ONE-DIMENSIONAL CHAOTIC LAMINAR FLOW WITH COMPETITIVE EXOTHERMIC AND ENDOTHERMIC REACTIONS

2020 ◽  
pp. 1-23
Author(s):  
S. D. WATT ◽  
Z. HUANG ◽  
H. S. SIDHU ◽  
A. C. MCINTOSH ◽  
J. BRINDLEY
Keyword(s):  
Laminar Flow ◽  
Numerical Solution ◽  
Strong Dependence ◽  
Activation Energies ◽  
Steady States ◽  
Chaotic Advection ◽  
Competitive Reaction ◽  
One Dimensional ◽  
Reaction Fronts ◽  
Endothermic Reactions

We consider the numerical solution of competitive exothermic and endothermic reactions in the presence of a chaotic advection flow. The resulting behaviour is characterized by a strong dependence on the competitive reaction history. The burnt temperature is not immediately connected to simple enthalpy calculations, so there is a subtlety in the interplay between the major parameters, notably the Damköhler number, the ratio of the heats of exothermic and endothermic reactions, as well as the ratio of their respective activation energies. This paper seeks to explore the way these parameters affect the steady states of these reaction fronts and their stability.

Approximate Calculation of Pressure Drop in Laminar Flow of Generalized Newtonian Liquid Through Channel of Noncircular Cross Section

1994 ◽  
Vol 59 (3) ◽  
pp. 603-615 ◽  
Author(s):  
Václav Dolejš ◽  
Ivan Machač ◽  
Petr Doleček
Keyword(s):  
Pressure Drop ◽  
Laminar Flow ◽  
Numerical Solution ◽  
Cross Section ◽  
Approximate Calculation ◽  
Newtonian Liquid ◽  
Straight Channel ◽  
Suggested Procedure ◽  
Noncircular Cross Section ◽  
Calculation Results

The paper presents a modification of the equations of Rabinowitsch-Mooney type for an approximate calculation of pressure drop in laminar flow of generalized Newtonian liquid through a straight channel whose cross section forms a simple continuous area. The suitability of the suggested procedure of calculation of pressure drop is demonstrated by the comparison of calculation results with both the published and original results of numerical solution and experiments.

scholarly journals Hydrogenation of alkynyl substituted aromatics over rhodium/silica

2021 ◽  
Author(s):  
Joseph W. Gregory ◽  
S. David Jackson
Keyword(s):  
Cascade Reactions ◽  
Activation Energies ◽  
Competitive Reaction ◽  
Fresh Catalyst ◽  
Hydrogen Flux ◽  
Rate Determining Step ◽  
Surface Hydrogen ◽  
Alkyne Hydrogenation ◽  
Competitive Hydrogenation ◽  
Styrene Hydrogenation

AbstractThe cascade reactions of phenylacetylene to ethylcyclohexane and 1-phenyl-1-propyne to propylcyclohexane were studied individually, under deuterium and competitively at 343 K and 3 barg pressure over a Rh/silica catalyst. Both systems gave similar activation energies for alkyne hydrogenation (56 ± 4 kJ mol−1 for phenylacetylene and 50 ± 4 kJ mol−1 for 1-phenyl-1-propyne). Over fresh catalyst the order of reactivity was styrene > phenylacetylene ≫ ethylbenzene. Whereas with the cascade hydrogenation starting with phenylacetylene, styrene hydrogenated much slower phenylacetylene even once all the phenylacetylene was hydrogenated. The activity of ethylbenzene was also reduced in the cascade reaction and after styrene hydrogenation. These reductions in rate were likely due to carbon laydown from phenylacetylene and styrene. Similar behavior was observed with the 1-phenyl-1-propyne cascade. Deuterium experiments revealed similar positive KIEs for phenylacetylene (2.6) and 1-phenyl-1-propyne (2.1). Ethylbenzene hydrogenation/deuteration gave a KIE of 1.6 obtained after styrene hydrogenation in contrast to the inverse KIE of 0.4 found with ethylbenzene hydrogenation/deuteration over a fresh catalyst, indicating a change in rate determining step. Competitive hydrogenation between phenylacetylene and styrene reduced the rate of phenylacetylene hydrogenation but increased selectivity to ethylbenzene suggesting a change in the flux of sub-surface hydrogen. In the competitive reaction between 1-phenyl-1-propyne and propylbenzene, the rate of hydrogenation of 1-phenyl-1-propyne was increased and the rate of alkene isomerization was decreased, likely due to an increase in the hydrogen flux for hydrogenation and a decrease in the hydrogen species active in methylstyrene isomerization.

scholarly journals EXACT SOLUTION OF AN IRREVERSIBLE ONE-DIMENSIONAL MODEL WITH FULLY BIASED SPIN EXCHANGES

1996 ◽  
Vol 10 (25) ◽  
pp. 3451-3459 ◽  
Author(s):  
ANTÓNIO M.R. CADILHE ◽  
VLADIMIR PRIVMAN
Keyword(s):  
Exact Solution ◽  
Domain Wall ◽  
Nearest Neighbor ◽  
Spin Exchange ◽  
Initial Conditions ◽  
Strong Dependence ◽  
Zero Temperature ◽  
Dimensional Model ◽  
One Dimensional ◽  
Temperature Dynamics

We introduce a model with conserved dynamics, where nearest neighbor pairs of spins ↑↓ (↓↑) can exchange to assume the configuration ↓↑ (↑↓), with rate β(α), through energy decreasing moves only. We report exact solution for the case when one of the rates, α or β, is zero. The irreversibility of such zero-temperature dynamics results in strong dependence on the initial conditions. Domain wall arguments suggest that for more general, finite-temperature models with steady states the dynamical critical exponent for the anisotropic spin exchange is different from the isotropic value.

Numerical solution of two-dimensional first kind Fredholm integral equations by using linear Legendre wavelet

2016 ◽  
Vol 14 (01) ◽  
pp. 1650004 ◽  
Author(s):  
M. Tahami ◽  
A. Askari Hemmat ◽  
S. A. Yousefi
Keyword(s):  
Integral Equation ◽  
Tensor Product ◽  
Numerical Solution ◽  
Fredholm Integral Equation ◽  
Fredholm Integral Equations ◽  
Wavelet Basis ◽  
Two Dimensional ◽  
Legendre Wavelets ◽  
Numerical Examples ◽  
One Dimensional

In one-dimensional problems, the Legendre wavelets are good candidates for approximation. In this paper, we present a numerical method for solving two-dimensional first kind Fredholm integral equation. The method is based upon two-dimensional linear Legendre wavelet basis approximation. By applying tensor product of one-dimensional linear Legendre wavelet we construct a two-dimensional wavelet. Finally, we give some numerical examples.

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