scholarly journals Electro-osmotic flow of biological fluid in divergent channel: drug therapy in compressed capillaries

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Yun-Jie Xu ◽  
Mubbashar Nazeer ◽  
Farooq Hussain ◽  
M. Ijaz Khan ◽  
M. K. Hameed ◽  
...  
Keyword(s):  
Biological Fluid ◽  
Nonlinear Differential Equations ◽  
Closed Form Solution ◽  
Form Solution ◽  
Jeffrey Fluid ◽  
Nonlinear Thermal Radiation ◽  
Gold Particles ◽  
Osmotic Flow ◽  
Divergent Channel ◽  
Electro Osmotic Flow

AbstractThe multi-phase flow of non-Newtonian through a divergent channel is studied in this article. Jeffrey fluid is considered as the base liquid and tiny gold particles for the two-phase suspension. Application of external electric field parallel to complicated capillary with net surface charge density causes the bulk motion of the bi-phase fluid. In addition to, electro-osmotic flow with heat transfer, the simultaneous effects of viscous dissipation and nonlinear thermal radiation have also been incorporated. Finally, cumbersome mathematical manipulation yields a closed-form solution to the nonlinear differential equations. Parametric study reveals that more thermal energy is contributed in response to Brinkman number which significantly assists gold particles to more heat attain high temperature, as the remedy for compressed or swollen capillaries/arteries.

scholarly journals Theoretical study of an unsteady ciliary hemodynamic fluid flow subject to the Newton’s boundary conditions

2021 ◽  
Vol 13 (8) ◽  
pp. 168781402110404 ◽  
Author(s):  
Mubbashar Nazeer ◽  
Farooq Hussain ◽  
Fayyaz Ahmad ◽  
Sadia Iftikhar ◽  
Gener S Subia
Keyword(s):  
Boundary Conditions ◽  
Stokes Equations ◽  
Biological Fluid ◽  
Nonlinear Differential Equations ◽  
Closed Form Solution ◽  
Form Solution ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Ciliary Motion ◽  
Hemodynamic Flow

This article addresses the hemodynamic flow of biological fluid through a symmetric channel. Methachronal waves induced by the ciliary motion of motile structures are the main source of Couple stress nanofluid flow. Darcy’s law is incorporated in Navier-Stokes equations to highlight the influence of the porous medium. Thermal transport by the microscopic collision of particles is governed by Fourier’s law while a separate expression is obtained for net diffusion of nanoparticles by using Fick’s law. A closed-form solution is achieved of nonlinear differential equations subject to Newton’s boundary conditions. Moreover, the current findings are compared with previous outcomes for the limiting case and found a complete coherence. Parametric study reveals that nanoflow is resisted by employing Newton’s boundary conditions. Thermal profile enhancement is contributed by the viscous dissipation parameter. Finally, one infers that hemodynamic flow of non-Newtonian fluid is an effective mode of heat and mass transfer especially, in medical sciences for the rapid transport of medicines in drug therapy.

Mathematical modeling and simulation of MHD electro-osmotic flow of Jeffrey fluid in convergent geometry

2021 ◽  
pp. 1-17
Author(s):  
A. Al-Zubaidi ◽  
Mubbashar Nazeer ◽  
Gener S. Subia ◽  
Farooq Hussain ◽  
S. Saleem ◽  
...  
Keyword(s):  
Mathematical Modeling ◽  
Modeling And Simulation ◽  
Jeffrey Fluid ◽  
Osmotic Flow ◽  
Electro Osmotic Flow

Postbuckling Analysis of a Nonlocal Nanorod Under Self-Weight

2020 ◽  
Vol 12 (04) ◽  
pp. 2050035
Author(s):  
Chinnawut Juntarasaid ◽  
Tawich Pulngern ◽  
Somchai Chucheepsakul
Keyword(s):  
Boundary Condition ◽  
Differential Equations ◽  
Nonlocal Elasticity ◽  
Nonlinear Differential Equations ◽  
Closed Form Solution ◽  
Constraint Equation ◽  
Form Solution ◽  
Postbuckling Behavior ◽  
Euler Beam ◽  
Softening Behavior

This paper presents the postbuckled configurations of simply supported and clamped-pinned nanorods under self-weight based on elastica theory. Numerical solution is considered in this work since closed-form solution of postbuckling analysis under self-weight cannot be obtained. The set of nonlinear differential equations of a nanorod including the effect of nonlocal elasticity are investigated. The constraint equation at boundary condition technique is introduced for the solution of postbuckling analysis. In order to solve the set of nonlinear differential equations, the shooting method is utilized, where the set of these equations along with boundary conditions are integrated by the fourth-order Runge-Kutta algorithm. Numerical results are obtained and the highlighting influences of the nonlocal elasticity on postbuckling behavior of nanorods are discussed. The obtained results indicate that the rotation angle and the postbuckled configurations of nanorods are varied by changing the nonlocal elasticity parameter. The effect of nonlocal elasticity shows the softening behavior in comparison with the Euler beam. The present formulation together with constraint boundary condition technique is an effective solution for postbuckling analysis of a nanorod under self-weight including the effect of nonlocal elasticity.

scholarly journals The Sustainable Characteristic of Bio-Bi-Phase Flow of Peristaltic Transport of MHD Jeffrey Fluid in the Human Body

2018 ◽  
Vol 10 (8) ◽  
pp. 2671 ◽  
Author(s):  
Ahmed Zeeshan ◽  
Nouman Ijaz ◽  
Tehseen Abbas ◽  
Rahmat Ellahi
Keyword(s):  
Volume Fraction ◽  
Closed Form Solution ◽  
Pressure Rise ◽  
Expansion Method ◽  
Form Solution ◽  
Peristaltic Transport ◽  
Jeffrey Fluid ◽  
Physical Parameters ◽  
Phase Flow ◽  
Special Cases

This study deals with the peristaltic transport of non-Newtonian Jeffrey fluid with uniformly distributed identical rigid particles in a rectangular duct. The effects of a magnetohydrodynamics bio-bi-phase flow are taken into account. The governing equations for mass and momentum are simplified using the fact that wavelength is much greater than the amplitude and small Reynolds number. A closed-form solution for velocity is obtained by means of the eigenfunction expansion method whereby pressure rise is numerically calculated. The results are graphically presented to observe the effects of different physical parameters and the suitability of the method. The results for hydrodynamic, Newtonian fluid, and single-phase problems can be respectively obtained by taking the Hartmann number (M = 0), relaxation time (λ1=0), and volume fraction (C = 0) as special cases of this problem.

Improved Parker-Sochacki Approach for Closed Form Solution of Enzyme Catalyzed Reaction Model

2017 ◽  
Vol 8 (1-2) ◽  
pp. 90
Author(s):  
Babatunde Sunday Ogundare ◽  
Saheed O Akindeinde ◽  
Adebayo O Adewumi ◽  
Adebayo A Aderogba
Keyword(s):  
Closed Form ◽  
Series Solution ◽  
Nonlinear Differential Equations ◽  
Closed Form Solution ◽  
Processing Technique ◽  
Reaction Model ◽  
Form Solution ◽  
Post Processing ◽  
Analytical Technique ◽  
Comparison Of The Results

In this article, a new analytical technique called Improved Parker-Sochacki Method (IPSM) for solving nonlinear Michaelis-Menten enzyme catalyzed reaction model is proposed. The global form of the solution for the concentrations of the substrate, enzyme and the enyzme-free product are obtained. Employing the Laplace-Pade resummation as a post processing technique on the computed series solution, the domain of convergence of the solution is greatly extended. The solution is therefore devoid of limited convergence interval that is typical of series solution of nonlinear differential equations.  The proposed method showed a significant improvement  over the conventional Parker-Sochacki Method (PSM). Furthermore, comparison of the results with numerically computed solutions elucidated the simplicity and accuracy of the proposed method.

Time Periodic Electro-Osmotic-Flow of Jeffrey Fluid in a Circular Microtube

2011 ◽  
Author(s):  
Y. J. Jian ◽  
Q. S. Liu ◽  
H. Z. Duan ◽  
L. Chang ◽  
L. G. Yang ◽  
...  
Keyword(s):  
Jeffrey Fluid ◽  
Osmotic Flow ◽  
Time Periodic ◽  
Electro Osmotic Flow

Design for Buckle-Free Shapes in Pressure Vessels

1985 ◽  
Vol 107 (4) ◽  
pp. 387-393 ◽  
Author(s):  
W. Szyszkowski ◽  
P. G. Glockner
Keyword(s):  
Pressure Vessel ◽  
Nonlinear Differential Equations ◽  
Closed Form Solution ◽  
Numerical Procedure ◽  
Pressure Vessels ◽  
Form Solution ◽  
Loading Conditions ◽  
Loading Case ◽  
Present Design ◽  
Axisymmetric Structures

There are many applications of thin-walled axisymmetric structures as pressure vessels in which buckle-free in-service behavior can only be guaranteed by reinforcements, such as stringers and girths, which not only raise the weight of the structure but also increase its cost. Buckle-free behavior, however, can also be assured by “correcting” the shape of the pressure vessel by a small amount in the area of impending instability. This paper proposes the use of the theory of inflatable membranes to obtain the shape of a pressure vessel subjected to tension only stress state, whereby the possibility of buckling is excluded. Such a shape will be referred to as the “buckle-free” shape. A set of nonlinear differential equations are derived which are valid for any axisymmetric pressure vessel subjected to axisymmetric loadings. The shape obtained from the solution of the equations is an “extremum” to possible stable shapes under the given loading conditions; i.e., there are other stable shapes, for which the circumferential compressive stiffness of the structure has to be relied upon. A closed-form solution for the set of equations was obtained for the constant pressure loading case. For hydrostatic pressure a numerical procedure is applied. Results on “buckle-free” shapes for typical pressure vessel strucures for these two loading conditions are presented. It is established that the deviation of such shapes from the shapes obtained by present design methods and code specifications is small so that this proposed method and the resulting “corrections’ leading to “buckle-free” inservice behavior should not present an aesthetic problem in design.

Analysis of Performance of Pneumatic Impact Absorbers

1978 ◽  
Vol 100 (2) ◽  
pp. 236-241 ◽  
Author(s):  
M. S. Hundal
Keyword(s):  
Nonlinear Differential Equations ◽  
Closed Form Solution ◽  
Form Solution ◽  
Initial Portion ◽  
Orifice Area ◽  
Fixed Area ◽  
And Performance ◽  
Two Stages ◽  
Mass Spring ◽  
Integrated Performance

Performance of impact absorbers employing a pneumatic damper and a linear spring in parallel is analyzed. The governing nonlinear differential equations are derived and converted to nondimensional form. For case of a damper with fixed area orifice the equations are numerically integrated. Performance charts are presented in terms of three dimensionless parameters: mass, spring stiffness and orifice area ratio. Then, a second case is considered in which the damper orifice area is made to vary in two stages. During an initial portion of the stroke the orifice is closed and the air pressure rises to a certain value. In the second stage the orifice area varies in such a manner that a constant deceleration of the mass is achieved. A closed form solution of the governing equations is presented for the second case. The design and performance are compared with that of an impact absorber consisting of a spring only, and with those employing hydraulic dampers.

scholarly journals A Nonlinear Circuit Analysis Technique for Time-Variant Inductor Systems

Sensors ◽  
2019 ◽  
Vol 19 (10) ◽  
pp. 2321 ◽  
Author(s):  
Xinning Wang ◽  
Chong Li ◽  
Dalei Song ◽  
Robert Dean
Keyword(s):  
Closed Form ◽  
Eddy Currents ◽  
High Efficiency ◽  
Nonlinear Differential Equations ◽  
Closed Form Solution ◽  
Form Solution ◽  
Circuit Analysis ◽  
Nonlinear Method ◽  
Sensors And Actuators ◽  
Computation Efficiency

Time-variant inductors exist in many industrial applications, including sensors and actuators. In some applications, this characteristic can be deleterious, for example, resulting in inductive loss through eddy currents in motors designed for high efficiency operation. Therefore, it is important to investigate the electrical dynamics of systems with time-variant inductors. However, circuit analysis with time-variant inductors is nonlinear, resulting in difficulties in obtaining a closed form solution. Typical numerical algorithms used to solve the nonlinear differential equations are time consuming and require powerful processors. This investigation proposes a nonlinear method to analyze a system model consisting of the time-variant inductor with a constraint that the circuit is powered by DC sources and the derivative of the inductor is known. In this method, the Norton equivalent circuit with the time-variant inductor is realized first. Then, an iterative solution using a small signal theorem is employed to obtain an approximate closed form solution. As a case study, a variable inductor, with a time-variant part stimulated by a sinusoidal mechanical excitation, is analyzed using this approach. Compared to conventional nonlinear differential equation solvers, this proposed solution shows both improved computation efficiency and numerical robustness. The results demonstrate that the proposed analysis method can achieve high accuracy.

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