations and the thickness of the stagnant lid are calculated to be in excellent agreement with the experimental data. One condition for the existence of a stagnant lid is that the applied temperature difference exceeds a threshold value equal to (2ΔTv).

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