Numerical Study Of Flow And Heat And Mass Transfer For Non-newtonian Nanofluids By Finite Element Method

Since the term “nanofluid” was proposed,it has been applied widely to industrial manufacture and science research fields because of its ultrahigh performance in heat transferring.And nanofluids do solve the problem which traditional heat-transfer medium cannot meet the need of modern industrial equipment.Although it has wide potential prospects of application,the theoretical system of heat transfer enhancement of nanofluids has not been perfected.There still have been a large number of scholars who make an effort to study on the related problems of nanofluids.From the perspective of modeling and simulating calculation,many classical research problems of heat transfer could be simplified into homologous non-linearly partial differential equations(PDE).Finite element method(FEM)is one of the numerical methods which could obtain PDE's numerical solution.By studying the newest achievements of modeling and simulation of nanofluids,from the perspective of system science,knowledge of multi-discipline such as new energy,hydromechanics and theory of heat transfer,numerical analysis,magnetohydrodynamics are involved,several classical models of boundary layer flow and convective heat transfer of nanofluids has been investigated,and some realistic problems such as non-Newtonian fluids,nonlinearity of stretching sheet and thermal radiation are considered,and relevant mathematical models have been built.Numerical computation method based on similarity transformation and Galerkin finite element method is proposed for solving non-linearly partial differential equations.Numerical simulation of flow and heat transfer models of non-Newtonian nanofluids has been developed,and some related parameters' influence on flow and heat transferring have been discussed.Analysis of non-linear system models have value in industrial application.First of all,heat and mass transfer of non-Newtonian nanofluids over a non-linearly stretching sheet is studied,and a mathematical model which takes thermal conductivity and radiation into account is built.The code of the algorithm which is based on Galerkin finite element method has been executed in Matlab running on a PC and the numerical solution has been obtained.The comparison between the solution and the results in the reference verifies the program's feasibility and accuracy.Meanwhile,the coefficient of viscosity,nonlinearity of the velocity and temperature of stretching sheet has been considered in the flow.In addition,the effects of Brownian motion and thermophoresis in the flow have been investigated,which was first proposed in Buongiorno's theory.Next,the magnetohydrodynamic(MHD)boundary layer flow of non-Newtonian nanofluids over a non-linearly stretching sheet which applies a transverse magnetic field has been modeled.Except for the parameters above,the magnetic field intensity and Navier's slip has been considered.On this basis,MHD stagnation-point flow of non-Newtonian nanofluids has been investigated,and the effect of mix convection of the flow has been studied.The skin friction coefficient,the local Nusselt number and the Sherwood number,which are above-mentioned in the models and used to characterize the flow,are exhibited in the dissertation.