Mantle Heat Flow Distribution Calculator

Surface heat flow is the conductive flux escaping from the deep interior, obtained by combining a borehole temperature gradient with the thermal conductivity of the rock through the Fourier law, q equals minus k times dT/dz. Typical continental gradients are 25 to 30 degrees C per km and typical crustal conductivities are 2 to 3.5 W per m per K, which is why continental values cluster near 65 mW per square meter. The distribution is strongly bimodal by tectonic setting. Archean cratons such as the Canadian Shield and the Kaapvaal craton run 40 to 50 mW per square meter beneath lithospheric roots 200 to 300 km thick, active extensional provinces such as the Basin and Range reach 80 to 100, and young seafloor near a spreading ridge exceeds 250. Oceanic heat flow follows the half-space cooling prediction that q declines as the inverse square root of crustal age. Integrated globally the mean flux is near 87 mW per square meter, which over the 5.10 x 10^14 square meter surface of the Earth gives a planetary total close to 44 terawatts, roughly 31 TW escaping through ocean floor and 13 TW through continents; the denser 2010 compilation raises those figures to about 92 mW per square meter and 47 TW. Two sources supply it: decay of uranium-238, uranium-235, thorium-232, and potassium-40, concentrated in granitic crust at 1 to 3 microwatts per cubic meter, and secular cooling of the planet plus latent heat released by inner core crystallization. Their ratio, called the Urey ratio, remains contested and is usually placed between 0.4 and 0.7. The dominant measurement caveat is hydrothermal circulation. On seafloor younger than about 65 million years, water moving through fractured basalt carries heat advectively past the sediment where probes sit, so raw conductive readings underestimate true loss substantially and young-crust values must be corrected against the cooling model.

The subject begins as a failed attempt to date the planet. William Thomson, later Lord Kelvin, argued from 1862 onward that the measured near-surface geothermal gradient implied a conductively cooling Earth only 20 to 400 million years old, a result that flatly contradicted the geologists and Darwin. He was wrong for two reasons found later: radioactivity, discovered by Henri Becquerel in 1896, supplies continuous internal heat, and the mantle convects rather than merely conducting. Robert John Strutt measured radium concentrations in common rocks in 1906 and showed that crustal radioactivity alone could account for a large share of the observed surface flux. Systematic measurement started in 1939, when Arthur Benfield and Edward Bullard published the first purpose-designed borehole determinations in Britain and in South Africa. Bullard went on to develop a marine probe that Roger Revelle and Arthur Maxwell used in the early 1950s for the first seafloor measurements, which unexpectedly showed oceanic heat flow as high as continental heat flow and became early evidence for mantle convection and later for seafloor spreading. Global compilations followed: William Lee and Seiya Uyeda in 1965, then Henry Pollack, Suzanne Hurter, and Jeffrey Johnson in 1993 with 24,774 observations giving a mean near 87 mW per square meter, and a 2010 reassessment by John Davies and David Davies that put the global total close to 47 TW.