THROUGHOUT this note, the following notations are used: For a matrix A, A】0 means thatA is positive definite symmetric; R （A）, A′and A<sup>-</sup> stand for the column space, transposeand any g-inverse...THROUGHOUT this note, the following notations are used: For a matrix A, A】0 means thatA is positive definite symmetric; R （A）, A′and A<sup>-</sup> stand for the column space, transposeand any g-inverse of A respectively; P<sub>A</sub> = A （A′A）<sup>-</sup> A′and P<sub>A</sub> = I<sub>k</sub> - P<sub>A</sub>, where I<sub>k</sub> is theidentity matrix of order k that is the number of rows in A. R<sup>m×n</sup> is the totality of m×n realmatrices.展开更多
The main purpose of this study is to survey numerically comparison of two- phase and single phase of heat transfer and flow field of copper-water nanofluid in a wavy channel. The computational fluid dynamics （CFD） p...The main purpose of this study is to survey numerically comparison of two- phase and single phase of heat transfer and flow field of copper-water nanofluid in a wavy channel. The computational fluid dynamics （CFD） prediction is used for heat transfer and flow prediction of the single phase and three different two-phase models （mixture, volume of fluid （VOF）, and Eulerian）. The heat transfer coefficient, temperature, and velocity distributions are investigated. The results show that the differences between the temperature fie].d in the single phase and two-phase models are greater than those in the hydrodynamic tleld. Also, it is found that the heat transfer coefficient predicted by the single phase model is enhanced by increasing the volume fraction of nanoparticles for all Reynolds numbers; while for the two-phase models, when the Reynolds number is low, increasing the volume fraction of nanoparticles will enhance the heat transfer coefficient in the front and the middle of the wavy channel, but gradually decrease along the wavy channel.展开更多
文摘THROUGHOUT this note, the following notations are used: For a matrix A, A】0 means thatA is positive definite symmetric; R （A）, A′and A<sup>-</sup> stand for the column space, transposeand any g-inverse of A respectively; P<sub>A</sub> = A （A′A）<sup>-</sup> A′and P<sub>A</sub> = I<sub>k</sub> - P<sub>A</sub>, where I<sub>k</sub> is theidentity matrix of order k that is the number of rows in A. R<sup>m×n</sup> is the totality of m×n realmatrices.
文摘The main purpose of this study is to survey numerically comparison of two- phase and single phase of heat transfer and flow field of copper-water nanofluid in a wavy channel. The computational fluid dynamics （CFD） prediction is used for heat transfer and flow prediction of the single phase and three different two-phase models （mixture, volume of fluid （VOF）, and Eulerian）. The heat transfer coefficient, temperature, and velocity distributions are investigated. The results show that the differences between the temperature fie].d in the single phase and two-phase models are greater than those in the hydrodynamic tleld. Also, it is found that the heat transfer coefficient predicted by the single phase model is enhanced by increasing the volume fraction of nanoparticles for all Reynolds numbers; while for the two-phase models, when the Reynolds number is low, increasing the volume fraction of nanoparticles will enhance the heat transfer coefficient in the front and the middle of the wavy channel, but gradually decrease along the wavy channel.
