Equivalent circuit for transient conduction and convection systems
Bassam Sabry Mohammad Abdelnabi · 2007
Transient response of a natural convection system is investigated by numerical simulation using FLUENT code. An Integrator Circuit analogy was recently proposed for natural convection system. The proposed analogy was further confirmed by these recent simulations. New simulation results also suggest that a natural convection system acts as a “Low Pass” filter for transients. Transient transmission/ attenuation factor was found to be a function of both fluid properties and the flow characteristics. Transmission/attenuation factor was also found to be a strong function of fluctuation frequency. These results may prove a significant design tool for Gen IV natural convection system particularly for LFR. Explicit formulas for the elements of the inverse of tridiagonal matrices are developed. The formulas are recursive and applicable to symmetric, non-symmetric, equal and non-equal coefficient matrices. For the case of a general tridiagonal matrix four recursive formulas are developed to obtain the elements of the matrix inverse. All formulas are deduced based on the fact that a matrix multiplied by its inverse result in a unit matrix. Also three special cases are discussed. First is the inverse of a symmetric tridiagonal matrix. Second is the inverse of a tridiagonal Toeplitz symmetric matrix. Third is the inverse for a general constant diagonal matrix (Toeplitz). These results are very helpful in economical simulation of reactor physics, heat and mass transport, electrical circuit solution, fluid flow and many other engineering problems.