scholarly journals Tank Drainage for an Electrically Conducting Newtonian Fluid with the use of the Bessel Function

2020 ◽  
Vol 10 (2) ◽  
pp. 5377-5381
Author(s):  
M. A. Khaskheli ◽  
K. N. Memon ◽  
A. H. Sheikh ◽  
A. M. Siddiqui ◽  
S. F. Shah
Keyword(s):  
Velocity Field ◽  
Analytical Solution ◽  
Unsteady Flow ◽  
Flow Rate ◽  
Average Velocity ◽  
Series Solution ◽  
Solution Method ◽  
Electrically Conducting ◽  
Velocity Flow ◽  
Time Required

In this study, an unsteady flow for drainage through a circular tank of an isothermal and incompressible Newtonian magnetohydrodynamic (MHD) fluid has been investigated. The series solution method is employed, and an analytical solution is obtained. Expressions for the velocity field, average velocity, flow rate, fluid depth at different times in the tank and time required for the wide-ranging drainage of the fluid (time of efflux) have been obtained. The Newtonian solution is attained by assuming σΒ02=0. The effects of various developing parameters on velocity field υz and depth of fluid H(t) are presented graphically. The time needed to drain the entire fluid and its depth are related and such relations are obtained in closed form. The effect of electromagnetic forces is analyzed. The fluid in the tank will drain gradually and it will take supplementary time for complete drainage.

scholarly journals Solving the Coupled Aerodynamic and Thermal Problem for Modeling the Air Distribution Devices with Perforated Plates

Energies ◽  
2019 ◽  
Vol 12 (18) ◽  
pp. 3488 ◽  
Author(s):  
Serhii Khovanskyi ◽  
Ivan Pavlenko ◽  
Jan Pitel ◽  
Jana Mizakova ◽  
Marek Ochowiak ◽  
...  
Keyword(s):  
Velocity Field ◽  
Flow Rate ◽  
Average Velocity ◽  
Distribution Systems ◽  
Air Flow ◽  
Linear Regression Analysis ◽  
Air Distribution ◽  
Analytical Determination ◽  
Perforated Plates ◽  
Hydraulic Losses

The article is focused on the comprehensive analysis of the aerodynamics of air distribution devices with the combined heat and mass exchange, with the aim to improve the following hydro- and thermodynamic parameters of ventilation systems: flow rate, air velocity, hydraulic losses, and temperature. The inadequacy of the previously obtained characteristics has confirmed the need for more rational designs of air distribution systems. Consequently, the use of perforated plates was proposed to increase hydraulic losses for reducing the average velocity and ensuring a uniform distribution of the velocity field on the outlet of the device. The effectiveness of one of the five possible designs usage is confirmed by the results of numerical simulation. The coefficient of hydraulic losses decreased by 2.5–3.0 times, as well as the uniformity of the outlet velocity field for the air flow being provided. Based on the three-factor factorial experiment, the linear mathematical model was obtained for determining the dependence of the average velocity on the flow rate, plate’s area, and diameter of holes. This model was significantly improved using the multiparameter quasi-linear regression analysis. As a result, the nonlinear mathematical models were obtained, allowing the analytical determination of the hydraulic losses and average velocity of the air flow. Additionally, the dependencies for determining the relative error of measuring the average velocity were obtained.

scholarly journals Unsteady MHD Flow Due to Non-Coaxial Rotations of a Porous Disk and a Fluid at Infinity Subjected to a Periodic Suction

2018 ◽  
Vol 23 (3) ◽  
pp. 623-633
Author(s):  
M. Guria
Keyword(s):  
Magnetic Field ◽  
Fixed Point ◽  
Velocity Field ◽  
Unsteady Flow ◽  
Mhd Flow ◽  
Transverse Magnetic ◽  
Shear Stresses ◽  
Porous Disk ◽  
Electrically Conducting ◽  
Electrically Conducting Fluid

Abstract The unsteady flow of a viscous incompressible electrically conducting fluid due to non-coaxial rotations of a porous disk subjected to a periodic suction and the fluid at infinity in the presence of applied transverse magnetic field has been studied. The fluid at infinity passes through a fixed point. The velocity field, shear stresses are obtained in a closed form.

Frequency and Time Domain Methods for Forced Vibration Analysis of an Oscillating Cascade

2016 ◽  
Author(s):  
M. T. Rahmati
Keyword(s):  
Analytical Solution ◽  
Unsteady Flow ◽  
Frequency Domain ◽  
Solution Method ◽  
Frequency Domain Method ◽  
Time Saving ◽  
Simple Method ◽  
Flow Equations ◽  
Frequency Domain Methods ◽  
Oscillating Plate

Unsteady flow around an oscillating plate cascade has been computationally studied, aimed at examining the predictive ability of a non-linear frequency solution method for hydro-elasticity analysis compared with a standard analytical solution. The comparison of computational and analytical solutions for flow around an oscillating plate configuration demonstrates the capabilities of the frequency domain method compared with the analytical solution in capturing the unsteady flow. It also shows the great advantage of significant CPU time saving by the frequency methods over the nonlinear time method. This approach is based on casting the unsteady flow equations into a set of steady-like equations at a series of phases of a period of unsteadiness. So, One of the advantages of this method compared with other conventional time-linearized frequency domain methods is that any steady flow solution method can be easily used in a straightforward simple method for modelling unsteady perturbations.

scholarly journals A Numerical Study of Sub-Millisecond Integrated Mix-and-Inject Microfluidic Devices for Sample Delivery at Synchrotron and XFELs

2021 ◽  
Vol 11 (8) ◽  
pp. 3404
Author(s):  
Majid Hejazian ◽  
Eugeniu Balaur ◽  
Brian Abbey
Keyword(s):  
Molecular Dynamics ◽  
Flow Rate ◽  
Numerical Study ◽  
Three Dimensional ◽  
Microfluidic Devices ◽  
Liquid Jets ◽  
Mixing Efficiency ◽  
X Ray Diffraction ◽  
Cross Sectional ◽  
Time Required

Microfluidic devices which integrate both rapid mixing and liquid jetting for sample delivery are an emerging solution for studying molecular dynamics via X-ray diffraction. Here we use finite element modelling to investigate the efficiency and time-resolution achievable using microfluidic mixers within the parameter range required for producing stable liquid jets. Three-dimensional simulations, validated by experimental data, are used to determine the velocity and concentration distribution within these devices. The results show that by adopting a serpentine geometry, it is possible to induce chaotic mixing, which effectively reduces the time required to achieve a homogeneous mixture for sample delivery. Further, we investigate the effect of flow rate and the mixer microchannel size on the mixing efficiency and minimum time required for complete mixing of the two solutions whilst maintaining a stable jet. In general, we find that the smaller the cross-sectional area of the mixer microchannel, the shorter the time needed to achieve homogeneous mixing for a given flow rate. The results of these simulations will form the basis for optimised designs enabling the study of molecular dynamics occurring on millisecond timescales using integrated mix-and-inject microfluidic devices.

Mixed convection flow of an electrically conducting fluid in a vertical channel with boundary conditions of the third kind

2014 ◽  
Vol 92 (11) ◽  
pp. 1387-1396 ◽  
Author(s):  
J.C. Umavathi ◽  
A.J. Chamkha
Keyword(s):  
Mixed Convection ◽  
Average Velocity ◽  
Vertical Channel ◽  
Perturbation Parameter ◽  
Conducting Fluid ◽  
Integration Scheme ◽  
Electrically Conducting ◽  
Nusselt Numbers ◽  
Electrically Conducting Fluid ◽  
External Fluid

In this study, the effects of viscous and Ohmic dissipation in steady, laminar, mixed, convection heat transfer for an electrically conducting fluid flowing through a vertical channel is investigated in both aiding and opposing buoyancy situations. The plates exchange heat with an external fluid. Both conditions of equal and different reference temperatures of the external fluid are considered. First, the simpler cases of either negligible Brinkman number or negligible Grashof number are addressed with the help of analytical solutions. The combined effects of buoyancy forces and viscous dissipation are analyzed using a perturbation series method valid for small values of the perturbation parameter. To relax the conditions on the perturbation parameter, the governing equations are also evaluated numerically by a shooting technique that uses the classical explicit Runge–Kutta method of four slopes as an integration scheme and the Newton–Raphson method as a correction scheme. In the examined cases of velocity and temperature fields, the Nusselt numbers at both the walls and the average velocity are explored. It is found that the velocity profiles for an open circuit (E > 0 or E < 0) lie in between the short circuit (E = 0). The graphical results illustrating the effects of various parameters on the flow as well as the average velocity and Nusselt numbers are presented for open and short circuits. In the absence of electric field load parameter and Hartmann number, the results agree with Zanchini (Int. J. Heat Mass Transfer, 41, 3949 (1998)). Further, the analytical and numerical solutions agree very well for small values of the perturbation parameter.

Analytical Solution to Steady-State Heat-Conduction Problems With Irregularly Shaped Boundaries

1971 ◽  
Vol 93 (4) ◽  
pp. 449-454 ◽  
Author(s):  
D. M. France
Keyword(s):  
Heat Conduction ◽  
Steady State ◽  
Analytical Solution ◽  
Least Squares ◽  
Series Solution ◽  
Point Matching ◽  
State Heat ◽  
Temperature Heat ◽  
Steady State Heat ◽  
Least Squares Approach

A method of obtaining an analytical solution to two-dimensional steady-state heat-conduction problems with irregularly shaped boundaries is presented. The technique of obtaining the coefficients to the series solution via a direct least-squares approach is compared to the “point-matching” scheme. The two methods were applied to problems with known solutions involving the three heat-transfer boundary conditions, temperature, heat flux, and convection coefficient specified. Increased accuracy with substantially fewer terms in the series solution was obtained via the least-squares technique.

scholarly journals Increased take-off level in automatic milking systems – effects on milk flow, milk yield and milking efficiency at the quarter level

2018 ◽  
Vol 86 (1) ◽  
pp. 85-87 ◽  
Author(s):  
Sabine Ferneborg ◽  
Måns Thulin ◽  
Sigrid Agenäs ◽  
Kerstin Svennersten-Sjaunja ◽  
Peter Krawczel ◽  
...  
Keyword(s):  
Flow Rate ◽  
The Other ◽  
Mean Flow ◽  
Flow Rates ◽  
Decline Phase ◽  
Flow Profiles ◽  
Milk Flow ◽  
Automatic Milking ◽  
Automatic Milking Systems ◽  
Time Required

AbstractThis research communication describes how different detachment levels (0.48, 0.3 and 0.06 kg milk/min) at the quarter-level affect milk flow profiles and overall milking efficiency in automatic milking systems. We hypothesized a higher detachment level would result in greater mean flow rates without affecting the volume of harvested milk per cow during 24 h compared to lower detachment levels. The data suggest milk flow decreased to a rate below the overmilking limit within the 6-s delay time required for termination in all treatments, but the duration of overmilking was shorter for the greatest detachment level compared to the other treatments. We conclude that setting a detachment level at a greater milk flow rate reduces the duration of overmilking without affecting the amount of milk harvested when applied to cows in mid-lactation during quarter-level milking. We also suggest that the steepness of the decline phase of the milk flow curve might have a larger effect than the actual detachment level on the duration of overmilking.

scholarly journals Two Dimensional Flow Analysis of a Laboratory Centrifugal Pump

1990 ◽  
Author(s):  
S. M. Miner ◽  
R. D. Flack ◽  
P. E. Allaire
Keyword(s):  
Velocity Field ◽  
Stagnation Point ◽  
Centrifugal Pump ◽  
Flow Rate ◽  
Flow Analysis ◽  
Tangential Component ◽  
Design Flow ◽  
Experimental Results ◽  
Two Dimensional ◽  
Flow Angle

Two dimensional potential flow was used to determine the velocity field within a laboratory centrifugal pump. In particular, the finite element technique was used to model the impeller and volute simultaneously. The rotation of the impeller within the volute was simulated by using steady state solutions with the impeller in 10 different angular orientations. This allowed the interaction between the impeller and the volute to develop naturally as a result of the solution. The results for the complete pump model showed that there are circumferential asymmetries in the velocity field, even at the design flow rate. Differences in the relative velocity components were as large as 0.12 m/sec for the radial component and 0.38 m/sec for the tangential component, at the impeller exit. The magnitude of these variations was roughly 25% of the magnitude of the average radial and tangential velocities at the impeller exit. These asymmetries were even more pronounced at off design flow rates. The velocity field was also used to determine the location of the tongue stagnation point and to calculate the slip within the impeller. The stagnation point moved from the discharge side of the tongue to the impeller side of the tongue, as the flow rate increased from below design flow to above design flow. At design flow, values of slip ranged from 0.96 to 0.71, from impeller inlet to impeller exit. For all three types of data (velocity profiles, stagnation point location, and slip factor) comparison was made to laser velocimeter data, taken for the same pump. At the design flow, the computational and experimental results agreed to within 17% for the velocity magnitude, and 2° for the flow angle. The stagnation point locations coincided for the computational and experimental results, and the values for slip agreed to within 10%.

scholarly journals Semi-analytical solution for the problem of extended Pom-Pom fluid flow in a round pipe

2021 ◽  
Vol 2057 (1) ◽  
pp. 012007
Author(s):  
A I Kadyirov ◽  
E K Vachagina
Keyword(s):  
Experimental Data ◽  
Fluid Flow ◽  
Analytical Solution ◽  
Solution Method ◽  
Parametric Method ◽  
Single Equation ◽  
Weissenberg Number ◽  
Normal Stresses ◽  
Rheological Equation ◽  
Rheological Equation Of State

Abstract A semi-analytical solution to the problem of the steady flow of viscoelastic single equation eXended Pom-Pom (XPP) fluid in a round pipe using the four-mode rheological equation of state of XPP is presented. An original parametric method for solving the set problem is used. The resulting method is applicable for solving a similar problem in a flat slit. The developed solution method is tested by comparing it with numerical results and experimental data. Using a polyacrylamide solution as an example, the influence of the Weissenberg number on the axial velocity profiles and the components of normal stresses is studied.

scholarly journals Analysis of dynamics variation against thixotropic parameter’s preferential range

2018 ◽  
Vol 45 (2) ◽  
pp. 231-251
Author(s):  
Nazish Shahid
Keyword(s):  
Shear Stress ◽  
Pressure Gradient ◽  
Flow Rate ◽  
Axial Velocity ◽  
Fluid Model ◽  
Current Model ◽  
Velocity Shear ◽  
Structural Parameter ◽  
Velocity Flow ◽  
Analysis Of Dynamics

Variation in the dynamics of a steady-state blood flow through a stenosed tapered artery has been investigated corresponding to changes in thixotropic parameter ? over the range [0,1]. To probe the role of parameter ? and differentiate the current model from other known non-Newtonian models, expressions of axial velocity, shear stress, wall shear stress and flow rate have been calculated depending upon this parameter and pressure gradient. Also, pressure gradient has been deduced uniquely with the help of the continuity equation. Our choice of calculating pressure gradient has led to obtaining shear stress such that its dependence on the structural parameter of our model, unlike most available results, motivates for further investigation. The simultaneous effects of varying yield stress and parameter ? on axial velocity, flow resistance and flow rate have been studied such that the differences between the Herschel?Bulkley fluid model and our current model can be pointed out. To validate the suitability of our model and some results in history, we have also obtained limiting results for particular values of ?.

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