rbeucher
commented
5 years ago The model has no radiogenic heat production, so in steady-state the heat flux should be constant everywhere below the land-air interface.
The model has no radiogenic heat production and the diffusivity is constant, at steady state, the gradient of the geotherm should be constant...
In this model, diffusivity is homogeneous, as is heat capacity, so thermal conductivity should be proportional to density (k=alpha rho Cp).
Yes I agree with that...
Because density of the mantle is greater than density of the crust, conductivity of the mantle should be greater and, given q=-k * grad(T), thermal gradient should be less in the mantle than in the crust. Instead, what I see (figure below) is a constant gradient in the temperature field and relatively greater heat flux in the mantle than in the crust.
Because density is higher, conductivity of the mantle should be higher (assuming constant diffusivity) and as the gradient is constant, the heat flow should be higher in the mantle than in the crust... I think what you see is correct.
plovely
PatriceFRey
julesghub
rcarluccio
In doing so I realized that in addition to boundary conditions at the ends and continuity of temperature across the material boundary, an additional constraint is needed to relate the temperature gradient across the material boundary. UW (and many or most other dynamic solutions of the heat equation) appears to solve the problem such that k(grad(T)) is continuous across the boundary (where k is diffusivity). However, I don't think there is any physical basis for this constraint. Conservation of energy dictates that heat flux should be constant across the boundary; thus the additional constraint across the material transition should require that Kappa(grad(T)) is continuous across the material transition, where Kappa is thermal conductivity.
Hi Romain,
Another issue related to the same model I just sent but with appropriate diffusivity (Model.diffusivity = 7.72e-7 * u.metre**2 / u.second).
The model has no radiogenic heat production, so in steady-state the heat flux should be constant everywhere below the land-air interface.
In this model, diffusivity is homogeneous, as is heat capacity, so thermal conductivity should be proportional to density (k=alpha rho Cp).
Because density of the mantle is greater than density of the crust, conductivity of the mantle should be greater and, given q=-k * grad(T), thermal gradient should be less in the mantle than in the crust. Instead, what I see (figure below) is a constant gradient in the temperature field and relatively greater heat flux in the mantle than in the crust.
Note: I calculate heat flux in ParaView by: 1) calculating the gradient of the temperature field using the "Gradient of Unstructured DataSet" filter 2) calculate heat flux using the calculator: q=grad(T) k = grad(T) alpha rho Cp, where grad(T) and rho come from paraview and alpha and Cp are constants.
Thanks, Peter