Question

The differential energy equation for incompressible two-dimensional flow through a “Darcy-type" porous mediumis approximately \rho c_{p} \frac{\sigma}{\mu} \frac{\partial p}{\partial x} \frac{\partial T}{\partial x}+\rho c_{p} \frac{\sigma}{\mu} \frac{\partial p}{\partial y} \frac{\partial T}{\partial y}+k \frac{\partial^{2} T}{\partial y^{2}}=0 where o is the permeability of the porous medium. symbols have their usual meanings. (a) What are the appropriate dimensions for o? (b) Non dimensionalize this equation, using (L, U. p. T.) as scaling constants, and discuss any dimensionless parameters that arise.

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