Study On The Flow And Heat Transfer Of Several Kinds Of Fluid In Porous Medium Based On The Homotopy Analysis Method

Due to the widespread application in modern industry,the problem of flow in porous media has become a hot area in fluid mechanics.Porous medium refers to single phase or poly-phase medium saturated in the pore space constituted by porous solid skeleton.Physical parameters such as porosity and permeability of porous media have great influence on the flow and heat transfer of the fluid.In this paper,the flow and heat transfer of several types of fluid in porous media have been investigated.The nonlinear governing equations have been established and solved by homotopy analysis method.The homotopy analysis method is an effective method for solving nonlinear equations proposed by Professor Liao shijun according to the concept of homotopy in topology.The main idea of the method is to transform a nonlinear equations into a system of linear equations by establishing a deformation equation.The homotopy analysis method has overcome the dependency on small parameters and been applied to many nonlinear problems,especially for solving strong nonlinear equations.In order to further investigate the characteristics of flow and heat transfer for the incompressible viscous fluid flow and nanofluid flow in porous medium,non-similar transformation is introduced to transform thegoverning equation system into nonlinear partial differential equations solved by homotopy analysis method.A new empirical correlation for thermal conductivity of the nanofluid saturated in porous medium is proposed based on the influence of nanoparticle shape,solid matrix and porosity of porous media on thermal conductivity.Graphs are plotted to analyze the effects of corresponding physical parameters on heat transfer.In the process of solving nonlinear equations by the homotopy analysis method,the optional value of auxiliary parameter for HAM is not unique,meanwhile the speed of convergence is affected by the value of auxiliary parameter.In this paper,the optimal homopoty analysis method is applied to research three-dimensional flow of Powell-Eyring fluid through porous medium in rotating system.The optimal auxiliary parameters are selected by the minimum value of the residual square residue error,and the rapid convergent series solution of the nonlinear equations is obtained by this method.Moreover,the effects of characteristic parameters and rotational speed on flow and heat transfer have been studied.