Mathematical modelling for nutrient uptake by plant root which is considered as cylindrical

P.S. Avhale a,* and S.B. Kiwneb

Mathematical modelling for nutrient uptake by plant root which is considered as cylindrical

Authors :

P.S. Avhale ^a,*and S.B. Kiwne^b

Author Address :

^a,*Department of Mathematics, Shivaji Arts and Science College Kannad, Dist. Aurangabad (MH), India.
^bHead of Department of Mathematics, Deogiri College Aurangabad, India.

*Corresponding author.

Abstract :

In this article, we drive mathematical model for nutrient uptake by the plant root which is considered as cylindrical, i.e, we obtain concentration of nutrient entering into the root surface by advection diffusion equation. The equation is written in the radial form and solved using Michal Menten boundary condition, which is nonlinear boundary condition. It is found that generally advection diffusion is solved taking Peclet number as zero, then equation reduces to the diffusion equation and solved by Laplace method[9]. But we solve the advection diffusion equation without taking Plect number as zero and solved by re-scaling and using separation of variable which reduces it into Bessel’s equation. For particular solution, we use extreme parameters.