Why is the study of Earth's internal heat so important ?
Earth's internal heat play vital role in control internal terrestrial processes such as
i/ Generation of geomagnetic field
ii/ Motion of global lithospheric plates.
Sources of Internal Earth's heat.
Earth derived its internal heat from the following major sources
i/ Radioactive decay: This is regarded as the main source of Earth internal heat as a results of disentigration of long lived radioactive isotopes. Heat from this source is regarded to power most of geodynamic processes. Since radioisotopes such as Uranium (U) , Thorium (Th) presents as Uraninite and Uranothorite minerals in granite and pegmatite respectively.
ii/ Cooling of the Earth: Heat remained in Earth as the residual after cooling during Earth formation.
Apart from how Earth heat generated, the Earth continues to constantly lose heat from its Interior via different processes but the follows are regarded as major,
i/ Earthquake: heat is lost as seismic energy released during Large shock, it is this energy that causes vibration and ground shaking during the shock.
ii/ Rotation of the Earth: As a result of tidal friction that opposes the Earth rotation.
Temperature inside the Earth
Temperature can be measured in the immediate vicinity of the Earth's surface, in boreholes and in deep mines. At near surface the temperature increase rapidily with depth at about roughly 30°c/km.
However the deep temperatures and pressures can be calculated from experiments in lab seismology, adiabatic and melting point temperature with reasonable assumptions.
The relationship between actual temperatures to the melting point determines how different parts of the Earth's interior behave rheologically.
Such that the temperature of the inner solid core must be lower than melting point. The same reason applies to the nature of solid mantle and the crust, that their tempetaure must be below that of melting point.
When regarded to molten outer core its temperature is above that of melting point.
However the temperature of the asthenosphere is closely to melting point, such as Solidus (softening point) that is why it behaves with low rigidity.
HEAT TRANSPORT (TRANSFER) WITHIN THE EARTH
Heat transfer is the transition of thermal energy from hotter object or area to cooler object or area as described by the Law of thermadynamics or by Clausius statement.
Mainly there are 3 major means of heat flow within the Earth,
i/ Conduction
ii/ Convection
iii/ Radiation
N.B , With conduction and convection requires material medium for heat to flow while radiation requires the space or vaccuum for heat to flow.
i/ Conduction
It involves heat transfer from one point to another by vibration of medium but without actual movement of their atoms. It transfer through physical contact of materials with different temperatures. For instance: when you touch a hot pan.
This occurs mostly in solid example in crust and Lithosphere. It also requires Band theory of solids.
Consider the diagram below
If we take , (T2 - T1)/ L for Temperature gradient (K/m) and Q/At for Heat flux (W/m2)
Since, Heat flux is directly proportional to Temperature gradient
Then, Q/At = K [T2 - T1]/L
where K is Thermal Conductivity (W/mK), A is Cross sectional area (m2)
Hence, Q/t = KA [T2 - T1]/L
If we consider the equation above as heat flow vertically out from the Earth.
By differentiate with respect to (w.r.t) time, Fourier equation.
G = - dQ/Adt = - K(dT/dz)
Then dT/dz is the geothermal gradient (K/m)
G is the geothermal flux (W/m2)..
Geothermal gradient: defines Earth's temperature variation with depth of the Earth.
Geothermal Flux : Is defined as the flow of heat per unit area per second.
N.B : Negative sign accounts for the direction the heat flow. Such that heat flow is upward direction
Measurement of geothermal Flux
Challenging problems encountered when measure geothermal gradient
i/ Thermal equilibrium: The fact that temperature became equal, it makes difficult to measure what is required to be consistent, This interferes with the Geothermal gradient measurement at some areas.
ii/ Solar radiation: The solar radiation, tend to add heat energy, hence it interferes with real measurement of temperature variation with depth.So the measured results does not represent the reality of geothermal gradient.
iii/ Topography : uneven surface of the Earth results to variation of temperature measurement. such that at Valleys favours results high temperature while at mountain favours results low temperature.
ii/ Convection
Is the thermal conduction by free movement of fluid. Example in mantle viscous and outer core (fluid). It transfer through physical ‘flow’ of matter. For instance if you leave the windows in your house open, warmth will leave because either warm air is flowing out the window, or in the other direction, colder air is flowing into your house. This is an example of convection by gas molecules; it can also happen with liquids, and theoretically with solids.
Newton’s Law of Cooling,
Q = hAsdT
where:
Q = Heat flow from surface, (W)
h = Heat transfer coefficient (which is not a thermodynamic property of the material, but may depend on geometry of surface, flow characteristics, thermodynamic properties of the fluid, etc. (W/m2 K)
As = Surface area from which convection is occurring (m2).
dT = Temperature Difference between surface and coolant (K).
It can either occurs under two (2) conditions
a/ Natural (Free) Convection : This is induced by buoyancy forces under natural conditions.
b/ Forced Convection : This is induced by external means such that fan, wind, pump
iii/ Radiation
Is the when heat flow through electromagnetic radiation or ‘light’, particularly infrared radiation. Example How you feel the heat of a lamp or a fire when you are not touching it.
Also heat from the Sun reaches us on Earth by radiation. Radiation does not need matter.
The rate at which radiation can be emitted from the surface of a body is described by Steffan - Boltzmann Law of radiation as
Emissive power of a surface is given as E= σeTs4 (W/ m2)
Where:
e = emissivity, which is a surface property (e = 1 for black body)
σ = Steffan Boltzmann Constant = 5.67 x 108 W/m2 K4 .
Ts = Absolute temperature of the surface (K).
When a body is surrounded by environment of different temperature (low), Heat radiated is accounted as the Net radiation given by
Q = ε∙σ∙A∙(Ts4– Tsur4)
Where:
Q = Net rate of heat emitted by radiation
ε = Surface Emissivity
A = Surface Area
Ts = Absolute temperature of surface (K).
Tsur = Absolute temperature of surroundings (K).
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