symmetric flow
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2022 ◽  
Vol 0 (0) ◽  
Author(s):  
Shobhit Kumar Srivastava ◽  
Rahul Kumar Chaturvedi ◽  
Lal Pratap Singh

Abstract This article concerns the study of various parameter effects on the propagation of weak discontinuities by using the method of characteristics. Analytical solutions of the quasi-linear system of hyperbolic partial differential equations (PDEs) are obtained and examined the evolutionary behavior of shock in the characteristic plane. The general behavior of solutions to the Bernoulli equation, which determines the evolution of weak discontinuity in a nonlinear system, is studied in detail. Also, we discuss the formation and distortion of compressive and expansive discontinuities under the van der Waals parameter effect and small particles for planar and cylindrical symmetric flow. The comparison between planar flow and cylindrical symmetric flow is studied under the influence of nonidealness and mass fraction of dust particles. It is found that the compressive waves become shock after a certain lapse of time. The medium considered here is the mixture of van der Waals gas with small dust particles.


Author(s):  
Srikant Venkatakrishnan ◽  
Meeka Khanna ◽  
Anupam Gupta

Abstract Background Transcranial color-coded duplex sonography (TCCD) provides information on intracranial blood flow status in stroke patients and can predict rehabilitation outcomes. Objective This study aimed to assess middle cerebral artery (MCA) parameters using TCCD in MCA territory stroke patients admitted for rehabilitation and correlate with clinical outcome measures. Material and Methods Patients aged 18 to 65 years with a first MCA territory stroke, within 6 months of onset were recruited. The clinical outcome scales and TCCD parameters were assessed at both admission and discharge. The scales used were the Scandinavian stroke scale (SSS), Barthel Index (BI), modified Rankin Scale (mRS), Fugl–Meyer upper extremity scale (FMA-UE), modified motor assessment scale (mMAS) scores. TCCD parameters measured were MCA peak systolic, end diastolic, mean flow velocities (MFV), and index of symmetry (SI) and were correlated with clinical scores. Results Fourteen patients were recruited with median age of 56.5 years, median duration of stroke was 42.5 days. Mean flow velocities of affected and unaffected MCA were 46.2 and 50.7 cm/s, respectively. Flow velocities and SI did not change between the two assessments. There was significant improvement in clinical outcome scores at discharge. Significant correlation was observed for patient group with SI > 0.9 at admission with FMA-UE, SSS, and BI scores at discharge (p < 0.05). Conclusion Flow velocity parameters did not change during in-patient rehabilitation. Patients with symmetric flow at admission had improved clinical outcomes measure scores at discharge. Thus SI can predict rehabilitation outcomes in stroke survivors.


Symmetry ◽  
2021 ◽  
Vol 13 (11) ◽  
pp. 2087
Author(s):  
Hemalatha Balasundaram ◽  
Senthamilselvi Sathiamoorthy ◽  
Shyam Sundar Santra ◽  
Rifaqat Ali ◽  
Vediyappan Govindan ◽  
...  

Cerebrospinal fluid (CSF) is a symmetric flow transport that surrounds brain and central nervous system (CNS). Congenital hydrocephalusis is an asymmetric and unusual cerebrospinal fluid flow during fetal development. This dumping impact enhances the elasticity over the ventricle wall. Henceforth, compression change influences the force of brain tissues. This paper presents a mathematical model to establish the effects of ventricular elasticity through a porous channel. The current model is good enough for immediate use by a neurosurgeon. The mathematical model is likely to be a powerful tool for the better treatment of hydrocephalus and other brain biomechanics. The non-linear dimensionless governing equations are solved using a perturbation technique, and the outcome is portrayed graphically with the aid of MATLAB.


2021 ◽  
Vol 927 ◽  
Author(s):  
Anna Ipatova ◽  
K.V. Smirnov ◽  
E.I. Mogilevskiy

The paper deals with the steady axially symmetric flow of a viscous liquid layer over a rotating disk. The liquid is fed near the axis of rotation and spreads due to inertia and the centrifugal force. The viscous shallow-water approach gives a system of ordinary differential equations governing the flow. We consider inertia, gravity, centrifugal and Coriolis forces and estimate the effect of surface tension. We found four qualitatively different flow regimes. Transition through these regimes shows the continuous evolution of the flow structure from a hydraulic jump on a static disk to a monotonic thickness decrease on a fast rotating one. We show that, in the absence of surface tension, the intensity of the jump gradually vanishes at a finite distance from the axis of rotation while the angular velocity increases. The surface tension decreases the jump radius and destroys the steady solution for a certain range of parameters.


Author(s):  
Talat Rafiq ◽  
M Mustafa ◽  
Junaid Ahmad Khan

This research features one parameter family of solutions representing rotationally symmetric flow of non-Newtonian fluid obeying Reiner-Rivlin model. Such flows take place over a revolving plane permeable surface through origin such that fluid at infinity also undergoes uniform rotation about the vertical axis. Heat transfer accompanied with viscous heating effect is also analyzed. A similarity solution is proposed that results into a coupled non-linear system with four unknowns. Boundary layer structure is characterized by a parameter [Formula: see text] that compares angular velocity of external flow with that of the rotating surface. Solutions are developed by a well-known package bvp4c of MATLAB for full range of [Formula: see text]. Flow pattern for different choices of [Formula: see text] is scrutinized by computing both 2 D and 3 D streamlines. It is further noted that value of suction velocity is important with regards to the sign of axial velocity component. Boundary layer suppresses considerably whenever the surface is permeable. For sufficiently high suction velocity with [Formula: see text], entire fluid undergoes rigid body rotation. In no suction case, axially upward flow accelerates for increasing values of parameter [Formula: see text] in the range [Formula: see text], whereas opposite trend is apparent in the case [Formula: see text]. Results for normalized wall shear and Nusselt number are scrutinized for various choices of embedded parameters.


Symmetry ◽  
2021 ◽  
Vol 13 (7) ◽  
pp. 1109
Author(s):  
Constantin Fetecau ◽  
Dumitru Vieru

Unidirectional unsteady flows of the incompressible Burgers’ fluids between two infinite horizontal parallel plates are analytically studied when the magnetic and porous effects are taken into consideration. The fluid motion is induced by the two plates, which move in their planes with time-dependent velocities. Exact general expressions are established both for the dimensionless velocity and shear stress fields as well as the corresponding Darcy’s resistance in the channel using the Laplace transform. If both plates move with equal velocities in the same direction, the fluid motion becomes symmetric with respect to the mid-plane between them. Otherwise, its motion is non-symmetric. To bring to light the behavior of the fluid, the dimensionless velocity profiles versus the spatial variable as well as its time evolution are presented both for the symmetric and asymmetric case. Finally, for comparison, similar graphical representations are presented together for the velocities of the incompressible Oldroyd-B and Burgers’ fluids. For large values of the time t, as expected, the behavior of the two different fluids is almost identical. The Darcy’s resistance against y is also graphically represented for the symmetric flow at different values of the time t. The influence of the magnetic field on the fluid motion is graphically revealed and discussed.


Symmetry ◽  
2021 ◽  
Vol 13 (6) ◽  
pp. 915
Author(s):  
Vahabodin Goodarzi ◽  
Saeed Hayati Jafarbeygi ◽  
Ramezan Ali Taheri ◽  
Mikhail Sheremet ◽  
Mohammad Ghalambaz

Mixing is essential in microdevices. Therefore, increasing the mixing efficiency has a significant influence on these devices. Using conductive obstacles with special geometry can improve the mixing quality of the micromixers. In this paper, a numerical study on the mixing caused by an induced-charge electrokinetic micromixer was carried out using a conductive plate with a curved arc shape instead of a conductive flat plate or other non-conductive obstacles for Newtonian fluids. This study also explored the effect of the different radius curves, span length, the number of curved arc plates in the channel, the pattern of arrangement, concavity direction, and the orientation angle against the flow on the mixing. Furthermore, the efficiency of the T-micromixer against a flow with a low diffusion coefficient was investigated. It should be noted that the considered channel is symmetric regarding to the middle horizontal plane and an addition of flat plate reflects a formation of symmetric flow structures that do not allow to improve the mixture process. While an addition of non-symmetric curved arc plates al-lows to increase the mixing by creating vortices. These vortices were created owing to the non-uniform distribution of induced zeta potential on the curved arc plate. A rise in the span length of the curved arc plate when the radius was constant improved the mixing. When three arc plates in one concavity direction were used, the mixing efficiency was 91.86%, and with a change in the concavity direction, the mixing efficiency increased to 95.44%. With a change in the orientation angle from 0 to 25, the mixing efficiency increased by 19.2%.


Meccanica ◽  
2021 ◽  
Author(s):  
J. H. Merkin ◽  
Y. Y. Lok ◽  
I. Pop

AbstractIn this note, we extend the problem treated in (Lok, Math Modelling Anal 24:617–634 (2019)) to the case of permeable surface which is shrinking in mutually orthogonal directions. Both numerical and asymptotic solutions are obtained for two important governing parameters, $$\gamma $$ γ the shrinking rate and S characterizing the fluid transfer through the boundary. In this problem, a restriction on S is required for a solution to exist. This contrasts with the problem in (Lok, Math Modelling Anal 24:617–634 (2019)) where no restriction on S is needed. Numerical solutions show that for a fixed value of S, two critical points $$\gamma _c$$ γ c are observed for $$S > 2$$ S > 2 . Conversely, two critical points $$S_c$$ S c are found for a given value of $$\gamma $$ γ when $$S > 2$$ S > 2 . A discussion on the nonexistence of solution for $$S = 2$$ S = 2 is given and asymptotic solutions for S large and $$(S-2)$$ ( S - 2 ) small are also presented.


2021 ◽  
Vol 11 (7) ◽  
pp. 3182
Author(s):  
Václav Ficaj ◽  
Pavel Pech ◽  
Daniel Kahuda

As the climate is changing, greater exploitation of groundwater reserves is becoming evident; however, this would have been apparent even without climate change. Therefore, increasing emphasis is given to maintaining well functionality. Wells are susceptible to aging, which reduces their efficiency. Today, there exist several solutions for determining the size of additional resistance (the skin effect), which indicates a well’s current state and that of its close surroundings. The implementation of most of these solutions is often time-consuming. To improve our tools, a goal has been set to accelerate and facilitate the method of determining the size of additional resistance. In this study, we present new software that accelerates this process. It applies an innovative method based upon a partial differential equation describing the radially symmetric flow to a real well, which occurs under an unsteady regime, using the Laplace transform. Stehfest algorithm 368 is used to invert the Laplace transform. Such software can be used to evaluate an additional-resistance well, even when a straight section evaluated using the Cooper–Jacob method is not achieved in the semilogarithmic plot of drawdown vs. log time during the pumping test. This solution is demonstrated in the comprehensive evaluation of 10 wells and 3 synthetic pumping tests.


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