The heat flow due to the thermal conductivities of both the fluid j_m,w and the matrix j_m,s is described by Fourier's law (1822):

and

with

j_m,w = heat flow in the fluid [W]

j_m,s = heat flow in the matrix [W]

λ_w = thermal conductivity of the fluid [W/(m K)]

λ_s = thermal conductivity of the matrix [W/(m K)]

A = cross-section of flow [m²]

= temperature gradient [K/m]

This part of the energy flow is independent of the movement of the water. Analogous to Darcy's law, the negative sign results from the fact that the energy flow occurs from high to low temperatures and the temperature gradient is opposite.

Hydromechanic dispersion