This article may be too technical for most readers to understand.(April 2013) |
The thermal history of Earth involves the study of the cooling history of Earth's interior. It is a sub-field of geophysics. (Thermal histories are also computed[ by whom? ] for the internal cooling of other planetary and stellar bodies.) The study of the thermal evolution of Earth's interior is uncertain and controversial in all aspects, from the interpretation of petrologic observations used to infer the temperature of the interior, to the fluid dynamics responsible for heat loss, to material properties that determine the efficiency of heat transport.
Observations that can be used to infer the temperature of Earth's interior range from the oldest rocks on Earth to modern seismic images of the inner core size. Ancient volcanic rocks can be associated with a depth and temperature of melting through their geochemical composition. Using this technique and some geological inferences about the conditions under which the rock is preserved, the temperature of the mantle can be inferred. The mantle itself is fully convective, so that the temperature in the mantle is basically constant with depth outside the top and bottom thermal boundary layers. This is not quite true because the temperature in any convective body under pressure must increase along an adiabat, but the adiabatic temperature gradient is usually much smaller than the temperature jumps at the boundaries. Therefore, the mantle is usually associated with a single or potential temperature that refers to the mid-mantle temperature extrapolated along the adiabat to the surface. The potential temperature of the mantle is estimated to be about 1350 C today. There is an analogous potential temperature of the core but since there are no samples from the core its present-day temperature relies on extrapolating the temperature along an adiabat from the inner core boundary, where the iron solidus is somewhat constrained.
This section possibly contains original research .(April 2013) |
The simplest mathematical formulation of the thermal history of Earth's interior involves the time evolution of the mid-mantle and mid-core temperatures. To derive these equations one must first write the energy balance for the mantle and the core separately. They are,
for the mantle, and
for the core. is the surface heat flow [W] at the surface of the Earth (and mantle), is the secular cooling heat from the mantle, and , , and are the mass, specific heat, and temperature of the mantle. is the radiogenic heat production in the mantle and is the heat flow from the core mantle boundary. is the secular cooling heat from the core, and and are the latent and gravitational heat flow from the inner core boundary due to the solidification of iron.
Solving for and gives,
and,
This section possibly contains original research .(September 2013) |
In 1862, Lord Kelvin calculated the age of the Earth at between 20 million and 400 million years by assuming that Earth had formed as a completely molten object, and determined the amount of time it would take for the near-surface to cool to its present temperature. Since uniformitarianism required a much older Earth, there was a contradiction. Eventually, the additional heat sources within the Earth were discovered, allowing for a much older age. This section is about a similar paradox in current geology, called the thermal catastrophe.
The thermal catastrophe of the Earth can be demonstrated by solving the above equations for the evolution of the mantle with . The catastrophe is defined as when the mean mantle temperature exceeds the mantle solidus so that the entire mantle melts. Using the geochemically preferred Urey ratio of and the geodynamically preferred cooling exponent of the mantle temperature reaches the mantle solidus (i.e. a catastrophe) in 1-2 Ga. This result is clearly unacceptable because geologic evidence for a solid mantle exists as far back as 4 Ga (and possibly further). Hence, the thermal catastrophe problem is the foremost paradox in the thermal history of the Earth.
The "New Core Paradox" [1] posits that the new upward revisions to the empirically measured thermal conductivity of iron [2] [3] [4] at the pressure and temperature conditions of Earth's core imply that the dynamo is thermally stratified at present, driven solely by compositional convection associated with the solidification of the inner core. However, wide spread paleomagnetic evidence for a geodynamo [5] older than the likely age of the inner core (~1 Gyr) creates a paradox as to what powered the geodynamo prior to inner core nucleation. Recently it has been proposed that a higher core cooling rate and lower mantle cooling rate can resolve the paradox in part. [6] [7] [8] However, the paradox remains unresolved.
Two additional constraints have been recently proposed. Numerical simulations of the material properties of high pressure-temperature iron [9] claim an upper limit of 105 W/m/K to the thermal conductivity. This downward revision to the conductivity partially alleviates the issues of the New Core Paradox by lowering the adiabatic core heat flow required to keep the core thermally convective. However, this study was later retracted by the authors, [10] who stated that their calculations were in error by a factor of two, due to neglecting spin degeneracy. That would halve the electron-electron resistivity, supporting earlier estimates of high iron conductivity.
Also, recent geochemical experiments [11] have led to the proposal that radiogenic heat in the core is larger than previously thought. This revision, if true, would also alleviate issues with the core heat budget by providing an additional energy source back in time.
Convection is single or multiphase fluid flow that occurs spontaneously due to the combined effects of material property heterogeneity and body forces on a fluid, most commonly density and gravity. When the cause of the convection is unspecified, convection due to the effects of thermal expansion and buoyancy can be assumed. Convection may also take place in soft solids or mixtures where particles can flow.
The Prandtl number (Pr) or Prandtl group is a dimensionless number, named after the German physicist Ludwig Prandtl, defined as the ratio of momentum diffusivity to thermal diffusivity. The Prandtl number is given as:
In thermal fluid dynamics, the Nusselt number is the ratio of convective to conductive heat transfer at a boundary in a fluid. Convection includes both advection and diffusion (conduction). The conductive component is measured under the same conditions as the convective but for a hypothetically motionless fluid. It is a dimensionless number, closely related to the fluid's Rayleigh number.
The thermal conductivity of a material is a measure of its ability to conduct heat. It is commonly denoted by , , or and is measured in W·m−1·K−1.
In fluid mechanics, the Rayleigh number (Ra, after Lord Rayleigh) for a fluid is a dimensionless number associated with buoyancy-driven flow, also known as free (or natural) convection. It characterises the fluid's flow regime: a value in a certain lower range denotes laminar flow; a value in a higher range, turbulent flow. Below a certain critical value, there is no fluid motion and heat transfer is by conduction rather than convection. For most engineering purposes, the Rayleigh number is large, somewhere around 106 to 108.
Conduction is the process by which heat is transferred from the hotter end to the colder end of an object. The ability of the object to conduct heat is known as its thermal conductivity, and is denoted k.
In the study of heat transfer, Newton's law of cooling is a physical law which states that
The rate of heat loss of a body is directly proportional to the difference in the temperatures between the body and its environment.
Seafloor spreading, or seafloor spread, is a process that occurs at mid-ocean ridges, where new oceanic crust is formed through volcanic activity and then gradually moves away from the ridge.
The Biot number (Bi) is a dimensionless quantity used in heat transfer calculations, named for the eighteenth-century French physicist Jean-Baptiste Biot (1774–1862). The Biot number is the ratio of the thermal resistance for conduction inside a body to the resistance for convection at the surface of the body. This ratio indicates whether the temperature inside a body varies significantly in space when the body is heated or cooled over time by a heat flux at its surface.
Thermal history modelling is an exercise undertaken during basin modelling to evaluate the temperature history of stratigraphic layers in a sedimentary basin.
The lumped-element model is a simplified representation of a physical system or circuit that assumes all components are concentrated at a single point and their behavior can be described by idealized mathematical models. The lumped-element model simplifies the system or circuit behavior description into a topology. It is useful in electrical systems, mechanical multibody systems, heat transfer, acoustics, etc. This is in contrast to distributed parameter systems or models in which the behaviour is distributed spatially and cannot be considered as localized into discrete entities.
A heat sink is a passive heat exchanger that transfers the heat generated by an electronic or a mechanical device to a fluid medium, often air or a liquid coolant, where it is dissipated away from the device, thereby allowing regulation of the device's temperature. In computers, heat sinks are used to cool CPUs, GPUs, and some chipsets and RAM modules. Heat sinks are used with high-power semiconductor devices such as power transistors and optoelectronics such as lasers and light-emitting diodes (LEDs), where the heat dissipation ability of the component itself is insufficient to moderate its temperature.
In thermodynamics, the heat transfer coefficient or film coefficient, or film effectiveness, is the proportionality constant between the heat flux and the thermodynamic driving force for the flow of heat. It is used in calculating the heat transfer, typically by convection or phase transition between a fluid and a solid. The heat transfer coefficient has SI units in watts per square meter per kelvin (W/m2/K).
Earth's inner core is the innermost geologic layer of planet Earth. It is primarily a solid ball with a radius of about 1,220 km (760 mi), which is about 20% of Earth radius or 70% of the Moon's radius.
Mantle convection is the very slow creeping motion of Earth's solid silicate mantle as convection currents carry heat from the interior to the planet's surface.
There are a number of possible ways to measure thermal conductivity, each of them suitable for a limited range of materials, depending on the thermal properties and the medium temperature. Three classes of methods exist to measure the thermal conductivity of a sample: steady-state, time-domain, and frequency-domain methods.
In heat transfer, thermal engineering, and thermodynamics, thermal conductance and thermal resistance are fundamental concepts that describe the ability of materials or systems to conduct heat and the opposition they offer to the heat current. The ability to manipulate these properties allows engineers to control temperature gradient, prevent thermal shock, and maximize the efficiency of thermal systems. Furthermore, these principles find applications in a multitude of fields, including materials science, mechanical engineering, electronics, and energy management. Knowledge of these principles is crucial in various scientific, engineering, and everyday applications, from designing efficient temperature control, thermal insulation, and thermal management in industrial processes to optimizing the performance of electronic devices.
Earth's internal heat budget is fundamental to the thermal history of the Earth. The flow of heat from Earth's interior to the surface is estimated at 47±2 terawatts (TW) and comes from two main sources in roughly equal amounts: the radiogenic heat produced by the radioactive decay of isotopes in the mantle and crust, and the primordial heat left over from the formation of Earth.
In geology, numerical modeling is a widely applied technique to tackle complex geological problems by computational simulation of geological scenarios.
The depth of the seafloor on the flanks of a mid-ocean ridge is determined mainly by the age of the oceanic lithosphere; older seafloor is deeper. During seafloor spreading, lithosphere and mantle cooling, contraction, and isostatic adjustment with age cause seafloor deepening. This relationship has come to be better understood since around 1969 with significant updates in 1974 and 1977. Two main theories have been put forward to explain this observation: one where the mantle including the lithosphere is cooling; the cooling mantle model, and a second where a lithosphere plate cools above a mantle at a constant temperature; the cooling plate model. The cooling mantle model explains the age-depth observations for seafloor younger than 80 million years. The cooling plate model explains the age-depth observations best for seafloor older that 20 million years. In addition, the cooling plate model explains the almost constant depth and heat flow observed in very old seafloor and lithosphere. In practice it is convenient to use the solution for the cooling mantle model for an age-depth relationship younger than 20 million years. Older than this the cooling plate model fits data as well. Beyond 80 million years the plate model fits better than the mantle model.