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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
| LaTeX Math Inline |
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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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and Thermal Conductivity | LaTeX Math Inline |
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| body | --uriencoded--\lambda_e(%7B\bf r%7D) |
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to be homogeneous across location area:
| LaTeX Math Block |
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| {\bf j}({\bf r}) ={\bf j}(x,y,z)={ \bf j}(z) |
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| LaTeX Math Block |
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| \lambda_e({\bf r}) =\lambda_e(z) |
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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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