Development of a Periodic Flow in a Rigid Tube

1968 ◽  
Vol 90 (3) ◽  
pp. 395-399 ◽  
Author(s):  
P. J. Florio ◽  
W. K. Mueller
Keyword(s):  
Velocity Field ◽  
Analytical Solution ◽  
Axial Velocity ◽  
Circular Tube ◽  
Approximate Analytical Solution ◽  
Experimental Results ◽  
Oscillating Flow ◽  
Periodic Flow ◽  
Mean Flow ◽  
Rigid Tube

The development of a pulsating velocity field in a rigid, circular tube was experimentally investigated. The wall pressure and the radial variation of the axial velocity were measured at several axial locations. The measured inlet velocities were compared with the fully developed velocities. The experimental results show that, for the range of parameters investigated, the developing pulsating flow can be considered to be simply a superposition of a developing mean flow and a fully developed oscillating flow. These results are in agreement with a previous approximate analytical solution by Atabek and Chang.

scholarly journals Mass Transfer in a Rigid Tube With Pulsatile Flow and Constant Wall Concentration

2010 ◽  
Vol 132 (8) ◽  
Author(s):  
T. E. Moschandreou ◽  
C. G. Ellis ◽  
D. Goldman
Keyword(s):  
Mass Transfer ◽  
Analytical Solution ◽  
Sherwood Number ◽  
Pulsatile Flow ◽  
Approximate Analytical Solution ◽  
Perturbation Expansion ◽  
Mixing Efficiency ◽  
Bulk Concentration ◽  
Rigid Tube ◽  
Positive Peak

An approximate-analytical solution method is presented for the problem of mass transfer in a rigid tube with pulsatile flow. For the case of constant wall concentration, it is shown that the generalized integral transform (GIT) method can be used to obtain a solution in terms of a perturbation expansion, where the coefficients of each term are given by a system of coupled ordinary differential equations. Truncating the system at some large value of the parameter N, an approximate solution for the system is obtained for the first term in the perturbation expansion, and the GIT-based solution is verified by comparison to a numerical solution. The GIT approximate-analytical solution indicates that for small to moderate nondimensional frequencies for any distance from the inlet of the tube, there is a positive peak in the bulk concentration C1b due to pulsation, thereby, producing a higher mass transfer mixing efficiency in the tube. As we further increase the frequency, the positive peak is followed by a negative peak in the time-averaged bulk concentration and then the bulk concentration C1b oscillates and dampens to zero. Initially, for small frequencies the relative Sherwood number is negative indicating that the effect of pulsation tends to reduce mass transfer. There is a band of frequencies, where the relative Sherwood number is positive indicating that the effect of pulsation tends to increase mass transfer. The positive peak in bulk concentration corresponds to a matching of the phase of the pulsatile velocity and the concentration, respectively, where the unique maximum of both occur for certain time in the cycle. The oscillatory component of concentration is also determined radially in the tube where the concentration develops first near the wall of the tube, and the lobes of the concentration curves increase with increasing distance downstream until the concentration becomes fully developed. The GIT method proves to be a working approach to solve the first two perturbation terms in the governing equations involved.

Numerical Approximations to Solution of Biochemical Reaction Model

2011 ◽  
Vol 9 (1) ◽  
Author(s):  
Ahmet Yildirim ◽  
Ahmet Gökdogan ◽  
Mehmet Merdan
Keyword(s):  
Analytical Solution ◽  
Approximate Analytical Solution ◽  
Transformation Method ◽  
Reaction Model ◽  
Biochemical Reaction ◽  
Graphical Form ◽  
Kutta Method ◽  
Transform Method ◽  
Runge Kutta Method ◽  
Differential Transform

In this paper, approximate analytical solution of biochemical reaction model is used by the multi-step differential transform method (MsDTM) based on classical differential transformation method (DTM). Numerical results are compared to those obtained by the fourth-order Runge-Kutta method to illustrate the preciseness and effectiveness of the proposed method. Results are given explicit and graphical form.

New Approximate Analytical Solution of the Diode-Resistance Equation

2021 ◽  
pp. 153665
Author(s):  
José A. Gazquez ◽  
Manuel Fernandez-Ros ◽  
Blas Torrecillas ◽  
José Carmona ◽  
Nuria Novas
Keyword(s):  
Analytical Solution ◽  
Approximate Analytical Solution ◽  
Resistance Equation

Oscillating Flow of a Viscous Compressible Fluid Through a Rigid Tube: A Theoretical Model

1981 ◽  
Vol BME-28 (5) ◽  
pp. 416-420 ◽  
Author(s):  
H. Franken ◽  
J. Cement ◽  
M. Cauberghs ◽  
K. P. Van de Woestijne
Keyword(s):  
Theoretical Model ◽  
Compressible Fluid ◽  
Oscillating Flow ◽  
Viscous Compressible Fluid ◽  
Rigid Tube
Sign in / Sign up

Export Citation Format

Share Document