HA Diffusion Equation with Higher Order Derivatives

3 HA Diffusion Equation with Higher Order Derivatives 

In certain situations it is useful to have an approximation to the problem with convection and adsorption in the micro-domain by including a term c. If we take the unknown of (9.27), and substitute the characteristic function of (9.24), we obtain the following higher (i.e., second) order microscale equation  

Since each term of (9.37) must be null because of the arbitrariness of c , we obtain the following equations for determining N22(x ), A 23(J ) and A124(a )  

The diffusion problem with two scale domains including second order differentials can be solved as follows  

Specify the homogenized diffusion coefficient DfJ by substituting Nj into (9.31). 

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