A FIRST-ORDER TIME CONSTANT ESTIMATION FOR NONLINEAR DIFFUSION PROBLEMS

作者：Simon Laurent^*; Ospina Juan

来源：Chemical Engineering Communications, 2014, 201(6): 719-736.

DOI：10.1080/00986445.2013.785948

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

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%26apos;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.

• 出版日期2014-6-3