english deutsch Applied Geophysics : Geothermcis


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 :


Table of Content
HOWTO
Example
Comments
Model SURFACE
Model DIKE
Model CONTACT
Model "PIZZA""
Model WAVE
Download


HOWTO ( Menue and graphical displays )

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
and depeding on the material parameters
thermal conductivity : K  [ W / m / K ]
density : ρ  [ kg / m³ ]
specific heat : c  [ W s / kg / K ]
and, derived from the above parameters,
temperature conductivity : κ = K / ( ρ c )  [ m² / s ]

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

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Rev. 30-may-2006

Comments to
Fritz Keller   ( Home )    oder    Guenter Buntebarth   ( Home )
( ned gschempfd isch globd gnueg )

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