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The low thermal diffusivity of Earth’s rocks and its large size signify that even today, thermal transport in the lower mantle and core are independent of that in the outer layers. This situation permits construction of thermal profiles of the deep Earth from internal constraints: namely, the two-phase metallic core follows the solidus of iron alloy, and the top of the lower mantle lies below the dry peridotite solidus. Thermal conductivity of the core is irrelevant. Without samples, mantle thermal conductivity is estimated considering data and models for dense solids, leading to “hot silicate” and “cold oxide” geotherms. Temperatures are reasonably constrained, except for the height and position of the local maximum in the lower mantle. Meteoritic values for radionuclide contents of the lower mantle are consistent with present-day temperatures and progressive melting of the core.

This chapter summarizes diverse observations pertaining to heat flow inside the Earth. Information on temperatures, flux, various material properties, heat sources, internal layering, and lateral differences are summarized because they pertain to the boundary and initial conditions used to construct thermal models of planets. We show how the presence and location of molten layers constrain both temperatures and flux, and discuss the implications for Earth’s thermal structure and evolution. Problems in assuming adiabatic gradients and internal homogeneity are discussed. Energy sources in addition to radionuclide decay are covered: we show that an important gravitational source, dissipation of spin via friction during differential rotation, has been overlooked. Spin exerts crucial control on plate tectonics, as proved by abundant evidence reviewed here.

Chondritic meteorites are detrital aggregates that can include both high- and low-temperature materials, one of many characteristics they share with clastic sedimentary rocks. Their distinctive chondrules are rounded, well-sorted, sand-sized grains whose quantitative size distribution indicates aeolian processing. High-speed winds are consistent with the rapid spin rates and huge Coriolis forces of accreting planets. Most grains originally formed in the nebula, possibly by cold welding. Upon deposition on the surface of an accreting planet, chondrules plus dusty matrix were variously subjected to compaction, fluid infiltration, recrystallization, overgrowth development, cementation, and other processes that produced the textural and petrographic variety of chondrites. Impacts ejected some consolidated material into space and provided shock structures and some melting. A sedimentary origin of chondrites is consistent with their petrographic character, their large relative abundance, and the assembly of the rocky planets from the diverse types of solid phases known to exist in nebulae.

Formation of the Solar System is discussed to constrain the initial conditions of thermal models. Large amounts of primordial heat are unexpected because accretion predominantly converts gravitational potential energy into orbital and axial spin energies. This deduction is supported by measured characteristics of the planets being close to those expected from the Virial Theorem. Any heat produced was lost to the surroundings during accretion to meet second law requirements. Late stage impacts added heat to the outer layers of planets and so did not raise interior temperatures. Subsequent dissipation of spin gradually released heat. We argue that the iron cores of planets accreted first due to magnetic attraction and friction welding, which addresses a key problem in accretionary models. These early cores grew subsequently due to gravitational sorting of subsequently accreted, heterogeneous material. Sorting sent radionuclides upward, cooling the Earth, as did outgassing, consistent with energy minimization and entropy maximization.

Thermal histories of the rocky bodies are controlled by their initial inventories of energy, and by the subsequent production and loss of heat. This chapter places constraints on these inventories and processes of large rocky bodies of the inner Solar System, which began with cold accretion, as demonstrated by the icy-rocky bodies of the outer Solar System. Inventories per unit mass of heat generated over geologic time by radionuclides vary tenfold for these bodies, whereas the inventory generated by spin dissipation varies from near zero to significant. Both correlate with body mass, and the power generated has decreased exponentially with time. Distance from the Sun controls heat supplied to the surface by impacts and radiation, and thus volatile speciation, which affects thermo-chemical evolution. Planetary interiors are cooler than commonly imagined, and some may be warming even as their outer zones are cooling. The tectonic and magmatic activity of the rocky bodies is weak and shallow, and is declining with time.

This chapter evaluates mechanisms for heat transfer in large bodies, which include several processes that occur on scales and/or conditions that cannot be reproduced in the laboratory. Planetary interiors contrast with laboratory conditions by being layered, self-compressed spheroids, and moreover are open systems with internally graded gravitational acceleration, high temperatures, and high pressures. The large time- and length-scales of planets permit diffusion of visible radiation, even within their metallic cores. Advection of fluids coexisting with solids is very important in planets, due to fluid buoyancy, mobility, low viscosity, and their ability to carry latent heat and heat-producing elements: such behavior is covered in detail in this chapter. Theoretical problems in mantle convection models are reviewed, which include not conserving mass, and incorrectly representing the response of condensed matter to differential stress as the diffusion of momentum, rather than as elastic and plastic deformation.

Plate models, which purportedly describe cooling of oceanic lithosphere, violate conservation of mass and do not solve Fourier’s 2-dimensional equation. Steady-state conditions are a valid description of Earth’s lithosphere over the last 0.3 Ga. We use surface flux measurements and thermal conductivity for a layered lithosphere to calculate geotherms. Thermal boundary thicknesses of ~69 km agree with various seismic determinations. From petrologic evidence, the low velocity zone is buffered by the peridotite solidus where water content decreases downwards to nothing by 320 km. We show that most subducting slabs thermally equilibrate above 320 km, which involves thinning, but the few which are thick, steep, and fast reach 660 km. Inferred times for upper mantle recycling are consistent with ophiolite ages and modest chemical inhomogeneity. Our findings show that layers above and below 660 km are independent systems, thermally, mechanically, and probably chemically.

Recent work discloses shortcomings in models for heat transport properties. Some errors involve simple numerical factors, but others are substantial, such as not accounting for the finite lifetimes of interactions, nor weighting thermal conductivity in summations, nor realizing that thermal diffusivity depends on thickness. This chapter discusses the consequences in view of the ambiguities contributed by multiplied parameters in models, and provides an improved model for heat transport in solids. We show that radiative diffusion describes all heat transfer, when the association of various processes in matter with limited frequency ranges of light is addressed. Dimensionless thermal conductivity of solids from 0 to ~300K, including the cryogenic peak, is fit by one parameter; but including high temperature data requires more. Theoretical pressure derivatives agree well with reliable data. To better understand heat transport requires measuring transport properties as a function of length and spectra at low frequencies and temperatures.

This chapter reviews measurements and theory of heat transport properties (thermal conductivity, k , and thermal diffusivity, D ) of electric insulators that are partially transparent to light (i.e., most minerals in Earth's mantle). We focus on the effects of temperature ( T ) because the specific dependence of k or D on T largely determines conductive and convective model outcomes.

This chapter reviews measurements and theory of heat transport properties (thermal conductivity, k, and thermal diffusivity, D) of electrical insulators, for example, mantle minerals. Recent developments regarding the highly accurate, contact-free laser-flash method for measuring D permit isolation of the lattice contribution (Dlat) for partially transparent silicate and oxide minerals from spurious (direct or boundary-to-boundary) radiative transfer effects. Laser-flash measurements, which provide absolute values, give Dlat near room temperature for hard minerals that is ∼20% higher than methods involving multiple contacts, and ∼10% higher than single-contact methods. Contact methods underestimate Dlat near 298 K due to loss of heat at interfaces. Use of long cylinder geometries mixes the directional dependences of Dlat for anisotropic samples, due to differences in coupling between the longitudinal and transverse components of the lattice vibrations with the transverse electromagnetic field of the propagating phonons. As temperature (T) increases, data obtained using contact methods are increasingly contaminated with spurious radiative transfer, sometimes even at 298 K. Pressure determinations share these problems, but numerous studies of olivine and NaCl set constraints. Picosecond transient grating spectroscopy also underestimates Dlat, possibly due to electronic–vibronic coupling. Reliable laser-flash data exist for few minerals (olivine, garnet, and quartz). We provide new results for MgO and MgAl2O4. Trustworthy, verified data agree with the damped harmonic oscillator model. This model and laser-flash data of structural analogs set constraints on D for high-pressure phases. Diffusive radiative transport (krad,dif), as occurs in the mantle, is not constrained by laboratory experiments, and is therefore calculated. The latest model accounts for grain-size and emissivity. Spectral data needed for model input are inadequate, so results for olivine are generalized to other mantle phases at the expense of accuracy. For all phases, krad,dif depends nonlinearly on T, grain-size, and Fe content. In summary, not only has klat been grossly underestimated at room temperature, but also the high-temperature responses of both the lattice and radiative components for silicates and oxides have been misrepresented to varying degrees in mineral physics experiments and calculations. Heat transport in the core is uncertain because available measurements on Fe and Ni metals at low pressure do not agree with the Weidemann–Franz model used to extrapolate k to core conditions. Improved measurements of diverse types of Earth materials are needed, which will improve our understanding of microscopic processes, and will impact lithospheric studies, estimation of the global power, and the outcome of geodynamic models.