An analytic benchmark solution to the linear, time-dependent isothermal laminar flow fission-product plateout problem

Durkee, Joe W.; Lee, C.E.

doi:10.1016/0306-4549(84)90046-x

Cited by 2 publications

(1 citation statement)

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“…Small leaks of these products into the coolant are transported along cylindrical ducts, which then deposit onto the duct wall and undergo radioactive decay. An accurate estimate of these deposits would allow determining maintenance requirements to minimize any possible health hazards to the operators (Durkee, 1984). Durkee and Lee (1984) provide a solution for the estimation of the deposition profile, but the solution is limited due to the mathematical simplification made (i.e.…”

Section: Applicationsmentioning

confidence: 99%

Generalized semi-analytical solution of advection–diffusion–reaction in finite and semi-infinite cylindrical ducts

Mehmani

Balhoff

2014

International Journal of Heat and Mass Transfer

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A semi-analytical solution for the transient advection-diffusion-reaction problem within finite and semi-infinite ducts is derived. The solution allows for general radial-and time-dependent inlet/outlet conditions, complex boundary conditions on the duct wall including adsorption and decay, and arbitrary velocity profiles of the transporting fluid. The only numerical step of the solution is the inverse Laplace transform in the time variable. Therefore, the approach also produces fully analytical steady-state solutions. The solution is verified against computational fluid dynamics (CFD) simulations under various boundary conditions and velocity profiles (Newtonian and power-law), and in all cases good agreement is obtained. Although theoretically applicable to all regimes, the solution is computationally difficult at very high Peclet numbers and very early times due to numerical instabilities as a result of finite precision arithmetic of computers. A convergence analysis is conducted to delineate the boundaries of this limit for two important cases. The solution was derived using a new approach for solving two-dimensional partial differential equations (PDEs) with non-constant coefficients which parallels the Frobenius and power series methods for solving ordinary differential equations (ODEs). The approach reduces the original PDE to a single infinite-order ODE with constant coefficients. The approach is suspected to provide solutions to a large class of PDEs of this type. The solution may find applications in a number of engineering and/or biomedical fields, it can be used to verify numerical simulators, and serve as a simple and easy-toimplement alternative where access to numerical simulators is not available.

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Section: Applicationsmentioning

confidence: 99%