scholarly journals Extended Stokes' First Problem of an Oldroyd-B Fluid for Relatively Moving Half-Planes

2011 ◽  
Vol 2011 ◽  
pp. 1-16 ◽  
Author(s):  
Chi-Min Liu
Keyword(s):  
Exact Solution ◽  
Relaxation Time ◽  
Stokes Problem ◽  
Original System ◽  
Rheological Parameters ◽  
Retardation Time ◽  
Series Form ◽  
Integral Transformations ◽  
Potential Applications ◽  
Induced Flow

An Oldroyd-B fluid suddenly disturbed by relatively moving half-planes is theoretically studied in this paper. This new problem, extended from the traditional Stokes' problem, recently attracts a great deal of attention due to its potential applications in engineering. Using integral transformations and dividing the original system into two subsystems, the exact solution is derived and shown in a series form. In addition to the general understanding of velocity developments, the effects of the relaxation time and the retardation time on the velocity profiles are examined in a series of figures. It is found that above two rheological parameters influence the induced flow in an opposite way. Other interesting characteristics are also elucidated from present results.

Diffraction of impulsive elastic waves by a fluid cylinder

1974 ◽  
Vol 75 (3) ◽  
pp. 391-404 ◽  
Author(s):  
Ramanand Jha
Keyword(s):  
Exact Solution ◽  
Circular Cylinder ◽  
Elastic Medium ◽  
Elastic Waves ◽  
Line Source ◽  
Inviscid Fluid ◽  
Geometrical Theory ◽  
Shadow Zone ◽  
Integral Transformations ◽  
Geometrical Theory Of Diffraction

AbstractIn this paper, the problem of diffraction of an impulsive P wave by a fluid circular cylinder has been considered. The cylinder is embedded in an unbounded isotropic homogeneous elastic medium and it is filled with inviscid fluid material. The line source, giving rise to the incident front, is situated outside the cylinder parallel to its axis.The exact solution of the problem is obtained by using the method of dual integral transformations. The solution is evaluated approximately to obtain the motion on the wave front in the shadow zone of the elastic medium. Further, we interpret the approxi mate solutions in terms of Keller's geometrical theory of diffraction. Our result also gives a correction to an earlier investigation of the similar problem by Knopoff and Gilbert(s).

UNSTEADY MODEL OF TRANSPORTATION OF JEFFREY-FLUID BY PERISTALSIS

2010 ◽  
Vol 03 (04) ◽  
pp. 473-491 ◽  
Author(s):  
S. K. PANDEY ◽  
DHARMENDRA TRIPATHI
Keyword(s):  
Relaxation Time ◽  
Flow Rate ◽  
Volume Flow Rate ◽  
Cylindrical Tube ◽  
Maximum Flow ◽  
Mechanical Efficiency ◽  
Volume Flow ◽  
Jeffrey Fluid ◽  
Retardation Time ◽  
Circular Cylindrical Tube

The investigation is to explore the transportation of a viscoelastic fluid by peristalsis in a channel as well as in a circular cylindrical tube by considering Jeffrey-model. In order to apply the model to the swallowing of food-bolus through the oesophagus, the wave equation assumed to propagate along the walls is such that the walls contract in the transverse/radial direction and relax but do not expand further. Solutions have been presented in the closed form by using small Reynolds number and long wavelength approximations. The expressions of pressure gradient, volume flow rate and average volume flow rate have been derived. It is revealed on the basis of computational investigation that for a fixed flow rate, pressure decreases when the ratio of relaxation time to retardation time is increased. In both the channel and tubular flows, the pressure decreases on increasing the ratio of relaxation time to retardation time if the averaged flow rate is less than the maximum flow rate. It is also revealed that the maximum tubular flow rate is higher than that of the channel-flow. It is further found through the theoretical analysis that mechanical efficiency, reflux and local wall shear stress remain unaffected by viscoelastic property of the fluid modelled as Jeffrey-fluid.

scholarly journals USE OF ATANGANA–BALEANU FRACTIONAL DERIVATIVE IN HELICAL FLOW OF A CIRCULAR PIPE

Fractals ◽  
2020 ◽  
Vol 28 (08) ◽  
pp. 2040049 ◽  
Author(s):  
KASHIF ALI ABRO ◽  
ILYAS KHAN ◽  
KOTTAKKARAN SOOPPY NISAR
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Rheological Parameters ◽  
Shear Stresses ◽  
Fractional Differentiation ◽  
Retardation Time ◽  
Governing Equations ◽  
Partial Differential ◽  
Gamma Functions ◽  
Helical Pipe

There is no denying fact that helically moving pipe/cylinder has versatile utilization in industries; as it has multi-purposes, such as foundation helical piers, drilling of rigs, hydraulic simultaneous lift system, foundation helical brackets and many others. This paper incorporates the new analysis based on modern fractional differentiation on infinite helically moving pipe. The mathematical modeling of infinite helically moving pipe results in governing equations involving partial differential equations of integer order. In order to highlight the effects of fractional differentiation, namely, Atangana–Baleanu on the governing partial differential equations, the Laplace and Hankel transforms are invoked for finding the angular and oscillating velocities corresponding to applied shear stresses. Our investigated general solutions involve the gamma functions of linear expressions. For eliminating the gamma functions of linear expressions, the solutions of angular and oscillating velocities corresponding to applied shear stresses are communicated in terms of Fox- H function. At last, various embedded rheological parameters such as friction and viscous factor, curvature diameter of the helical pipe, dynamic analogies of relaxation and retardation time and comparison of viscoelastic fluid models (Burger, Oldroyd-B, Maxwell and Newtonian) have significant discrepancies and semblances based on helically moving pipe.

scholarly journals New exact solution for Rayleigh–Stokes problem of Maxwell fluid in a porous medium and rotating frame

2011 ◽  
Vol 1 (1) ◽  
pp. 9-12 ◽  
Author(s):  
Faisal Salah ◽  
Zainal Abdul Aziz ◽  
Dennis Ling Chuan Ching
Keyword(s):  
Exact Solution ◽  
Porous Medium ◽  
Stokes Problem ◽  
Maxwell Fluid ◽  
Rotating Frame

scholarly journals Observer Design for a Core Circadian Rhythm Network

2014 ◽  
Vol 2014 ◽  
pp. 1-8
Author(s):  
Yuhuan Zhang
Keyword(s):  
Differential Equation ◽  
Circadian Rhythm ◽  
Biological Networks ◽  
Original System ◽  
Equation Model ◽  
Observer Design ◽  
Differential Equation Model ◽  
Highly Nonlinear ◽  
Input Signals ◽  
Potential Applications

The paper investigates the observer design for a core circadian rhythm network inDrosophilaandNeurospora. Based on the constructed highly nonlinear differential equation model and the recently proposed graphical approach, we design a rather simple observer for the circadian rhythm oscillator, which can well track the state of the original system for various input signals. Numerical simulations show the effectiveness of the designed observer. Potential applications of the related investigations include the real-world control and experimental design of the related biological networks.

scholarly journals Exact Solution of Thermoelastic Problem for a One-Dimensional Bar without Energy Dissipation

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
A. M. Abd El-Latief ◽  
S. E. Khader
Keyword(s):  
Exact Solution ◽  
Relaxation Time ◽  
Thermal Stress ◽  
Energy Dissipation ◽  
Heat Source ◽  
Half Space ◽  
Time Dependent ◽  
One Dimensional ◽  
The Laplace Transform ◽  
Without Energy Dissipation

We consider a homogeneous isotropic thermoelastic half-space in the context of the theory of thermoelasticity without energy dissipation. There are no body forces or heat source acting on the half-space. The surface of the half-space is affected by a time dependent thermal shock and is traction free. The Laplace transform with respect to time is used. The inverse transforms are obtained in an exact manner for the temperature, thermal stress, and displacement distributions. These solutions are represented graphically and discussed for several cases of the applied heating. Comparison is made between the predictions here and those of the theory of thermoelasticity with one relaxation time.

Counteracting Dynamical Degradation of Digital Chaotic Chebyshev Map via Perturbation

2017 ◽  
Vol 27 (03) ◽  
pp. 1750033 ◽  
Author(s):  
Yunqi Liu ◽  
Yuling Luo ◽  
Shuxiang Song ◽  
Lvchen Cao ◽  
Junxiu Liu ◽  
...  
Keyword(s):  
Complex Dynamics ◽  
High Reliability ◽  
Dynamic Performance ◽  
Chaotic Map ◽  
Approximate Entropy ◽  
Original System ◽  
Pseudorandom Number Generator ◽  
Chebyshev Map ◽  
Potential Applications ◽  
Chaos Attractor

The chaotic map has complex dynamics under ideal conditions however it suffers from the problem of performance degradation in the case of finite computing precision. In order to prevent the dynamics degradation, in this paper the continuous Chen chaotic system is used to perturb both the inputs and parameters of Chebyshev map to minimize the chaotic degradation phenomenon under finite precision. Experimental evaluations and corresponding performance analysis demonstrate that the Chebyshev chaotic map has a good randomness and complex dynamic performance by using the proposed perturbation method, and some attributes of the proposed system are stronger than the original system (e.g. chaos attractor and approximate entropy). Finally, the corresponding pseudorandom number generator (PRNG) is constructed by this method and then its randomness is evaluated via NIST SP800-22 and TestU01 test suites, respectively. Statistical test results show that the proposed PRNG has high reliability of randomness, thus it can be used for cryptography and other potential applications.

NUMERICAL STUDY ON PERISTALTIC TRANSPORT OF FRACTIONAL BIO-FLUIDS

2011 ◽  
Vol 11 (05) ◽  
pp. 1045-1058 ◽  
Author(s):  
DHARMENDRA TRIPATHI
Keyword(s):  
Relaxation Time ◽  
Numerical Study ◽  
Approximate Solutions ◽  
Peristaltic Transport ◽  
Graphical Form ◽  
Retardation Time ◽  
Long Wavelength ◽  
Homotopy Analysis ◽  
Channel Analysis ◽  
Fractional Parameter

A numerical study is presented to examine the peristaltic transport of fractional bio-fluids (viscoelastic fluids with fractional Oldroyd-B model) through the channel. Analysis is carried out under the assumptions of long wavelength and low Reynolds number. Numerical and analytical approximate solutions of problem are obtained by using homotopy analysis method. It is assumed that the cross section of the channel varies sinusoidally along the length of channel. The effects of fractional parameters, material constants (relaxation time and retardation time), time and amplitude on the pressure and frictional force across one wavelength are studied with particular emphasis. The computational results are presented in graphical form. It is found that the effect of both fractional parameters on pressure is opposite to each other i.e., pressure reduces with increasing magnitude of the first fractional parameter whereas it increases with increasing magnitude of the second fractional parameter. The effects of relaxation time and retardation time on pressure are similar to that of first and second fractional parameters, respectively.

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