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Numerical and analytical investigations of transport processes in composite domains (macro and micro) exist in many practical applications. These applications include biological, geophysical and many others. The book presents studies on numerical and analytical solutions for the flows formation inside the horizontal macro and micro parallel-plate channel partially filled with a uniform porous material in the presence of suction/injection. An attempt is also made to present analytical solution for the fluid flow using Brinkman-Darcy-extended-Forchheimer model in the porous region and compared with the traditional numerical method. The Approximate analytical solutions presented for both horizontal and composite channels can be efficiently used to solve nonlinear differential equation models arising from Brinkman Forchheimer extended fluid flows.