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Applied Geophysics : Geothermcis
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A 1-D Modelling Applet
Applet
( in separate window )
The applet simulates the conductive cooling / heating of simple
1-d model structures with simplified material properties and
for simplified boundary conditions :
- SURFACE
- temperature step of magnitude D_TEMP at time T = 0 at the
surface X = 0 of a halfspace X >= 0,
- DIKE
- sudden intrusion of magma into a dike |X| <= D
( at time T = 0 : temperature difference D_TEMP to
surrounding rock |X| > D of identical thermal properties ),
- CONTACT
- contact of two halfspaces of different thermal properties
( halfspace X <&0 : initial temperature difference D_TEMP
to halfspace X > 0 at T = 0 ),
- "PIZZA"
- temperature step of magnitude D_TEMP at time T = 0 at both
surfaces |X| = D of a plate |X| < D,
- WAVE
- harmonic temperature variaton of amplitude D_TEMP at the surface
Z = 0 of a halfspace Z >= 0.
Table of Content
- HOWTO
- Example
- Comments
- Model SURFACE
- Model DIKE
- Model CONTACT
- Model "PIZZA""
- Model WAVE
- Download
HOWTO ( Menue and graphical displays )
- TEMP ( X, T_REF )
- spatial temperature distribution for time T = T_REF
- TEMP ( T, X_REF )
- temperature history at reference coordinate X = X_REF.
- HEAT FLOW
- displays a curve ( green ) representing the heat flow.
- If TEMP ( X, T_REF ) is displayed :
- RUN / HALT or STEP advances T = T_REF
along a logarithmic scale ( linear for WAVE ).
- If halted ( by HALT, STEP or RESET ) :
- selection of model type and materials is eneabled,
- display range, T_REF, X_REF and model
dimensions ( if applicable ) can be adjusted,
- HELP displays possible mouse interactions,
- INFO displays the actual cursor postion,
- RESCALE rescales the vertical axes.
- RESET
- restores initial condition T = T_REF = 0
( and stops the animation ).
To Table of content
Example DIKE
Dialogue :
TEMP ( X, T_REF ) :
TEMP ( T, X_REF ) :
To Table of content
Comments
- Literature :
- BUNTEBARTH, G. (1984) : Geothermics - an introduction, 144 pp.,
Springer New York Heidelberg Berlin,
- BUNTEBARTH, G. (1994) : Geothermia - introduction a los aspectos aplicados
y teorecos de la conduccion del calor en la terra,
Mexico (Conacyt), 184 pp.
( Spanish translation of : BUNTEBARTH, Geothermie, 1980 ).
For a spacially constant thermal conductivity the temperature
distribution T can be derived from the differential equation
In regions free of heat sources ( A = 0 ) and for
1-dimensional problems this equation reduces to
with idependent variables
| t = time and
x = distance
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and depeding on the material parameters
| thermal conductivity :
| K [ W / m / K ]
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| density :
| ρ [ kg / m³ ]
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| specific heat :
| c [ W s / kg / K ]
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| and, derived from the above parameters,
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| temperature conductivity :
| κ = K / ( ρ c ) [ m² / s ]
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- With simplifying asumptions, only approximatly fullfilled in real
cases, i.e.
- isotropic material parameters, independent of temperature,
- "ideal" boundary conditions ( ideal contact at material
boundaries ),
- identical material parameters for magma and surrounding rock ( model
DIKE ),
- constant temperature at |x| >= D ( model
"PIZZA" ),
for the 1-d model structers simulated in the applet analytic solutions
can be derived, for which the heat flow density
can be calculated.
To Table of content
SURFACE
Boundary conditions ( t = 0 ) :
Temperature distribution ( t > 0, x >= 0 ) :
Heat flow density ( t > 0, x >= 0 ) :
To Table of content
DIKE
Boundary conditions ( t = 0 ) :
Temperature distribution ( t > 0 ) :
Heat flow density ( t > 0 ) :
To Table of content
CONTACT
Material parameters :
Boundary conditions ( t = 0 ) :
Temperature distribution ( t > 0 ) :
Heat flow density ( t > 0 ) :
To Table of content
"PIZZA"
Boundary conditions ( t = 0 ) :
Temperature distribution ( t > 0, |x| <= D ) :
Heat flow density ( t > 0, |x| <= D ) :
To Table of content
WAVE
Boundary condition :
Analytic solution for times >> T_PER
Temperature distribution ( t >= 0 ) :
Heat flow density ( t >= 0 ) :
To Table of content
Download
Class and html files for a local installation of the applet are available as
a
zip file and as
a
tar.gz file.
More applets :
keller-clz.de
To Table of content
Rev. 30-may-2006
Comments to
Fritz Keller ( Home )
oder
Guenter Buntebarth ( Home )
( ned gschempfd isch globd gnueg )
To Top of Page
Table of Content
Example DIKE
Comments
To Applets Index
Geophysics Dept