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 language | English |
|---|---|
| Article number | 20150580 |
| Journal | Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences |
| Volume | 471 |
| Issue number | 2184 |
| DOIs | |
| Publication status | Published - Dec 8 2015 |
Fingerprint
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 journal › Article
}
TY - JOUR
T1 - Exact non-classical symmetry solutions of Arrhenius reaction-diffusion
AU - Broadbridge, P.
AU - Bradshaw-Hajek, B. H.
AU - Triadis, D.
PY - 2015/12/8
Y1 - 2015/12/8
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=84956867066&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84956867066&partnerID=8YFLogxK
U2 - 10.1098/rspa.2015.0580
DO - 10.1098/rspa.2015.0580
M3 - Article
AN - SCOPUS:84956867066
VL - 471
JO - Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
JF - Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
SN - 0080-4630
IS - 2184
M1 - 20150580
ER -