Title

Exact First Integrals For A Lane-Emden Equation Of The Second Kind Modeling A Thermal Explosion In A Rectangular Slab

Keywords

Bifurcation; First integrals; Lane-Emden equation; Thermal explosion

Abstract

The primary focus of the present paper will be the study of the exact first integral of a Lane-Emden equation of the second kind modeling a thermal explosion in a rectangular slab. Such results generalize those of Harley and Momoniat [Harley, C., Momoniat, E., 2008. J. Math. Anal. Appl. 344, 757-764], in which first integrals up to order were considered for the model. In particular, our results both generalize their results in the small regime and are valid in the large regime, for the k=0 case. As in Harley and Momoniat, we find that there is a critical value of δ beyond which solutions do not exist. Interestingly, we find that this critical value of δ is quite different than the one derived in Harley and Momoniat, thanks to the fact that we obtain exact, and not approximate, relations. Furthermore, we show that while multiple solutions exist in the case of thermal explosion in a rectangular slab, only one such solution is physically meaningful (positive over the domain). Hence, the physically meaningful solution is unique. Our exact analytical results are shown to be in agreement with numerical simulations. © 2011 Elsevier Ltd.

Publication Date

12-1-2011

Publication Title

New Astronomy

Volume

16

Issue

8

Number of Pages

492-497

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1016/j.newast.2011.04.006

Socpus ID

79957882042 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/79957882042

This document is currently not available here.

Share

COinS