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In many subsurface applications which require the knowledge of subsurface temperature distributions the land area of the study is small enough to consider the subsurface heat flux
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| body | --uriencoded--%7B \bf j%7D(x,y,z) = \%7B j_x, \, j_y, \, j_z \%7D |
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to be independent on areal location: and Thermal Conductivity | LaTeX Math Inline |
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| body | --uriencoded--\lambda_e(%7B\bf |
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j%7D to be homogeneous across location area: | LaTeX Math Block |
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{\bf j}({\bf r}) ={\bf j}(x,y,z)= |
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\lambda_e({\bf r}) =\lambda_e(z) |
where is true vertical depth.
Since the heat flux is conservative (see | LaTeX Math Block Reference |
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| anchor | rot_j |
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| page | Geothermal Temperature Field @model |
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) then it immediately implies that:
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{\bf j}=\{ j_x = {\rm const}, \, j_y = {\rm const} , \, j_z(z) \} |
Further admitting that a surface temperature over the study area is constant:
one can see that lateral components of the heat flux are vanishing: ...
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| body | \lambda_r(x,y,z) = \lambda_r(z) |
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{ j_x = 0, \, j_y = 0 , \, j_z(z) \ |
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Normally there are no heat sources within a subsurface volume under study other than upward Earth's Heat Flux which means that true vertical component
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| body | j_z(z) = j_z = \rm const |
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is constant along
true vertical direction. It varies across the
Earth but local value is usually well known....
