New integral representations of analytical solutions to boundary-value problems of nonstationary transfer in regions with moving boundaries

1999 ◽  
Vol 72 (5) ◽  
pp. 794-807 ◽  
Author(s):  
É. M. Kartashov
Keyword(s):  
Boundary Value Problems ◽  
Analytical Solutions ◽  
Boundary Value ◽  
Integral Representations ◽  
Moving Boundaries

scholarly journals An axially symmetric forced convection problem

1975 ◽  
Vol 20 (1) ◽  
pp. 1-17
Author(s):  
J. A. Belward
Keyword(s):  
Boundary Value Problems ◽  
Boundary Value ◽  
Convection Heat Transfer ◽  
Fundamental Solutions ◽  
Integral Representations ◽  
Original Equation ◽  
Transfer Model ◽  
Axially Symmetric ◽  
Simple Diffusion ◽  
Diffusion Convection

AbstractA simple diffusion-convection heat transfer model is formulated which leads to an axially symmetric partial differential equation. The equation is shown to be closely related to a second one which is adjoint to the original equation in one variable can and be interpreted as a description of another diffusion-convection model. Fundamental solutions of the original equation are constructed and interpreted with reference to both models. Some boundary value problems are solved in series form and integral representations of the solutions are also given. The boundary value problems are shown to be equivalent to an integral equation and the correspondence between the two formulations is understood in terms of the two diffusion-convection problems. A Péclet number is defined in one of the boundary value problems and the behaviour of the solutions is studied for large and small values of this parameter.

scholarly journals Solution of boundary value problems with moving boundaries by using an approximate method for constructing solutions of integro – differential equations

2021 ◽  
Vol 2131 (2) ◽  
pp. 022080
Author(s):  
V L Litvinov ◽  
A V Tarakanov
Keyword(s):  
Differential Equations ◽  
Boundary Value Problems ◽  
Initial Conditions ◽  
Boundary Value ◽  
Hyperbolic Type ◽  
Moving Boundaries ◽  
External Disturbances ◽  
Small Parameters ◽  
Dimensionless Variables ◽  
Made In

Abstract The problem of oscillations of objects with moving boundaries, formulated as a differential equation with boundary and initial conditions, is a non-classical generalization of a problem of hyperbolic type. To facilitate the construction of a solution to this problem and justify the choice of a solution form, equivalent integro-differential equations are constructed with symmetric and time-dependent kernels and integration limits varying in time. The method for constructing solutions of integro-differential equations is based on the direct integration of differential equations in combination with the standard replacement of the desired function with a new variable. The method is extended to a wider class of model boundary value problems that take into account the bending stiffness of an oscillating object, the resistance of the environment, and the rigidity of the substrate. Particular attention is paid to the consideration of the most common in practice case when external disturbances act at the boundaries. The solution is made in dimensionless variables accurate to second-order values of smallness with respect to small parameters characterizing the speed of the border.

Steady Motion of a Thread Over a Rotating Roller

1994 ◽  
Vol 61 (1) ◽  
pp. 16-22 ◽  
Author(s):  
R.-J. Yang
Keyword(s):  
Circular Cylinder ◽  
Boundary Conditions ◽  
Boundary Value Problems ◽  
Analytical Solutions ◽  
Boundary Value ◽  
Steady Motion ◽  
Dynamic Equations ◽  
Initial Value ◽  
Perturbation Result ◽  
The Third

Dynamic equations of steady motion governing the behavior of threads over rotating arbitrary-axisymmetric rollers are derived. Various types of boundary conditions resulting in initial value or boundary value problems are discussed. Analytical solutions for the case of a circular cylinder are found. Two of the integrals obtained are exact. The third one, being a perturbation result, is thus approximate. Comparisons of results for a circular cylinder with those for tapered and parabolic rollers are made.

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