Numerical Analysis for the Synthesis of Biodiesel Using Spectral Relaxation Method

Biodiesel is an alternative diesel fuel chemically defined as themono-alkyl esters of long chain fatty acids derived from vegetable oils or animal fat. It is becoming more attractive as an alternative fuel due to the depleting fossil fuel resources. A mathematical model for the synthesis of biodiesel from vegetable oils and animal fats is presented in this study. Numerical solutions of the model are found using a spectral relaxation method. The method, originally developed for boundary value problems, is an iterative scheme based on the Chebyshev spectral collocation method developed by decoupling systems of equations using Gauss-Seidel type of techniques. The effects of the reaction rate constants and initial concentrations of the reactants on the amount of the final product are being investigated. The accuracy of the numerical results is validated by comparison with known analytical results and numerical results obtained using ode45, an efficient explicit 4th and 5th order Runge-Kutta method used to integrate both linear and nonlinear differential equations.