Research On Flow And Heat Transfer In Porous Media Of Power Law Fluids

The method of volume averaging various parameters of flow and heat transfer in porous media and averaging theorem was introduced. The volume averaged forms of the continuity equation and momentum equation were obtained for the flow in porous media of power law fluids. The total drag force per unit volume was considered as the bulk damping resistance due to the porous structure and the resistance due to the inertia forces and boundary layer viscous forces, then the Brinkman-Forchheimer extended Darcy model and its modified form for power law fluids was obtained from the averaged momentum equation. The structural flow in a pipe containing porous medium saturated with a power law fluid was introduced in the present study. By means of the integral method, the boundary layer solutions were obtained for the flow core velocity and its corresponding radius. These theoretical solutions were used to analyze the effects of the Darcy number, inertia parameter, porosity and power law index on the axial velocity profile and the friction factor in the porous medium pipe. The characteristic and difference of flow in porous media between the pseudoplastic fluids and the dilatant fluids was described in detail. A new theoretical analysis of fully developed non-Darcy forced convection in a two dimensional channel containing a fibrous medium saturated with a power law fluid was conducted. Closed-form boundary layer solutions using the integral method were obtained for temperature fields and fully developed Nusselt number. These theoretical solutions can be used to predict primary characteristics of physical phenomena associated with forced convection of power law fluids in porous media, and are convenient to serve as a benchmark for more complicated numerical solutions. The acquired flow and heat transfer results of power law fluids in porous medium could give guides to oil & gas production and groundwater resource exploitation.