R. A. Joy et al. / Natural Science 3 (2011) 556-565
Copyright © 2011 SciRes. OPEN ACCESS
560
Figure 3. The normalized effectiveness factor η versus Thiele
moduilli φ for various values of parameter α. The curves are
plotted using Eq.13. Here h = –0.135.
effectiveness factor increases with increasing values of
.
6. CONCLUSIONS
A non-linear time independent equation has been
formulated and solved analytically using Homotopy
analysis method. The primary result of this work is the
first approximate calculations of substrate concentrations
and effectiveness factor for non-linear Michaelis-Menten
kinetic scheme. A simple closed form of analytical ex-
pressions of steady-state substrate and effectiveness fac-
tor are given. The analytical expressions for the substrate
concentration profiles for all values of parameters
and
are derived using Homotopy analysis method.
This method is an extremely simple method and it is also
a promising method to solve other non-linear equations.
The extension of this procedure to other direct reaction
of substrate at underlying microdisc electrode surface
seems possible.
7. ACKNOWLEDGEMENTS
This work was supported by the Department of Science and Tech-
nology (DST) Government of India. The authors also thank Mr.M.S.
Meenakshisundaram, Secretary, The Madura College Board, Principal
and S.Thiagarajan Head of the Department of Mathematics, The
Madura College, Madurai, India for their constant encouragement. It is
our pleasure to thank the referees for their valuable comments.
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