On the Mathematical Model of the Biomechanics of Green Plants
N. O. Uka *
Department of Mathematics and Statistics, University of Port-Harcourt, Nigeria.
J. D. Olisa
Department of Mathematics and Statistics, University of Port-Harcourt, Nigeria.
*Author to whom correspondence should be addressed.
Abstract
This study considers the biomechanics in the stem of green plants. The process of translocation and transpiration is discussed. The coupled non-linear differential equations governing the motion of the flow were non-dimensionlized and then solved using the homotopy perturbation method. The effects of various parameters such as Schmidt number, porosity, buoyancy forces (thermal and concentration Grashof numbers) and aspect ratio embedded in the flow were examined on the concentration field. The results showed that increasing the porosity, Schmidt number, Sherwood number and aspect ratio resulted to a decrease in the concentration field whereas increase in the buoyancy forces had a positive effect on the flow by increasing its concentration and hence enhancing the growth and productivity of the plant.
Keywords: Biomechanics, xylem flow, phloem flow, Homotopy Perturbation Method (HPM).