Fourrier

73 Consider a solid through which there is a flow q of heat (or some other quantity such as mass, chemical, etc...)

74 The rate of transfer per unit area is q

75 The direction of flow is in the direction of maximum "potential" (temperature in this case, but could be, piezometric head, or ion concentration) decreases (Fourrier, Darcy, Fick...).

q qx qy qz

d0 dx dy dy dz

D is a three by three (symmetric) constitutive/conductivity matrix The conductivity can be either

Isotropic

Anisotropic

Orthotropic

kxx

k xy

kxz

D ā€”

k yx

k kyy

kyz

kzx

kzy

kzz

kxx

0

0

Dā€”

0

kyy

0

0

0

Note that for flow through porous media, Darcy's equation is only valid for laminar flow.

0 0

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