scholarly journals Unsteady Unidirectional Flow of Second-Grade Fluid through a Microtube with Wall Slip and Different Given Volume Flow Rate

2010 ◽  
Vol 2010 ◽  
pp. 1-17 ◽  
Author(s):  
Cha'o-Kuang Chen ◽  
Hsin-Yi Lai ◽  
Wei-Fan Chen
Keyword(s):  
Flow Rate ◽  
Volume Flow Rate ◽  
Wall Slip ◽  
Volume Flow ◽  
Second Grade ◽  
Fully Developed Flow ◽  
Unidirectional Flow ◽  
Laplace Transform Technique ◽  
Grade Fluid ◽  
Flow Through

The second-grade flows through a microtube with wall slip are solved by Laplace transform technique. The effects of rarefaction and elastic coefficient are considered with an unsteady flow through a microtube for a given but arbitrary inlet volume flow rate with time. Five cases of inlet volume flow rate are as follows: (1) trapezoidal piston motion, (2) constant acceleration, (3) impulsively started flow, (4) impulsively blocked fully developed flow, and (5) oscillatory flow. The results obtained are compared to those solutions under no-slip and slip condition.

Analysis of Unsteady Flow Through a Microtube With Wall Slip and Given Inlet Volume Flow Rate Variations

2008 ◽  
Vol 75 (1) ◽  
Author(s):  
Chun-I Chen ◽  
Cha’o-Kuang Chen ◽  
Heng-Ju Lin
Keyword(s):  
Unsteady Flow ◽  
Flow Rate ◽  
Volume Flow Rate ◽  
Wall Slip ◽  
Volume Flow ◽  
Fully Developed Flow ◽  
Potential Core ◽  
Analysis Process ◽  
Flow Through ◽  
Trapezoidal Piston Motion

This study examines the effects of rarefaction of an unsteady flow through a microtube for a given but arbitrary inlet volume flow rate. Four cases of inlet volume flow rate proposed by Das and Arakeri (2000, ASME J. Appl. Mech., 67, pp. 274–281) are as follows: (1) trapezoidal piston motion, (2) constant acceleration, (3) impulsively started flow, and (4) impulsively blocked fully developed flow. During the analysis process, the Knudsen number (Kn) is used to represent the degree of rarefaction. The analytical results are presented graphically and compared to the results for a continuum under a no-slip condition. The effect of wall-slip became significant with the increasing degrees of rarefaction. The velocity in the boundary layer increased, whereas the velocity in the potential core of the microtube decreased, under the same condition. The influence of the rarefaction for the pressure gradient varied for the four cases.

Unsteady Unidirectional Flow of Bingham Fluid Through the Parallel Microgap Plates with Wall Slip and Given Inlet Volume Flow Rate Variations

2013 ◽  
Vol 29 (2) ◽  
pp. 355-362
Author(s):  
Y.W. Lin ◽  
C.-I. Chen ◽  
C.-K. Chen
Keyword(s):  
Flow Rate ◽  
Volume Flow Rate ◽  
Flow Behavior ◽  
Linear Acceleration ◽  
Wall Slip ◽  
Transformation Method ◽  
Bingham Fluid ◽  
Volume Flow ◽  
Unidirectional Flow ◽  
Flow Motion

AbstractIn this paper, Laplace transformation method is used to solve the velocity profile and pressure gradient of the unsteady unidirectional flow of Bingham fluid. Between the parallel microgap plates, the flow motion is induced by a prescribed arbitrary inlet volume flow rate which varies with time. Due to the rarefaction, the wall slip condition is existed; therefore, the complexity of solution is also increased. In order to understand the flow behavior of Bingham fluid, there are two basic flow situations are solved. One is a suddenly started flow and the other is constant acceleration flow. Furthermore, linear acceleration and oscillatory flow are also considered. The result indicates when the yield stress τ0 is zero; the solution of the problem reduces to Newtonian fluid.

Unsteady Laminar Duct Flow With a Given Volume Flow Rate Variation

1999 ◽  
Vol 67 (2) ◽  
pp. 274-281 ◽  
Author(s):  
D. Das ◽  
J. H. Arakeri
Keyword(s):  
Cross Section ◽  
Flow Rate ◽  
Volume Flow Rate ◽  
Circular Cross Section ◽  
Volume Flow ◽  
Rate Variation ◽  
Two Dimensional ◽  
Duct Flow ◽  
Fully Developed Flow ◽  
Gradient Variation

In this paper we give a procedure to obtain analytical solutions for unsteady laminar flow in an infinitely long pipe with circular cross section, and in an infinitely long two-dimensional channel, created by an arbitrary but given volume flow rate with time. In the literature, solutions have been reported when the pressure gradient variation with time is prescribed but not when the volume flow rate variation is. We present some examples: (a) the flow rate has a trapezoidal variation with time, (b) impulsively started flow, (c) fully developed flow in a pipe is impulsively blocked, and (d) starting from rest the volume flow rate oscillates sinusoidally. [S0021-8936(00)01702-5]

Unsteady Rotating Electroosmotic Flow Through a Slit Microchannel

2016 ◽  
Vol 32 (5) ◽  
pp. 603-611 ◽  
Author(s):  
D.-Q. Si ◽  
Y.-J. Jian ◽  
L. Chang ◽  
Q.-S. Liu
Keyword(s):  
Flow Rate ◽  
Electroosmotic Flow ◽  
Volume Flow Rate ◽  
Electrical Potential ◽  
Velocity Fields ◽  
Volume Flow ◽  
Half Height ◽  
Poisson Boltzmann ◽  
Flow Through ◽  
Poisson Boltzmann Equation

AbstractUsing the method of Laplace transform, an analytical solution of unsteady rotating electroosmotic flow (EOF) through a parallel plate microchannel is presented. The analysis is based upon the linearized Poisson-Boltzmann equation describing electrical potential distribution and the Navies Stokes equation representing flow field in the rotating coordinate system. The discrepancy of present problem from classical EOF is that the velocity fields are two-dimensional. The rotating EOF velocity profile and flow rate greatly depend on time t, rotating parameter ω and the electrokinetic width K (ratio of half height of microchannel to thickness of electric double layer). The influence of the above dimensionless parameters on transient EOF velocity, volume flow rate and EO spiral is investigated.

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