Asymptotic Solution For Laminar Flow In A Porous Channel With Expanding Or Contracting Walls

The flow of fluid in expansion-shrinkage pipeline has an important application value both in theory and in practice.In this paper,we first study the asymptotic solution of the nonlinear boundary value problem(BVP)in a rectangular pipe with expansion and shrinkage by means of singular perturbation method.Considering the influence of exponential small term,this paper mainly uses a method which contains exponential small term in perturbation series.We modify the internal and external solutions and obtain two analytical solutions,which makes the numerical solution and the asymptotic solution agree better.When the expansion ratio is zero,Terrill discusses a special case.In addition,on the basis of Newtonian fluid,the fluid is further studied in a circular pipe with expansion,shrinkage and permeability.In this paper,the asymptotic solution of multiple solutions is given.The numerical solution is compared with the asymptotic solution and the results show that the numerical solution is in good agreement with the asymptotic solution,which shows that the asymptotic solution constructed in this paper is reliable and effective.In this way,we can not only use this asymptotic solution to expand the study of dilatation and contraction in circular channels based on blood flow,but also enrich the understanding of multiple solutions,which is helpful to understand the flow law of blood in blood vessels.It has certain reference value for the treatment of cerebro-vascular diseases.