On solutions of convection-diffusion equation in fluid

Abstract

Convection and diffusion are fundamental transport mechanisms that govern the flow of mass, heat, or other quantities in various physical, biological and engineering systems. The work overviews theoretical underpinnings, mathematical formulations and numerical methods to analyze the convection-diffusion process in one and two dimensions, both in steady and transient states. We have compared the analytical and numerical results using finite difference and finite volume methods for fluid flow and temperature distribution. The numerical solutions are in agreement with the analytical solution in one dimension. The work compares convection-diffusion with convection-dominating for larger velocities of fluid flow. The solution obtained from FVM is in line with an analytical solution than the solution obtained from FDM. The numerical simulation for the transient flow is also discussed.