Characterization of Non-Newtonian Flow with Prescribed Volume Flow Rate under the Effect of either Wall-Slip or Magnetic Field

• Main Authors: Wei-FanChen, 陳威帆
• Other Authors: Cha`o-Kuang Chen
• Format: Others
• Language: zh-TW
• Published: 2012
• Online Access: http://ndltd.ncl.edu.tw/handle/03363490987192000498

博士 === 國立成功大學 === 機械工程學系碩博士班 === 100 === The rarefaction effect of wall-slip conditions associated with unsteady unidirectional flows of second-grade fluid and Voigt fluids passing through a microtube or parallel microgap plates are studied in this study. The velocity profile and pressure gradient of an unsteady unidirectional flows of second-grade fluids and MHD Voigt fluids moving between two parallel surfaces under magnetic field effect are solved subsequently by the Laplace transform method. The relationship between the change of volume flow rate and the pressure variations is analyzed for six different cases including：(1) trapezoidal piston motion, (2) constant acceleration, (3) impulsively started flow, (4) impulsively blocked fully-developed flow, (5) oscillatory flow, and (6) linear acceleration piston motion. The analytical solution of the velocity and pressure gradient for the momentum equations of unsteady flow in microtube are solved by using the Laplace transform technique. In the analysis process, we focus on the trapezoidal piston motion. The Knudsen number( Kn) is used to represent the level of rarefaction. The results are presented graphically and compared to those of the continuum under no-slip condition. From the results, we found that, the effects of wall-slip becomes significant with the increase of rarefaction. The boundary velocity also increases as the velocity of the tube decreases with the same condition. The influence of flow rarefaction on the pressure gradient is varied quite a lot for different cases.