scholarly journals Submersion of the system «anchor-tightrope» of longline

2017 ◽  
Vol 188 (1) ◽  
pp. 224-228
Author(s):  
Lyudmila A. Gabryuk ◽  
Viktor I. Gabryuk
Keyword(s):  
Reynolds Number ◽  
Numerical Methods ◽  
Differential Equations ◽  
Variable Mass ◽  
Hydrodynamic Forces ◽  
Inertia Force ◽  
Fishing Gear ◽  
Hydrodynamic Problem ◽  
Calculated Dependence ◽  
Environment Parameters

A hydrodynamic problem for the longline system «anchor-tightrope» in resting fluid is formulated and solved on base of the theory of dynamics for systems with variable mass. The system of initial differential equations is solved by means of numerical methods using the software designed in MathCad-14 environment; parameters of the «anchor-tightrope» system in the process of submersion are calculated. Dependence of the time and velocity of submersion on type of anchor is analyzed taking into account the hydrodynamic forces dependence on Reynolds number. Influence of inertia force is determined. Cited results for dependence of the submersion time for fishing gear elements on depth are overviewed.

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.

Glycemia monitoring

1998 ◽  
Vol 2 ◽  
pp. 23-30
Author(s):  
Igor Basov ◽  
Donatas Švitra
Keyword(s):  
Diabetes Mellitus ◽  
Mathematical Model ◽  
Numerical Methods ◽  
Differential Equations ◽  
Blood Sugar ◽  
Self Regulation ◽  
Physiological System ◽  
Non Linear ◽  
The Mathematical Model

Here a system of two non-linear difference-differential equations, which is mathematical model of self-regulation of the sugar level in blood, is investigated. The analysis carried out by qualitative and numerical methods allows us to conclude that the mathematical model explains the functioning of the physiological system "insulin-blood sugar" in both normal and pathological cases, i.e. diabetes mellitus and hyperinsulinism.

Entropy generation and heat transfer analysis for ferrofluid flow between two rotating disks with variable conductivity

2021 ◽  
pp. 095440622199118
Author(s):  
Anupam Bhandari
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Differential Equations ◽  
Entropy Generation ◽  
Heat Transfer Analysis ◽  
Entropy Generation Rate ◽  
Geometrical Parameters ◽  
Rotating Disks ◽  
Coupled Differential Equations ◽  
Lower Disk

Present model analyze the flow and heat transfer of water-based carbon nanotubes (CNTs) [Formula: see text] ferrofluid flow between two radially stretchable rotating disks in the presence of a uniform magnetic field. A study for entropy generation analysis is carried out to measure the irreversibility of the system. Using similarity transformation, the governing equations in the model are transformed into a set of nonlinear coupled differential equations in non-dimensional form. The nonlinear coupled differential equations are solved numerically through the finite element method. Variable viscosity, variable thermal conductivity, thermal radiation, and volume concentration have a crucial role in heat transfer enhancement. The results for the entropy generation rate, velocity distributions, and temperature distribution are graphically presented in the presence of physical and geometrical parameters of the flow. Increasing the values of ferromagnetic interaction number, Reynolds number, and temperature-dependent viscosity enhances the skin friction coefficients on the surface and wall of the lower disk. The local heat transfer rate near the lower disk is reduced in the presence of Harman number, Reynolds number, and Prandtl number. The ferrohydrodynamic flow between two rotating disks might be useful to optimize the use of hybrid nanofluid for liquid seals in rotating machinery.

Numerical methods for differential algebraic equations

Acta Numerica ◽  
1992 ◽  
Vol 1 ◽  
pp. 141-198 ◽  
Author(s):  
Roswitha März
Keyword(s):  
Numerical Methods ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Differential Algebraic Equations ◽  
Algebraic Equations ◽  
Image Position

Differential algebraic equations (DAE) are special implicit ordinary differential equations (ODE)where the partial Jacobian f′y(y, x, t) is singular for all values of its arguments.

Numerical methods for a class of nonlinear integro-differential equations

CALCOLO ◽  
2012 ◽  
Vol 50 (1) ◽  
pp. 17-33 ◽  
Author(s):  
R. Glowinski ◽  
L. Shiau ◽  
M. Sheppard
Keyword(s):  
Numerical Methods ◽  
Differential Equations
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