Numerical prediction of combined laminar convection in isothermal vertical tubes via the method of lines

We consider a two-step Sal’nikov reaction scheme occurring within a compressible viscous gas. The first step of the reaction may be either endothermic or exothermic, while the second step is strictly exothermic. Energy may also be lost from the system due to Newtonian cooling. An asymptotic solution for temperature perturbations of small amplitude is presented using the methods of strained coordinates and multiple scales, and a travelling wave solution with a sech-squared profile is derived. The method of lines is then used to approximate the full system with a set of ordinary differential equations, which are integrated numerically to track accurately the evolution of the reaction front. This numerical method is used to verify the asymptotic solution and investigate behaviours under different conditions. Using this method, temperature waves progressing as pulsatile fronts are detected at appropriate parameter values.

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An Application of the Method of Lines in Biological Mass Transfer

Biotechnology Progress ◽

10.1002/btpr.5420010411 ◽

1985 ◽

Vol 1 (4) ◽

pp. 269-272 ◽

Cited By ~ 3

Author(s):

Peter J. D. Mayes

Keyword(s):

Mass Transfer ◽

Method Of Lines ◽

The Method Of Lines

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Enhanced Reactor Performance with Pressure and Vacuum Swing Reaction

International Journal of Chemical Reactor Engineering ◽

10.2202/1542-6580.1143 ◽

2004 ◽

Vol 2 (1) ◽

Cited By ~ 2

Author(s):

Vincent G Gomes

Keyword(s):

Method Of Lines ◽

Fixed Bed ◽

Downstream Processing ◽

Operating Conditions ◽

Reactor Performance ◽

Orthogonal Collocation ◽

The Method Of Lines ◽

Dynamic Experiments ◽

Product Separation ◽

Pressure Swing

Product separation and regeneration of sorbent was accomplished in a novel pressure swing reactor through pressurisation, adsorption, blowdown and purge steps. The switching from sorption to reaction to regeneration was tested in a two bed sorption/reaction apparatus. Models developed for the mass and momentum transfer in the catalyst bed and sorber, were solved using orthogonal collocation within the method of lines. The effects of operating conditions and cycle configurations on performance were assessed. The results from dynamic experiments with propene metathesis to produce ethene and 2-butene in a fixed-bed catalytic reactor were in agreement with model predictions. Both pressure and vacuum swing demonstrated that conversion and product quality can be enhanced by periodic cycling with greater separation obtained with vacuum swing. The separation of products help reduce the downstream processing costs of exit mixtures, enable reactant utilisation by recycling and improve product handling at subsequent stages. The efficacy of the periodic separating reactor in terms of conversion, product purity and recovery were investigated.

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The method of lines for the analysis of mechanical structures

2012 13th International Thermal, Mechanical and Multi-Physics Simulation and Experiments in Microelectronics and Microsystems ◽

10.1109/esime.2012.6191784 ◽

2012 ◽

Author(s):

Amirali Taghavi ◽

Larissa Vietzorreck

Keyword(s):

Method Of Lines ◽

The Method Of Lines

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Periodic Forced Convection in a Darcy Metallic Foam: The LTNE Model

Volume 7: Fluids and Heat Transfer, Parts A, B, C, and D ◽

10.1115/imece2012-87276 ◽

2012 ◽

Author(s):

Eugenia Rossi di Schio ◽

Antonio Barletta

Keyword(s):

Forced Convection ◽

Outer Boundary ◽

Method Of Lines ◽

Mean Value ◽

Entrance Region ◽

Solid Matrix ◽

Metallic Foam ◽

The Method Of Lines ◽

Thermal Entrance Region ◽

Thermal Entrance

The present paper studies the thermal entrance region in a concentric annular duct filled by a fluid saturated porous metallic foam, with reference to steady forced convection and to a thermal boundary condition given by a wall temperature longitudinally varying with a sinusoidal law. The effect of viscous dissipation in the fluid is taken into account, and a two-temperature model is employed in order to evaluate separately the local fluid and solid matrix temperatures. The governing equations in the thermal entrance region are solved numerically by the method of lines. The Nusselt numer and its mean value in an axial period is evaluated, with reference both to the inner and the outer boundary.

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