Numerical solution of equations arising in energy transport in non-equilibrium chemically reacting systems

✍ Scribed by B.G. Ong; D.M. Mason

• Publisher: Elsevier Science
• Year: 1976
• Tongue: English
• Weight: 773 KB
• Volume: 31
• Category: Article
• ISSN: 0009-2509
• DOI: 10.1016/0009-2509(76)87009-1

✦ Synopsis

A two-point boundary value method is presented for avoiding the numerical instability which can occur when initial value methods are used for solving the non-linear differential equations describing transport of heat and mass in chemically reacting systems near equilibrium. The instability arises primarily owing to the slight computational errors that arise when the forward and reverse reaction-rate terms are large compared to the net rate. The method used to avoid this instability is to convert the continuity of species equation containing the reaction-rate terms into a second order differential equation in such a manner that small errors in computing the reaction rates do not appreciably affect the solution. Though equations leading to this instability have sometimes been referred to in the past as 'WT," today this term most commonly refers to quite a different situation, namely, a system of equations where at any point the ratio of the largest to smallest eigenvalue is very large. Thus, in this work the term "stiff" will be replaced by "instability." As an example of how to circumvent this-instability, the method is applied to the problem of heat transfer through a reacting gaseous mixture confined in a parallel plate conductivity cell. It is demonstrated that this case presents a more stringent test of the applicability of the method than the case of convective heat transfer.