Construction of exact solutions to singular perturbation problems for linear ordinary differential equations with power boundary layer

2006 ◽  
Vol 79 (5-6) ◽  
pp. 886-891 ◽  
Author(s):  
Yu. A. Konyaev
Keyword(s):  
Boundary Layer ◽  
Differential Equations ◽  
Singular Perturbation ◽  
Exact Solutions ◽  
Ordinary Differential Equations ◽  
Singular Perturbation Problems ◽  
Linear Ordinary Differential Equations ◽  
Perturbation Problems

Invariant manifolds in singular perturbation problems for ordinary differential equations

1990 ◽  
Vol 116 (1-2) ◽  
pp. 45-78 ◽  
Author(s):  
Kunimochi Sakamoto
Keyword(s):  
Differential Equations ◽  
Singular Perturbation ◽  
Ordinary Differential Equations ◽  
Invariant Manifold ◽  
Invariant Manifolds ◽  
Singular Perturbation Problems ◽  
Manifold Theory ◽  
Perturbation Problems ◽  
Geometric Idea ◽  
Normally Hyperbolic Invariant Manifolds

SynopsisBased on Fenichel's geometric idea, invariant manifold theory is applied to singular perturbation problems. This approach clarifies the nature of outer and inner solutions. A specific condition is given to ensure the existence of heteroclinic connections between normally hyperbolic invariant manifolds. A method to approximate the connections is also presented.

Convective transport of thermal and solutal energy in unsteady MHD Oldroyd-B nanofluid flow

2021 ◽  
Author(s):  
Muhammad Yasir ◽  
Masood Khan ◽  
Awais Ahmed ◽  
Malik Zaka Ullah
Keyword(s):  
Boundary Layer ◽  
Differential Equations ◽  
Thermal Radiation ◽  
Ordinary Differential Equations ◽  
Heat Generation ◽  
Axisymmetric Flow ◽  
Convective Transport ◽  
Buongiorno’S Model ◽  
Linear Ordinary Differential Equations ◽  
Non Linear

Abstract In this work, an analysis is presented for the unsteady axisymmetric flow of Oldroyd-B nanofluid generated by an impermeable stretching cylinder with heat and mass transport under the influence of heat generation/absorption, thermal radiation and first-order chemical reaction. Additionally, thermal and solutal performances of nanofluid are studied using an interpretation of the well-known Buongiorno's model, which helps us to determine the attractive characteristics of Brownian motion and thermophoretic diffusion. Firstly, the governing unsteady boundary layer equation's (PDEs) are established and then converted into highly non-linear ordinary differential equations (ODEs) by using the suitable similarity transformations. For the governing non-linear ordinary differential equations, numerical integration in domain [0, ∞) is carried out using the BVP Midrich scheme in Maple software. For the velocity, temperature and concentration distributions, reliable results are prepared for different physical flow constraints. According to the results, for increasing values of Deborah numbers, the temperature and concentration distribution are higher in terms of relaxation time while these are decline in terms of retardation time. Moreover, thermal radiation and heat generation/absorption are increased the temperature distribution and corresponding boundary layer thickness. With previously stated numerical values, the acquired solutions have an excellent accuracy.

Radiative Unsteady Rarefied Gaseous Flow Over a Stretching Sheet with Velocity Slip and Temperature Jump Effects

2020 ◽  
Vol 87 (3-4) ◽  
pp. 261
Author(s):  
Ram Prakash Sharma ◽  
N. Indumathi ◽  
S. Saranya ◽  
B. Ganga ◽  
A. K. Abdul Hakeem
Keyword(s):  
Boundary Layer ◽  
Differential Equations ◽  
Boundary Conditions ◽  
Ordinary Differential Equations ◽  
Stretching Sheet ◽  
Velocity Slip ◽  
Skin Friction Coefficient ◽  
Gaseous Flow ◽  
Linear Ordinary Differential Equations ◽  
Non Linear

In this study a mathematical analysis has been carried out to scrutinize the unsteady boundary layer flow of an incompressible, rarefied gaseous flow over a vertical stretching sheet with velocity slip and thermal jump boundary conditions in the presence of thermal radiation. Using boundary layer approach and suitable similarity transformations, the governing partial differential equations with the boundary conditions are reduced to a system of non-linear ordinary differential equations. The resulting non-linear ordinary differential equations are solved with the help of fourth order Runge-Kutta method with shooting technique. The results obtained for the velocity profile, temperature profile, skin friction coefficient and the reduced Nusselt number are described through graphs. It is predicted that the velocity and temperature profiles are lower for unsteady flow and has an opposite effect for steady flow.

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