Inversion of a Laplace Transform arising from a Problem in Applied Chemical Kinetics

Abstract

THE solution to a problem (Wood, T., unpublished work) arising from an analysis of a closed circuit consisting of a stirred-tank reactor and a tubular reactor in series, with first-order, isothermal, irreversible kinetics, involves finding the inverse of the Laplace transform : where β1, β2, β3 are known, positive, constants. The transform can be re-arranged: Since no tabulated transform could be found, the denominator was expanded as a power series, giving : The inverse of the transform is now readily shown to be1: where H(tnβ3) = 0 when tnβ3; H(tnβ3) = 1 where t > nβ3

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References

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    Carslaw, H. S., and Jaeger, J. C., Operational Methods in Applied Mathematics (Oxford Univ. Press, 1953).

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WOOD, T. Inversion of a Laplace Transform arising from a Problem in Applied Chemical Kinetics. Nature 191, 589 (1961). https://doi.org/10.1038/191589a0

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