Analytically And Numerically Studies On Several Typical Nanofluids Flow And Heat Transfer Problems

As wide applications in science and engineering, boundary-layer flow is an important topic of fluid mechanics. Though it has been developed over a century, many researchers still conduct research on this field for all kinds of new applications. In this dissertation, some new problems of nanofluids boundary layer and nanofluids natural convection flow with potential applications in science and engineering have been studied by means of approximate analytical method and numerical method.For nanofluids boundary layer flow, based on homogeneous model, we study the nanofluids boundary layer flow and heat transfer over a stretching sheeting. A modified differential transformation method (DTM-BF) is used to get the approximate analytical solution for this problem. It found that adding nanoparticles into based fluid can enhance thermal conduction capability, and selecting the appropriate volume fraction and type of nanoparticles can also strengthen mass transfer. Based on two phase model, firstly we consider the effect of velocity slip and temperature jump on flow and heat transfer of nanofluid over a stretching sheet. Then we investigate boundary flow and heat transfer of nanofluids toward stretching sheet assuming thermal conductivity and dynamic viscosity of nanofluids to be linear functions of the volume fraction of nanoparticles. By mean of the Homotopy Analysis Method (HAM), we give the explicit expressions of Nusselt number and Sherwood number of the two problems. Compared with the traditional linear regression fonnula, their advantage is to reduce error by calculating high order approximate solution of HAM.For nanofluids natural convection, we numerically simulate two problems by continuous finite-element method. We first extend nanofluids two-phase model to unsteady natural convection of nanofluid in a concentric annulus considering a sinusoidally heated source. Then, we consider the effect of magnetic field which orientation form an angle with horizontal axis on steady natural convection heat and mass transfer between circular tube and square cavity. We conclude that Nusselt number decreases and Sherwood number increase with synchronous increase in Brownian motion parameter and thermophoresis parameter.Thorough approximately studies on these nonlinear problems, we provide for nanofluids boundary layer problems analytical approximate solutions, which are uniformly valid in the whole region and further verified the accuracy and effectiveness of DTM-BF and HAM. We give numerical solutions for nanofluids natural convection in enclosure and visually simulate the flow and heat and mass transfer by drawing streamlines, isothermals and isoconcentration.