Exact non-classical symmetry solutions of Arrhenius reaction-diffusion

P. Broadbridge, B. H. Bradshaw-Hajek, D. Triadis

Research output: Contribution to journalArticle

8 Citations (Scopus)

Abstract

Exact solutions for nonlinear Arrhenius reaction- diffusion are constructed in n-dimensions. A single relationship between nonlinear diffusivity and the nonlinear reaction term leads to a non-classical Lie symmetry whose invariant solutions have a heat flux that is exponential in time (either growth or decay), and satisfying a linear Helmholtz equation in space. This construction also extends to heterogeneous diffusion wherein the nonlinear diffusivity factorizes to the product of a function of temperature and a function of position. Example solutions are given with applications to heat conduction in conjunction with either exothermic or endothermic reactions, and to soil-water flow in conjunction with water extraction by a web of plant roots.

Original languageEnglish
Article number20150580
JournalProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Volume471
Issue number2184
DOIs
Publication statusPublished - Dec 8 2015

Fingerprint

Reaction-diffusion
diffusivity
plant roots
endothermic reactions
Symmetry
exothermic reactions
Helmholtz equations
water flow
symmetry
Diffusivity
conductive heat transfer
heat flux
soils
Water
Invariant Solutions
Helmholtz equation
Lie Symmetry
decay
products
Helmholtz Equation

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Engineering(all)
  • Physics and Astronomy(all)

Cite this

Exact non-classical symmetry solutions of Arrhenius reaction-diffusion. / Broadbridge, P.; Bradshaw-Hajek, B. H.; Triadis, D.

In: Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 471, No. 2184, 20150580, 08.12.2015.

Research output: Contribution to journalArticle

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