A chemical engineering example for lagurre equation

[valentine_18h]

Is there anybody here can give me a chemical engineering example that the final differential equation will be LAGUERRE ?

 

[Astronuc]

I've tried finding an example that wasn't buried in a journal. Still working on it.

Laguerre functions/polynomials are obviously the solutions of the Laguerre differential equation:

x y'' + (1-x) y' + $\lambda$ y = 0.

http://www.math.uu.nl/people/ruijgrok/Cestlaguerre2.pdf

http://en.wikipedia.org/wiki/Laguerre_polynomials

http://mathworld.wolfram.com/LaguerrePolynomial.html
http://mathworld.wolfram.com/LaguerreDifferentialEquation.html

http://www.physics.drexel.edu/~tim/open/hydrofin/hyd.html

http://arxiv.org/PS_cache/math/pdf/0610/0610953v1.pdf


Laguerre functions show up in process control - http://www.chemengr.ucsb.edu/~ceweb/faculty/seborg/pdfs/Book_review_Cluett_pub.pdf

 

[tacman]

One potential example in chemical engineering where the Laguerre equation may be used is in the study of reaction kinetics. The Laguerre equation is a type of differential equation that is commonly used to model the behavior of chemical reactions in a system.

For instance, let's say we have a chemical reaction taking place in a batch reactor, where the concentration of the reactant is changing over time. The rate of this reaction can be described by a differential equation, and depending on the specific reaction and conditions, this equation may take the form of the Laguerre equation.

The Laguerre equation takes into account the distribution of reactant molecules in the system, as well as the rate at which they react with each other. It can also account for factors such as temperature and pressure, which can influence the reaction rate.

By solving the Laguerre equation, we can obtain valuable information about the reaction kinetics, such as the rate constant and the order of the reaction. This information can then be used to optimize the reaction conditions and improve the efficiency of the process.

Overall, the Laguerre equation is just one tool that chemical engineers can use to better understand and predict the behavior of chemical reactions in various systems. It is a powerful tool that helps us to design and optimize processes in industries such as pharmaceuticals, food and beverage, and petrochemicals.