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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 …
Approximate Solution For The Lane-Emden Equation Of The Second Kind In A Spherical Annulus, Moustafa A. Soliman
Approximate Solution For The Lane-Emden Equation Of The Second Kind In A Spherical Annulus, Moustafa A. Soliman
Chemical Engineering
In this paper, we derive accurate approximate solution of Lane-Emden equation of the second kind in a spherical annulus geometry. The approximate solution is obtained by analytic arguments, and perturbation methods in terms of small and large radial distance parameter. The approximate solution is compared with the numerical solution. The approximate solution obtained is valid for all values of the radial distance parameter. Our best approximation has a maximum relative error in the dependent variable of 20%. In most cases it is much less than this value. This maximum error decreases as the radius of the annulus increases.