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This temperature profile is very common in subsurface studies, particularly in modelling the temperature above and below the lateral reservoir flow with a temperature
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Outputs
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Inputs
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| Time lapse after the temperature step from up to |
| Spatial coordinate along the transversal direction to constant temperature plane |
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| Thermal diffusivity of the surroundings |
Equations
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| Driving equation | Initial conditions | Boundary conditions |
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| \frac{\partial T}{\partial t} = a^2 \Delta T = a^2\frac{\partial^2 T}{\partial z^2} |
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| T(t=0, z) = 0 |
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| T(t, z=0) = T_f = {\rm const} |
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| T(t, z \rightarrow \infty) = 0 |
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Solution
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| T(t,z) = T_f \cdot \left[ 1- \frac{2}{\sqrt{\pi}} \int_0^{z/\sqrt{4at}} e^{-\xi^2} d\xi \right] |
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Approximations
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See also
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Physics / Fluid Dynamics / Linear Fluid Flow
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