R. A. Joy et al. / Natural Science 3 (2011) 556-565

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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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