Motivation
The Temperature Flat Source Solution @model is one of the fundamental solutions of temperature diffusion equations modelling the temperature conduction in linear direction (see Fig. 1).
This temperature profile is very common in subsurface studies, particularly in modelling the temperature above and below the lateral reservoir flow with a temperature T_f and background Geothermal Temperature Profile T_G(z).
Fig. 1. Sample Subsurface Temperature Profile around Lateral Flow |
Outputs
T_b(t, z) | Temperature distribution |
Inputs
t | Time lapse after the temperature step from T_b(z=0) =0 up to T_b(z=0) =T_f |
z | Spatial coordinate along the transversal direction to constant temperature T_b(z)= T_f plane z=0 |
T_f | Boundary temperature at z=0 |
a | Thermal diffusivity of the surroundings |
T_G(z) | Geothermal Temperature Profile |
Equations
Driving equation | Initial conditions | Boundary conditions | ||||||||
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Solution
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See Also
Geology / Geothermal Temperature Field / Geothermal Temperature Profile
Physics / Fluid Dynamics / Linear Fluid Flow
[ Temperature Flat Source Solution @model ] [ Geothermal Temperature Profile @model ]