Renewable energy biodiesel: a mathematical approach from ecology to production

Paper presented at the 3rd Strathmore International Mathematics Conference (SIMC 2015), 3 - 7 August 2015, Strathmore University, Nairobi, Kenya.Biodiesel is one of promising renewable energy source and used as an alternative of conventional hydrocarbon fuels. Jatropha curcas plant oil (JCPO) is the most cost effective sources of biodiesel. The plant can be cultivated in wastelands and grows on almost any type of territory, even on sandy and saline soils. Judicious agricultural practices and effective crop management of Jatropha curcas is preliminary requisite to get maximum yield of oil. Production of biodiesel by transesterification of Jatropha oil significantly depends on four reaction parameters viz., reaction time, temperature, oil to alcohol molar ratio and stirrer speed. In this work, we have formulated a mathematical model of Jatropha curcas plant, which is affected by many type of pest with the aim to control the pest through Nuclear Polyhedrosis Virus (NPV). Here we have also concentrated on insecticide spraying as controlling measure to reduce the pest, to get maximum yield of Jatropha seeds, which gives Jatropha oil. We have also shown the effect of different variants on mass transfer in biodiesel production from JC oil and how the control theoretic approach flags the maximum production of biodiesel under the mathematical paradigm. Our analytical results provide an idea of the cost effective faster rate of biodiesel production, which satisfies our numerical conclusions