Corrigendum to ‘‘The application of the parametric continuation method for determining steady state diagrams in chemical enginnering’’ [Chem. Eng. Sci. 65/19 (2010) 5411–5414]

2016 ◽  
Vol 152 ◽  
pp. 795
Author(s):  
Marek Berezowski
Keyword(s):  
Steady State ◽  
Continuation Method ◽  
State Diagrams ◽  
Parametric Continuation

Determination of catastrophic sets of a tubular chemical reactor by two-parameter continuation method

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Marek Berezowski
Keyword(s):  
Continuation Method ◽  
Extreme Points ◽  
Chemical Reactor ◽  
Stationary States ◽  
Parameter Continuation Method ◽  
It Systems ◽  
Parametric Continuation ◽  
Parameter Continuation ◽  
Two Parameter

AbstractThe work relates to development and presentation a two-parameter continuation method for determining catastrophic sets of stationary states of a tubular chemical reactor with mass recycle. The catastrophic set is a set of extreme points occurring in the bifurcation diagrams of the reactor. There are many large IT systems that use the parametric continuation method. The most popular is AUTO’97. However, its use is sometimes not convenient. The method developed in this work allows to eliminate the necessity to use huge IT systems from the calculations. Unlike these systems, it can be inserted into the program as a short subroutine. In addition, this method eliminates time-consuming iterations from the calculations.

Steady-State Temperatures in an Infinite Medium Split by a Pair of Coplanar Cracks

1988 ◽  
Vol 110 (2) ◽  
pp. 283-289 ◽  
Author(s):  
Shangchow Chang
Keyword(s):  
Steady State ◽  
Integral Transform ◽  
Continuation Method ◽  
Infinite Medium ◽  
Analytical Continuation ◽  
Crack Plane ◽  
Solution Methods ◽  
Steady State Heat ◽  
Integral Transform Technique ◽  
Coplanar Cracks

This article presents a study on the steady-state heat conduction in an infinite medium containing two coplanar cracks. Using an integral transform technique, formal temperature solutions have first been worked out for both the fundamental symmetric and antisymmetric cases. The explicit and exact expressions for temperatures are then developed via both the conventional inversion transform approach and an analytical continuation method proposed in this paper. Numerical results prepared from analytic and numerical methods are presented in graphic form for temperatures on the horizontal crack plane and on a plane slant to the cracks. The relative merit of various possible solution methods is also discussed.

scholarly journals Variable thickness flow over a rotating disk under the influence of variable magnetic field: An application to parametric continuation method

2020 ◽  
Vol 12 (6) ◽  
pp. 168781402093638 ◽  
Author(s):  
Muhammad Shuaib ◽  
Rehan Ali Shah ◽  
Muhammad Bilal
Keyword(s):  
Magnetic Field ◽  
Heat Transfer ◽  
Variable Thickness ◽  
Numerical Scheme ◽  
Continuation Method ◽  
Finite Difference Methods ◽  
Rotating Disk ◽  
Variable Magnetic Field ◽  
Physical Parameters ◽  
Parametric Continuation

The present work explores the behavior of three-dimensional incompressible viscous fluid flow and heat transfer over the surface of a non-flat stretchable rotating disk. A variable thickness fluid is subjected under the influence of an external variable magnetic field and heat transfer. Navier–Stokes equation is coupled with Maxwell equations to examine the hydrothermal properties of fluid. The basic governing equations of motion are diminished to a system of nonlinear ordinary differential equations using appropriate similarity framework, which are further treated with numerical scheme known as parametric continuation method. The parametric continuation method has combined interesting characteristics of both shooting and implicit finite difference methods. For validity of the present numerical scheme, a comparison with the published work is performed and it is found that the results are in excellent agreement with each other. Numerical and graphical results for the velocity, temperature, and magnetic strength profiles as well as skin fractions and Nusselt number are presented and discussed in detail for various physical parameters. The heat transfer process is reduced with positive increment of no-flatness parameter [Formula: see text], while Prandtl number increases the heat transfer rate at the surface of the disk.

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