Mantle Heat Flow Distribution Calculator
Our planetary & earth system science calculator computes mantle heat flow distribution accurately. Enter your values for instant results.
Reviewed by Daniel Agrici, Founder & Lead Developer
Formula
T_eff = (S(1-a)/4sigma)^(1/4); T_surface = ((S(1-a)/4 + dF)/(eps*sigma))^(1/4)
Where S is solar constant, a is albedo, sigma is Stefan-Boltzmann constant, eps is effective emissivity, dF is additional radiative forcing.
Worked Examples
Example 1: Present-Day Earth Energy Balance
Problem:Calculate Earth energy balance with solar constant 1361 W/m2, albedo 0.30, effective emissivity 0.612.
Solution:Absorbed solar = (1361/4) * (1 - 0.30) = 238.18 W/m2\nT_eff = (238.18 / 5.67e-8)^0.25 = 254.8 K\nT_surface = (238.18 / (0.612 * 5.67e-8))^0.25 = 288.4 K\nGreenhouse warming = 288.4 - 254.8 = 33.6 K
Result:T_eff: 254.8 K | T_surface: 288.4 K (15.3 C) | Greenhouse warming: 33.6 K
Example 2: Doubled CO2 Forcing Scenario
Problem:Add 3.7 W/m2 radiative forcing (CO2 doubling) to present Earth energy balance.
Solution:Absorbed + forcing = 238.18 + 3.7 = 241.88 W/m2\nNew T_surface = (241.88 / (0.612 * 5.67e-8))^0.25 = 289.5 K\nWarming = 289.5 - 288.4 = 1.1 K (without feedbacks)
Result:New T_surface: 289.5 K | Direct warming: 1.1 K | Climate sensitivity: 0.30 K/(W/m2)
Frequently Asked Questions
What is geothermal heat flow and how is it measured?
Geothermal heat flow is the rate at which thermal energy escapes from Earth's interior through its surface, expressed in milliwatts per square meter (mW/m2). It is measured by drilling boreholes and recording the temperature gradient with depth alongside the thermal conductivity of the rock. Heat flow equals the product of thermal conductivity and the temperature gradient, which is Fourier's law of heat conduction: q equals negative k times dT/dz. Global average surface heat flow is approximately 87 mW/m2, representing the combined contribution of radiogenic heat production in the crust and primordial heat left from Earth's formation and differentiation.
What is Fourier's law of heat conduction and how does it apply to the mantle?
Fourier's law states that the heat flux through a material is proportional to the negative of the temperature gradient and the thermal conductivity of the material: q equals negative k times dT/dx, where q is heat flux in W/m2, k is thermal conductivity in W/(m K), and dT/dx is the temperature gradient in K/m. In the context of Earth's mantle, this law governs conductive heat transport through lithospheric plates. The mantle itself transfers heat primarily by slow convection rather than conduction, but the rigid lithosphere above it conducts heat conductively to the surface. Typical mantle thermal conductivity ranges from 3 to 4 W/(m K) for peridotite at relevant pressures.
How does continental heat flow differ from oceanic heat flow?
Oceanic crust has significantly higher average heat flow than continental crust, around 101 mW/m2 compared to approximately 70 mW/m2 for continents, though both values have wide variability. Young oceanic crust near mid-ocean ridges can exhibit heat flow exceeding 200 to 300 mW/m2 because hot mantle rock is close to the surface. As oceanic crust ages and moves away from spreading centers it cools and subsides, reducing heat flow to values around 50 mW/m2 for old ocean basins. Continental heat flow is elevated in active tectonic regions and geothermal areas but is lower in stable cratons that have not been volcanically or tectonically active for hundreds of millions of years.
What role does radioactive decay play in Earth's heat flow?
Radioactive decay is the dominant source of heat in Earth's continental crust, contributing roughly 50 percent of Earth's total heat output of about 47 terawatts. The primary heat-producing isotopes are uranium-238, uranium-235, thorium-232, and potassium-40, all of which undergo spontaneous decay that releases energy as heat. Granitic continental crust is enriched in these elements relative to oceanic crust and the mantle. Typical continental crustal heat production is 1 to 3 microwatts per cubic meter. The remaining heat flow comes from the cooling of the primordial Earth, the latent heat of inner core crystallization, and gravitational energy from core formation that occurred early in Earth's history.
References
Reviewed by Daniel Agrici, Founder & Lead Developer · Editorial policy