KIRTHIGA MURALI*, M  ABUKHALED**, S  BALAMURUGAN*, L  RAJENDRAN***^#

*Department of Mathematics, Government Arts and Science College, Melur, India

**Department of Mathematics and Statistics, American University of Sharjah, United Arab Emirates

***Department of Mathematics, Academy of Maritime Education and Training (AMET), Deemed to be University, Chennai-603112, India 300041

Mathematical models of ethanol fermentation in continuous conventional bioreactor (CCBR) and continuous membrane bioreactor (CMBR) are discussed theoretically. Each of these models is a system of nonlinear equations containing nonlinear terms related to Monod model for each retention time at non-steady condition. Analytical expressions of cell growth, glucose consumption, and ethanol production are obtained using a new approach of the homotopy perturbation method.  A detailed study of the parameters effects on each of the governing systems is also presented. The obtained analytical solution is shown to be in strong agreement with most reliable numerical methods.

Key words: Ethanol fermentation, membrane bioreactor, mathematical modelling, new homotopy perturbation method, nonlinear equations.

Corresponding author’s e-mail: raj_sms@rediffmail.com