Nanofluids have enjoyed a widespread use in many technological applications due to their peculiar properties.Numerical simulations are presented about the unsteady behavior of mixed convection of Fe_(3)O_(4)-water,Fe_...Nanofluids have enjoyed a widespread use in many technological applications due to their peculiar properties.Numerical simulations are presented about the unsteady behavior of mixed convection of Fe_(3)O_(4)-water,Fe_(3)O_(4)-kerosene,Fe_(3)O_(4)-ethylene glycol,and Fe_(3)O_(4)-engine oil nanofluids inside a lid-driven triangular cavity.In particular,a two-component non-homogeneous nanofluid model is used.The bottom wall of the enclosure is insulated,whereas the inclined wall is kept a constant(cold)temperature and various temperature laws are assumed for the vertical wall,namely:θ=1(Case 1),θ=Yð1YÞ(Case 2),andθ=sinð2-YÞ(Case 3).A tilted magnetic field of uniform strength is also present in the fluid domain.From a numerical point of view,the problem is addressed using the Galerkin weighted residual finite element method.The role played by different parameters is assessed,discussed critically and interpreted from a physical standpoint.We find that a higher aspect ratio can produce an increase in the average Nusselt number.Moreover,the Fe_(3)O_(4)-EO and Fe_(3)O_(4)-H2O nanofluids provide the highest and smallest rate of heat transfer,respectively,for all the considered(three variants of)thermal boundary conditions.展开更多
A numerical test case demonstrates that the Lobatto and the Gauss points are not natural superconvergent points of the cubic and the quartic finite elements under equilateral triangular mesh for the Poisson equation.
基金supported in part by the National Basic Research Program (2007CB814906)the National Natural Science Foundation of China (10471103 and 10771158)+2 种基金Social Science Foundation of the Ministry of Education of China (Numerical methods for convertible bonds, 06JA630047)Tianjin Natural Science Foundation (07JCYBJC14300)the National Science Foundation under Grant No. EAR-0934747
文摘This article summarizes our recent work on uniform error estimates for various finite elementmethods for time-dependent advection-diffusion equations.
文摘Nanofluids have enjoyed a widespread use in many technological applications due to their peculiar properties.Numerical simulations are presented about the unsteady behavior of mixed convection of Fe_(3)O_(4)-water,Fe_(3)O_(4)-kerosene,Fe_(3)O_(4)-ethylene glycol,and Fe_(3)O_(4)-engine oil nanofluids inside a lid-driven triangular cavity.In particular,a two-component non-homogeneous nanofluid model is used.The bottom wall of the enclosure is insulated,whereas the inclined wall is kept a constant(cold)temperature and various temperature laws are assumed for the vertical wall,namely:θ=1(Case 1),θ=Yð1YÞ(Case 2),andθ=sinð2-YÞ(Case 3).A tilted magnetic field of uniform strength is also present in the fluid domain.From a numerical point of view,the problem is addressed using the Galerkin weighted residual finite element method.The role played by different parameters is assessed,discussed critically and interpreted from a physical standpoint.We find that a higher aspect ratio can produce an increase in the average Nusselt number.Moreover,the Fe_(3)O_(4)-EO and Fe_(3)O_(4)-H2O nanofluids provide the highest and smallest rate of heat transfer,respectively,for all the considered(three variants of)thermal boundary conditions.
基金This research was partially supported by the U.S. National Science Foundation grant DMS-0311807.
文摘A numerical test case demonstrates that the Lobatto and the Gauss points are not natural superconvergent points of the cubic and the quartic finite elements under equilateral triangular mesh for the Poisson equation.
