Mathematical Modeling of Water Profile surrounding the root surface in Soil, in Cortex Tissues and in Xylem Tubes while Root Uptake the Water from the Soil

Avhale.P.S; Kiwne S.B

doi:https://doi.org/10.14445/22315373/IJMTT-V11P501

International Journal of Mathematics Trends and Technology

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Volume 11 | Number 1 | Year 2014 | Article Id. IJMTT-V11P501 | DOI : https://doi.org/10.14445/22315373/IJMTT-V11P501

Mathematical Modeling of Water Profile surrounding the root surface in Soil, in Cortex Tissues and in Xylem Tubes while Root Uptake the Water from the Soil

Avhale.P.S, Kiwne S.B

Abstract

The root system of plant uptake water and nutrient from the soil. The present paper explain systematic description of mathematical expression for water profile surrounding the root surface in porous soil, in root surface, i.e, in cortex tissues, and in stem, i.e., in xylem tune while root uptake water from the soil. We use basic principles of physics and uid-dynamics of water ow. Tiny xylem tubes as water transport channel in the stem, root surface work as semipermeable membrane and soil is considered as porous medium. We resolve mathematical model of water profile using variety of boundary conditions by analytically. As new approach, we obtain water profile surrounding the root surface by using constant internal pressure in the root as boundary condition and we solve radial diffusion equation by using Goodman integral transformation and separation of variables.

Keywords

Plant root, water uptake by root, water profile, soil water pressure, water pressure in xylem and water pressure at inner radius of root.

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Citation :

Avhale.P.S, Kiwne S.B, "Mathematical Modeling of Water Profile surrounding the root surface in Soil, in Cortex Tissues and in Xylem Tubes while Root Uptake the Water from the Soil," International Journal of Mathematics Trends and Technology (IJMTT), vol. 11, no. 1, pp. 1-9, 2014. Crossref, https://doi.org/10.14445/22315373/IJMTT-V11P501