scholarly journals Investigation of thermal behavior and fluid motion in DC magnetohydrodynamic pumps

2014 ◽  
Vol 18 (suppl.2) ◽  
pp. 551-562 ◽  
Author(s):  
Mehdi Kiyasatfar ◽  
Nader Pourmahmoud ◽  
Maqsood Golzan ◽  
Iraj Mirzaee
Keyword(s):  
Thermal Behavior ◽  
Equations Of Motion ◽  
Rectangular Channel ◽  
Fluid Motion ◽  
Mhd Flow ◽  
Finite Difference Approximation ◽  
Entropy Generation Rate ◽  
Difference Approximation ◽  
Magnetic Flux Density ◽  
Working Medium

Motivated by increasingly being used MHD micropumps for pumping biological and chemical specimens, this study presents a simplified MHD flow model based upon steady state, incompressible and fully developed laminar flow theory in rectangular channel to offer the characteristics of MHD pumps for prediction of pumping performance in MHD flow. The nonlinear governing equations of motion and energy including viscous and Joule dissipation are solved numerically for velocity and temperature distributions. To aim this goal a finite difference approximation based code is developed and utilized. In addition, the effects of magnetic flux density, applied electric current and channel size on flow velocity field as well as thermal behavior are investigated in various working medium with different physical properties. Also the entropy generation rate is discussed. The simulation results are in good agreement with experimental data from literature.

scholarly journals Time-space dependent fractional viscoelastic MHD fluid flow and heat transfer over accelerating plate with slip boundary

2017 ◽  
Vol 21 (6 Part A) ◽  
pp. 2337-2345
Author(s):  
Shengting Chen ◽  
Liancun Zheng ◽  
Chunrui Li ◽  
Jize Sui
Keyword(s):  
Heat Transfer ◽  
Numerical Solutions ◽  
Fluid Model ◽  
Mhd Flow ◽  
Constitutive Relationship ◽  
Finite Difference Approximation ◽  
Difference Approximation ◽  
Slip Boundary ◽  
Flow And Heat Transfer ◽  
Time Space

The MHD flow and heat transfer of viscoelastic fluid over an accelerating plate with slip boundary are investigated. Different from most classical works, a modified time-space dependent fractional Maxwell fluid model is proposed in depicting the constitutive relationship of the fluid. Numerical solutions are obtained by explicit finite difference approximation and exact solutions are also presented for the limiting cases in integral and series forms. Furthermore, the effects of parameters on the flow and heat transfer behavior are analyzed and discussed in detail.

scholarly journals Hall effect on steady mhd flow and heat transfer of a viscous fluid in a rectangular channel with suction and injection

2019 ◽  
Vol 128 ◽  
pp. 07008
Author(s):  
Ramana Murthy Josyula Venkata ◽  
Pavankumar Reddy Muduganti
Keyword(s):  
Magnetic Field ◽  
Viscous Fluid ◽  
Uniform Magnetic Field ◽  
Equations Of Motion ◽  
Rectangular Channel ◽  
Mhd Flow ◽  
Constant Heat Flux ◽  
Flow And Heat Transfer ◽  
Heating Effects ◽  
Two Sides

The flow of an incompressible viscous fluid under the influence of an applied uniform magnetic field in a rectangular channel with suction at the adjacent two side walls is studied by considering Hall current and Joule heating effects. The rectangular channel is subjected to a uniform suction from top wall and injection from right wall. An external uniform magnetic field is applied perpendicular tothe flow. Two sides (left and bottom) of the channel are kept at two constant but different temperature and other two sides (right and top) are maintained at constant heat flux. Viscous and Joule dissipations are considered in the energy equation. The relevant equations of motion are solved numericallyto yield the velocity and the temperature distribution. The current density is also studied

Extracting Time-Accurate Acceleration Vectors From Nontrivial Accelerometer Arrangements

2015 ◽  
Vol 137 (9) ◽  
Author(s):  
Jennifer A. Franck ◽  
Janet Blume ◽  
Joseph J. Crisco ◽  
Christian Franck
Keyword(s):  
Rotational Velocity ◽  
Equations Of Motion ◽  
Accurate Solution ◽  
Finite Difference Approximation ◽  
Difference Approximation ◽  
Accelerometer Data ◽  
Accurate Analysis ◽  
Centripetal Acceleration ◽  
The Impact ◽  
Acceleration Term

Sports-related concussions are of significant concern in many impact sports, and their detection relies on accurate measurements of the head kinematics during impact. Among the most prevalent recording technologies are videography, and more recently, the use of single-axis accelerometers mounted in a helmet, such as the HIT system. Successful extraction of the linear and angular impact accelerations depends on an accurate analysis methodology governed by the equations of motion. Current algorithms are able to estimate the magnitude of acceleration and hit location, but make assumptions about the hit orientation and are often limited in the position and/or orientation of the accelerometers. The newly formulated algorithm presented in this manuscript accurately extracts the full linear and rotational acceleration vectors from a broad arrangement of six single-axis accelerometers directly from the governing set of kinematic equations. The new formulation linearizes the nonlinear centripetal acceleration term with a finite-difference approximation and provides a fast and accurate solution for all six components of acceleration over long time periods (>250 ms). The approximation of the nonlinear centripetal acceleration term provides an accurate computation of the rotational velocity as a function of time and allows for reconstruction of a multiple-impact signal. Furthermore, the algorithm determines the impact location and orientation and can distinguish between glancing, high rotational velocity impacts, or direct impacts through the center of mass. Results are shown for ten simulated impact locations on a headform geometry computed with three different accelerometer configurations in varying degrees of signal noise. Since the algorithm does not require simplifications of the actual impacted geometry, the impact vector, or a specific arrangement of accelerometer orientations, it can be easily applied to many impact investigations in which accurate kinematics need to be extracted from single-axis accelerometer data.

scholarly journals Stable and Efficient Modeling of Anelastic Attenuation in Seismic Wave Propagation

2012 ◽  
Vol 12 (1) ◽  
pp. 193-225 ◽  
Author(s):  
N. Anders Petersson ◽  
Björn Sjögreen
Keyword(s):  
Wave Equation ◽  
Finite Difference ◽  
Half Space ◽  
Material Model ◽  
Second Order ◽  
Finite Difference Approximation ◽  
Difference Approximation ◽  
Space Problem ◽  
Standard Linear Solid ◽  
Standard Linear

AbstractWe develop a stable finite difference approximation of the three-dimensional viscoelastic wave equation. The material model is a super-imposition of N standard linear solid mechanisms, which commonly is used in seismology to model a material with constant quality factor Q. The proposed scheme discretizes the governing equations in second order displacement formulation using 3N memory variables, making it significantly more memory efficient than the commonly used first order velocity-stress formulation. The new scheme is a generalization of our energy conserving finite difference scheme for the elastic wave equation in second order formulation [SIAM J. Numer. Anal., 45 (2007), pp. 1902-1936]. Our main result is a proof that the proposed discretization is energy stable, even in the case of variable material properties. The proof relies on the summation-by-parts property of the discretization. The new scheme is implemented with grid refinement with hanging nodes on the interface. Numerical experiments verify the accuracy and stability of the new scheme. Semi-analytical solutions for a half-space problem and the LOH.3 layer over half-space problem are used to demonstrate how the number of viscoelastic mechanisms and the grid resolution influence the accuracy. We find that three standard linear solid mechanisms usually are sufficient to make the modeling error smaller than the discretization error.

Unit Mobility Ratio Displacement Calculations for Pattern Floods in Homogeneous Medium

1966 ◽  
Vol 6 (03) ◽  
pp. 217-227 ◽  
Author(s):  
Hubert J. Morel-Seytoux
Keyword(s):  
Oil Recovery ◽  
Numerical Solutions ◽  
Mobility Ratio ◽  
Finite Difference Approximation ◽  
Difference Approximation ◽  
Numerical Techniques ◽  
Sweep Efficiency ◽  
Closed Form Solutions ◽  
Regular Patterns ◽  
Quantities Of Interest

Abstract The influence of pattern geometry on assisted oil recovery for a particular displacement mechanism is the object of investigation in this paper. The displacement is assumed to be of unit mobility ratio and piston-like. Fluids are assumed incompressible and gravity and capillary effects are neglected. With these assumptions it is possible to calculate by analytical methods the quantities of interest to the reservoir engineer for a great variety of patterns. Specifically, this paper presentsvery briefly, the methods and mathematical derivations required to obtain the results of engineering concern, andtypical results in the form of graphs or formulae that can be used readily without prior study of the methods. Results of this work provide checks for solutions obtained from programmed numerical techniques. They also reveal the effect of pattern geometry and, even though the assumptions of piston-like displacement and of unit mobility ratio are restrictive, they can nevertheless be used for rather crude but quick, cheap estimates. These estimates can be refined to account for non-unit mobility ratio and two-phase flow by correlating analytical results in the case M=1 and the numerical results for non-Piston, non-unit mobility ratio displacements. In an earlier paper1 it was also shown that from the knowledge of closed form solutions for unit mobility ratio, quantities called "scale factors" could be readily calculated, increasing considerably the flexibility of the numerical techniques. Many new closed form solutions are given in this paper. INTRODUCTION BACKGROUND Pattern geometry is a major factor in making water-flood recovery predictions. For this reason many numerical schemes have been devised to predict oil recovery in either regular patterns or arbitrary configurations. The numerical solutions, based on the method of finite difference approximation, are subject to errors often difficult to evaluate. An estimate of the error is possible by comparison with exact solutions. To provide a variety of checks on numerical solutions, a thorough study of the unit mobility ratio displacement process was undertaken. To calculate quantities of interest to the reservoir engineer (oil recovery, sweep efficiency, etc.), it is necessary to first know the pressure distribution in the pattern. Then analytical procedures are used to calculate, in order of increasing difficulty: injectivity, breakthrough areal sweep efficiency, normalized oil recovery and water-oil ratio as a function of normalized PV injected. BACKGROUND Pattern geometry is a major factor in making water-flood recovery predictions. For this reason many numerical schemes have been devised to predict oil recovery in either regular patterns or arbitrary configurations. The numerical solutions, based on the method of finite difference approximation, are subject to errors often difficult to evaluate. An estimate of the error is possible by comparison with exact solutions. To provide a variety of checks on numerical solutions, a thorough study of the unit mobility ratio displacement process was undertaken. To calculate quantities of interest to the reservoir engineer (oil recovery, sweep efficiency, etc.), it is necessary to first know the pressure distribution in the pattern. Then analytical procedures are used to calculate, in order of increasing difficulty: injectivity, breakthrough areal sweep efficiency, normalized oil recovery and water-oil ratio as a function of normalized PV injected.

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