## Abstract

A Laplace transform-based procedure was proposed to calculate the effective time constant for a class of nonlinear diffusion problems. The governing mathematical representation was first estimated with a linear model by omitting the nonlinear term. The solution to this problem was later introduced into the original equation, which was solved with Laplace transforms, resulting in a first-order approximation of the real system's behavior. A time constant was calculated using frequency-domain expressions. Two case studies were considered to illustrate the methodology. As the rate of heat supplied to a rod is raised, the speed at which the temperature reached an equilibrium value decreased. Increasing the maximum velocity in reaction-diffusion transport by a factor of three lowered the time constant by only 1.7%. The applications of this method range from biosensor dynamics to process control.

Original language | English (US) |
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Pages (from-to) | 719-736 |

Number of pages | 18 |

Journal | Chemical Engineering Communications |

Volume | 201 |

Issue number | 6 |

DOIs | |

State | Published - Jun 1 2014 |

## All Science Journal Classification (ASJC) codes

- Chemistry(all)
- Chemical Engineering(all)

## Keywords

- Diffusion
- Effective time constant
- Heat transfer
- Kinetics
- Mathematical modeling
- Nonlinear dynamics