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LaTeX Math Inline
bodyt

Time lapse after the temperature step from 

LaTeX Math Inline
bodyT_b(z=0) =0
  up to 
LaTeX Math Inline
bodyT_b(z=0) =T_f

LaTeX Math Inline
bodyz

Spatial coordinate along the transversal direction to constant temperature 

LaTeX Math Inline
bodyT_b(z)= T_f
plane 
LaTeX Math Inline
bodyz=0

LaTeX Math Inline
bodyT_f

Boundary temperature at 

LaTeX Math Inline
bodyz=0

LaTeX Math Inline
bodya

Thermal diffusivity of the surroundings

LaTeX Math Inline
bodyT_G(z)

Geothermal Temperature Profile


Equations

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Driving equationInitial conditions Boundary conditions


LaTeX Math Block
anchor1
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\frac{\partial T_b}{\partial t} = a^2 \Delta T_b = a^2\frac{\partial^2 T_b}{\partial z^2}



LaTeX Math Block
anchor1
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T_b(t=0, z) = T_G(z)



LaTeX Math Block
anchor7685E
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T_b(t, z=0) = T_f = {\rm const}


LaTeX Math Block
anchor7685E
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T_b(t, z \rightarrow \infty) = T_G(z)


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