The velocity field and the associated shear stress corresponding to the longitudinal oscillatory flow of a generalized second grade fluid, between two infinite coaxial circular cylinders, are determined by means of th...The velocity field and the associated shear stress corresponding to the longitudinal oscillatory flow of a generalized second grade fluid, between two infinite coaxial circular cylinders, are determined by means of the Laplace and Hankel transforms. Initially, the fluid and cylinders are at rest and at t = 0＋ both cylinders suddenly begin to oscillate along their common axis with simple harmonic motions having angular frequencies Ω1 and Ω2. The solutions that have been obtained are presented under integral and series forms in terms of the generalized G and R functions and satisfy the governing differential equation and all imposed initial and boundary conditions. The respective solutions for the motion between the cylinders, when one of them is at rest, can be obtained from our general solutions. Furthermore, the corresponding solutions for the similar flow of ordinary second grade fluid and Newtonian fluid are also obtained as limiting cases of our general solutions. At the end, the effect of different parameters on the flow of ordinary second grade and generalized second grade fluid are investigated graphically by plotting velocity profiles.展开更多
Chromium nitride （Cr2N） thin films were prepared by a DC magnetron sputtering technique. The deposition temperature was raised from 50 to 300℃, and its influence on the film structure and refractive index was inves...Chromium nitride （Cr2N） thin films were prepared by a DC magnetron sputtering technique. The deposition temperature was raised from 50 to 300℃, and its influence on the film structure and refractive index was investigated. X-ray diffraction analysis shows that the crystalline strucure of the films transforms from the （101） to （002） oriented hexagonal CrzN phase as the increase of substrate tempera- ture above 50℃, and a highly texatred film grows at 100℃. An empirical relation between the crystalline orientation and infrared active modes of the films is obtained, i.e., the Fourier transform infrared （FTIR） spectrum of the film prepared at 50℃ exhibits only A1 （TO） mode. The prominent peak in the FTIR spectra of the film prepared above 50℃is assigned to the E1 （TO） mode and is correlated with the （002） or c-axis oriented hexagonal wurtzite phase of Cr2N. In the surface analysis of atomic force microscopy, a transformation from the featureless surface to columnar-type morphology is observed with the increase of substrate temperature from 50 to 100℃, exhibiting c-axis oriented crystallite growth. A further increase in substrate temperature to 200℃ causes the c-axis crystallites to merge, resulting in the formation of voids. The refractive index （n） of the deposited films is obtained using spectroscopic ellipsometry.展开更多
文摘The velocity field and the associated shear stress corresponding to the longitudinal oscillatory flow of a generalized second grade fluid, between two infinite coaxial circular cylinders, are determined by means of the Laplace and Hankel transforms. Initially, the fluid and cylinders are at rest and at t = 0＋ both cylinders suddenly begin to oscillate along their common axis with simple harmonic motions having angular frequencies Ω1 and Ω2. The solutions that have been obtained are presented under integral and series forms in terms of the generalized G and R functions and satisfy the governing differential equation and all imposed initial and boundary conditions. The respective solutions for the motion between the cylinders, when one of them is at rest, can be obtained from our general solutions. Furthermore, the corresponding solutions for the similar flow of ordinary second grade fluid and Newtonian fluid are also obtained as limiting cases of our general solutions. At the end, the effect of different parameters on the flow of ordinary second grade and generalized second grade fluid are investigated graphically by plotting velocity profiles.
基金financially supported by the National Institute of Laser and Optronics(NILOP)
文摘Chromium nitride （Cr2N） thin films were prepared by a DC magnetron sputtering technique. The deposition temperature was raised from 50 to 300℃, and its influence on the film structure and refractive index was investigated. X-ray diffraction analysis shows that the crystalline strucure of the films transforms from the （101） to （002） oriented hexagonal CrzN phase as the increase of substrate tempera- ture above 50℃, and a highly texatred film grows at 100℃. An empirical relation between the crystalline orientation and infrared active modes of the films is obtained, i.e., the Fourier transform infrared （FTIR） spectrum of the film prepared at 50℃ exhibits only A1 （TO） mode. The prominent peak in the FTIR spectra of the film prepared above 50℃is assigned to the E1 （TO） mode and is correlated with the （002） or c-axis oriented hexagonal wurtzite phase of Cr2N. In the surface analysis of atomic force microscopy, a transformation from the featureless surface to columnar-type morphology is observed with the increase of substrate temperature from 50 to 100℃, exhibiting c-axis oriented crystallite growth. A further increase in substrate temperature to 200℃ causes the c-axis crystallites to merge, resulting in the formation of voids. The refractive index （n） of the deposited films is obtained using spectroscopic ellipsometry.
