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| SOLUTION FOR THE POISEUILLE FLOW IN A FLUID CHANNEL WITH A POROUS MEDIUM INSERT BY CONSIDERING NON-DARCY EFFECTS |
| DAI Chuanshan1，2，LI Qi1，2，LEI Haiyan1，2 |
| (1. Key Laboratory of Efficient Utilization of Low and Medium Grade Energy，Ministry of Education，Tianjin University，Tianjin 300072，China；2. School of Mechanical Engineering，Tianjin University，Tianjin 300072，China) |
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Abstract The complicated mass and momentum transfer problems in the porous regions，especially at the interface between porous and open fluid regions were analyzed. By taking the Brinkman viscous dissipation term and Forchheimer nonlinear inertia term into account，a new and more general nondimensionalized governing equation was proposed. It was noticed that in the previous literature an analytical solution cannot be obtained freely，and a limitation equation for the given physical parameters had to be proposed，which believed that previous models need to deal with an infinite large number. In this paper，a method that the porous region can be divided into two regions，core region and near boundary region was proposed. Taking the Poiseuille flow model with one open fluid layer in the center and two porous layers aside as an example，the basic flow by solving the difference equation using the Runge-Kutta-Gill method was obtained，which was validated by comparing with those of previous literature. The results show that under the condition of constant Darcy number Da and porosity ?，there is less effect on the basic flow pattern by varying Reynolds number Re alone，while changing the Da or ? has a great influence.
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2015, Vol. 34 
