Narrow Results

This paper aims to look into the determination of effective area-average concentration and dispersion coefficient associated with unsteady flow through a small-diameter tube where a solute undergoes first-order chemical reaction both within the fluid and at the boundary. The reaction consists of a reversible component due to phase exchange between the flowing fluid and the wall layer, and an irreversible component due to absorption into the wall. To understand the dispersion, the governing equations along with the reactive boundary conditions are solved numerically using the Finite Difference Method. The resultant equation shows how the dispersion coefficient is influenced by the first-order chemical reaction. The effects of various dimensionless parameters e.g. Da (the Damkohler number), α (phase partitioning number) and Γ (dimensionless absorption number) on dispersion are discussed. One of the results exposes that the dispersion coefficient may approach its steady-state limit in a short time at a high value of Damkohler number (say Da ≥ 10) and a small but nonzero value of absorption rate (say Γ ≤ 0.5).

In this paper, an efficient numerical method is introduced for solving the fractional (Caputo sense) Fisher equation. We use the spectral collocation method which is based upon Chebyshev approximations. The properties of Chebyshev polynomials of the third kind are used to reduce the proposed problem to a system of ODEs, which is solved by the finite difference method (FDM). Some theorems about the convergence analysis are stated and proved. A numerical simulation is given and the results are compared with the exact solution.