scholarly journals An Approximate Solution for Flow between Two Disks Rotating about Distinct Axes at Different Speeds

2007 ◽  
Vol 2007 ◽  
pp. 1-16 ◽  
Author(s):  
H. Volkan Ersoy
Keyword(s):  
Reynolds Number ◽  
Approximate Solution ◽  
Angular Velocity ◽  
Analytical Solution ◽  
Viscous Fluid ◽  
Approximate Analytical Solution ◽  
Velocity Difference ◽  
Small Angular Velocity

The flow of a linearly viscous fluid between two disks rotating about two distinct vertical axes is studied. An approximate analytical solution is obtained by taking into account the case of rotation with a small angular velocity difference. It is shown how the velocity components depend on the position, the Reynolds number, the eccentricity, the ratio of angular speeds of the disks, and the parameters satisfying the conditionsu=0andν=0in midplane.

The slow motion of a sphere in a rotating, viscous fluid

1964 ◽  
Vol 20 (2) ◽  
pp. 305-314 ◽  
Author(s):  
Stephen Childress
Keyword(s):  
Reynolds Number ◽  
Angular Velocity ◽  
Viscous Fluid ◽  
Classical Problem ◽  
Slow Motion ◽  
Reynolds Numbers ◽  
Constant Angular Velocity ◽  
Axis Of Rotation ◽  
Small Reynolds Numbers ◽  
Analytical Result

The uniform, slow motion of a sphere in a viscous fluid is examined in the case where the undisturbed fluid rotates with constant angular velocity Ω and the axis of rotation is taken to coincide with the line of motion. The various modifications of the classical problem for small Reynolds numbers are discussed. The main analytical result is a correction to Stokes's drag formula, valid for small values of the Reynolds number and Taylor number and tending to the classical Oseen correction as the last parameter tends to zero. The rotation of a free sphere relative to the fluid at infinity is also deduced.

scholarly journals Magnetohydrodynamic Viscous Fluid Flow Between Parallel Plates with Base Injection and Top Suction With an Angular Velocity

2019 ◽  
Vol 9 (1) ◽  
pp. 1528-1530
Keyword(s):  
Reynolds Number ◽  
Fluid Flow ◽  
Angular Velocity ◽  
Viscous Fluid ◽  
Incompressible Liquid ◽  
Speed Profile ◽  
Parallel Plates ◽  
Liquid Stream ◽  
Viscous Fluid Flow ◽  
Vertical Speed

In this article manages the issue of stable electrically lead laminar progression of a gooey incompressible liquid stream associating two parallel permeable plates of a divert in the event of a transverse attractive field through base infusion and top suction. Dependable vertical stream is made and controlled by a weight slope. Vertical speed is enduring everywhere in the field stream. It implies v=vw=constant. Answer for little and huge Reynolds number is talk about and the diagram of speed profile for stream including parallel permeable plate with base infusion and top suction through a rakish speed Ω has been considered

Solute transport during unsteady, unsaturated soil water flow - the pulse input

Soil Research ◽  
1987 ◽  
Vol 25 (3) ◽  
pp. 223 ◽  
Author(s):  
WJ Bond
Keyword(s):  
Approximate Solution ◽  
Analytical Solution ◽  
Unsaturated Soils ◽  
Approximate Analytical Solution ◽  
Tritiated Water ◽  
Chloride Ion ◽  
Factors Affecting ◽  
Pulse Input ◽  
Structurally Stable ◽  
Good Agreement

A general approximate analytical solution was derived for the movement and dispersion of a solute pulse during unsteady flow of water in unsaturated soils. Two types of pulse were considered: that arising from a non-uniform distribution of solute initially in the soil, and that arising from a change in concentration of solute in the water supply. The movement of pulses of tritiated water and chloride ion was investigated experimentally for the specific case of constant flux horizontal infiltration of water into a strongly aggregated, structurally stable clay soil. Good agreement between the measured distributions of tritium and those predicted using the approximate solution confirmed the validity of the approximate solution. Agreement was much poorer for chloride. The approximate analytical solution was also used to examine factors affecting the shape of solute pulses. It was found that pulses may be asymmetric at short times, but that they rapidly become symmetric as time increases.

scholarly journals Magnetohydro Dynamic Steady Flow Between Two Parallel Porous Plates of a Viscous Fluid Under Angular Velocity with Inclined Magnetic Field

2019 ◽  
Vol 8 (4) ◽  
pp. 615-619
Keyword(s):  
Magnetic Field ◽  
Reynolds Number ◽  
Angular Velocity ◽  
Viscous Fluid ◽  
Inclined Magnetic Field ◽  
Fluid Stream ◽  
Course Of Action ◽  
Game Plan ◽  
Differential Condition ◽  
Comparative Rate

The Model is made as the Steady Magnetohydro dynamic streams with an exact speed between parallel penetrable plates are considered. The issue is seen methodically by using comparability change, whose game plan oversees growing fluid stream with a dashing velocity. The Major Applications of Magnetohydro dynamic (MHD) are the controller of generators, the system containing Cooling and thermal structures, improvement of polymer, Fuel industries etc. The objective of this paper is to look at the Steady Magnetohydro dynamic stream of thick fluid with a saucy speed between parallel porous plates when the fluid forced to their back position by the way of the dividers of each partition at a comparative rate. The issue is decreased to a third solicitation direct differential condition which depends upon a Suction Reynolds number R and M1 for which a right course of action is gotten.

The slow translation of a sphere in a rotating viscous fluid

1982 ◽  
Vol 117 ◽  
pp. 251-267 ◽  
Author(s):  
S. C. R. Dennis ◽  
D. B. Ingham ◽  
S. N. Singh
Keyword(s):  
Reynolds Number ◽  
Partial Differential Equations ◽  
Numerical Methods ◽  
Angular Velocity ◽  
Finite Difference ◽  
Differential Equations ◽  
Viscous Fluid ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Partial Differential

The motion of a sphere along the axis of rotation of an incompressible viscous fluid that is rotating as a solid mass is investigated by means of numerical methods for small values of the Reynolds and Taylor numbers. The Navier–Stokes equations governing the steady axisymmetric flow can be written as three coupled, nonlinear, elliptic partial differential equations for the stream function, vorticity and rotational velocity component. Two numerical methods are employed to solve these equations. The first is the method of series truncation in which the dependent variables are expressed as series of orthogonal Gegenbauer functions and the equations of motion are then reduced to three coupled sets of ordinary differential equations, which are integrated numerically subject to their boundary conditions. In the second method, specialized finite–difference techniques of solution are applied to the two-dimensional partial differential equations. These techniques employ finite-difference equations with coefficients that depend upon the exponential function; a particularly suitable form of approximation for use in calculating numerical solutions is obtained by expanding the exponential coefficients in powers of their exponents.Calculated results obtained by the two methods are in good agreement with each other. The calculations have been carried out according to theoretical assumptions that simulate the experiments of Maxworthy (1965) in which the sphere experiences no resultant torque exerted by the surrounding fluid and is free to rotate with constant angular velocity. Numerical estimates of this angular velocity and of the drag exerted by the fluid on the sphere are found to agree well with the experimental results for Reynolds and Taylor numbers in the range from zero to unity. The results for small values of the Reynolds number are also consistent with theoretical work of Childress (1963, 1964) which is valid as the Reynolds number tends to zero.

Half Sommerfeld Approximation for Finite Journal Bearings

1963 ◽  
Vol 85 (3) ◽  
pp. 435-438 ◽  
Author(s):  
J. V. Fedor
Keyword(s):  
Approximate Solution ◽  
Analytical Solution ◽  
Reynolds Equation ◽  
Approximate Analytical Solution ◽  
Journal Bearings ◽  
Finite Form ◽  
Oil Film

An approximate analytical solution is developed for full journal bearings which includes the effects of bearing finiteness and an incomplete oil film. The approximate solution is obtained by modifying the complete oil film solution to Reynolds equation. The developed equations are in finite form and are simple to evaluate. Calculated values agree well with published computer solutions.

Modified Lanczos Method for Optimal Polynomial Approximation of the Solution of Differential Equations with Polynomial Coefficients

1991 ◽  
Vol 02 (01) ◽  
pp. 243-245
Author(s):  
A.S. BERDNICOV
Keyword(s):  
Differential Equation ◽  
Approximate Solution ◽  
Analytical Solution ◽  
Approximate Analytical Solution ◽  
Analytical Form ◽  
Lanczos Method ◽  
Physical Models ◽  
Strict Solution ◽  
Polynomial Coefficients ◽  
Optimal Polynomial

The construction of an approximate analytical solution of a differential equation is an important task for a variety of physical models. A solution in analytical form allows to investigate the properties of a model, and the use of numerical methods allows to construct a parametrized approximate solution when the strict solution is absent.

Numerical Approximations to Solution of Biochemical Reaction Model

2011 ◽  
Vol 9 (1) ◽  
Author(s):  
Ahmet Yildirim ◽  
Ahmet Gökdogan ◽  
Mehmet Merdan
Keyword(s):  
Analytical Solution ◽  
Approximate Analytical Solution ◽  
Transformation Method ◽  
Reaction Model ◽  
Biochemical Reaction ◽  
Graphical Form ◽  
Kutta Method ◽  
Transform Method ◽  
Runge Kutta Method ◽  
Differential Transform

In this paper, approximate analytical solution of biochemical reaction model is used by the multi-step differential transform method (MsDTM) based on classical differential transformation method (DTM). Numerical results are compared to those obtained by the fourth-order Runge-Kutta method to illustrate the preciseness and effectiveness of the proposed method. Results are given explicit and graphical form.

New Approximate Analytical Solution of the Diode-Resistance Equation

2021 ◽  
pp. 153665
Author(s):  
José A. Gazquez ◽  
Manuel Fernandez-Ros ◽  
Blas Torrecillas ◽  
José Carmona ◽  
Nuria Novas
Keyword(s):  
Analytical Solution ◽  
Approximate Analytical Solution ◽  
Resistance Equation
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