Geothermics is the study of the Earth's heat within its interior. The term "geothermics" derived from two greek words,
"Geo " means Earth and
"therm" means heat or thermal energy. Hence geothermics simply deals with Earth's heat.
Earth's internal heat play an important role which inturn control internal terrestrial processes such as
i/ Generation of geomagnetic field
ii/ Motion of global lithospheric plates.
Sources of Internal Earth's heat.
The Earth derived its internal heat from the following major sources
1. 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 in granite and pegmatites rocks in form of uraninite and uranothorite minerals respectively.
2. Cooling of the Earth
This includes the heat remained in Earth as the residual after cooling during Earth's formation. This energy is also known as "premodial heat"
Since apart from how Earth heat is generated, the Earth continues to constantly lose heat from its interior through different processes such as,
Earthquake, at which heat is lost in form of seismic energy released during large shock, it is this energy that causes vibration and ground shaking during the shock.
Rotation of the Earth, here the heat is lost 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 rapidly with depth at approximately 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 temperature 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 TRANSFER WITHIN THE EARTH
Heat transfer is the transition of thermal energy from hotter object (area) to cooler object (area) as described by the law of thermodynamics or by Clausius statement.
Mainly there are three (3) major means of heat flow within the Earth,
1. Conduction
2. Convection
3. Radiation
N.B: Conduction and convection requires material medium for heat to flow while radiation requires the space or vacuum for heat to flow.
1. 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 to understand and describe how conduction occurs in solids.
When we consider the diagram of figure (1) below.
If we take, (T2 - T1)/ L to represent 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 towards upward direction.
Measurement of geothermal Flux
Challenges encountered when measure geothermal gradient are described as follows,
(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 do not represent the reality regarding geothermal gradient.
(iii) Topography
Most of uneven surface of the Earth results to variation of temperature measurement. These surfaces such that at valleys favours results high temperature while at mountain favours results low temperature.
2. 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.
It is governed by Newton’s law of cooling,
Q = hAsdT
where,
Q = Heat flow from surface, (W)
h = Heat transfer coefficient (W/m2 K). This is not a thermodynamic property of the material, but may depend on geometry of surface, flow characteristics, thermodynamic properties of the fluid,
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, Air pump
3. 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 actually not touching it (the object).
Also another example is heat from the Sun reaches us on Earth by radiation. Radiation does not need matter medium for transfer.
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 which can be given as,
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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