Open Access. Powered by Scholars. Published by Universities.®
- Discipline
Articles 1 - 2 of 2
Full-Text Articles in Engineering
Approximate Analytical Solution For Mathematical Models Of Thermal Ignition And Non-Isothermal Catalytic Zero Order Reaction In A Spherical Geometry, Moustafa A. Soliman
Approximate Analytical Solution For Mathematical Models Of Thermal Ignition And Non-Isothermal Catalytic Zero Order Reaction In A Spherical Geometry, Moustafa A. Soliman
Chemical Engineering
In this paper an approximate analytical solution for the Frank-Kamenetskii equation modeling thermal ignition without the depletion of the combustibles in a spherical annulus and non-isothermal zero order reaction in spherical catalyst particle is presented. The approximate solution is compared with the numerical solution and is in good agreement with the numerical solution. The approximate solution obtained is valid for all values of the distance parameter. Multiple solutions occur for some range of Frank-Kamenetskii parameter (λ). The multiplicity is infinite for the case of a solid sphere and λ=2.Interesting relation is obtained for λ at the turning points. For the …
A Modified Orthogonal Collocation Method For Reaction Diffusion Problems, Moustafa A. Soliman, Yousef S. Al-Zeghayer, Abdelhamid M. Ajbar
A Modified Orthogonal Collocation Method For Reaction Diffusion Problems, Moustafa A. Soliman, Yousef S. Al-Zeghayer, Abdelhamid M. Ajbar
Chemical Engineering
A low-order collocation method is often useful in revealing the main features such as concentration and temperature profiles and the effectiveness factor for porous catalyst particles. Two modifications are introduced in this paper to make the method more efficient. The first modification is to add an extra collocation point at the center of the particle. It is shown that such extra point introduces a single variable non-linear equation to be solved after obtaining the standard collocation method solution. In the second modification, the polynomial solution obtained from the application of the orthogonal collocation method is transformed to a rational function …