Analytical solution and numerical simulation of advection-diffusion equation related to fumigation problem

Abstract

The dissertation reports the analytical approach and numerical simulation of a transport phenomenon which is governed by the advection-diffusion equation. The main objective is to solve this governing equation by both analytical and numerical methods. One-dimensional advection-diffusion equation is solved by using Laplace Transformation method. Then, the solution is interpreted in two-dimensional graph of solute mass concentration over the distance. The graph is plotted using a mathematical tool i.e. MATLAB software. On the other hand, the numerical simulation is performed by using Computational Fluid Dynamics (CFD) software, ANSYS Fluent. In ANSYS Fluent, the solver discretizes the transport equation using Finite Volume Method where the computational flow domain is divided into control volumes. The transport model is partly adapted based on a phenomenon of solute mass concentration distribution in mixture with air in the flow domain of the cylindrical silo during fumigation. Based on this applications, the initial and boundary conditions are defined similar to the ones in analytical approach. From this simulation, data is obtained in form of graphical distribution profile of solute mass which can be compared against the works from analytical approach, hence, the verification is achieved. The verification demonstrates the accuracy of numerical solution on this transport phenomena, thus, it can be used for various experimental applications.