A comparison of some numerical methods for the advection-diffusion equation

This paper describes a comparison of some numerical methods for solving the advection-diffusion (AD) equation which may be used to describe transport of a pollutant. The one-dimensional advection-diffusion equation is solved by using cubic splines (the natural cubic spline and a ”special” AD cubic spline) to estimate first and second derivatives, and also by solving the same problem using two standard finite difference schemes (the FTCS and Crank-Nicolson methods). Two examples are used for comparison; the numerical results are compared with analytical solutions. It is found that, for the examples studied, the finite difference methods give better point-wise solutions than the spline methods

Three-dimensional transient mathematical model to predict the heat transfer rate of a heat pipe

A three-dimensional model was developed to simulate the heat transfer rate on a heat pipe in a transient condition. This article presents the details of a calculation domain consisting of a wall, a wick, and a vapor core. The governing equation based on the shape of the pipe was numerically simulated using the finite element method. The developed three-dimensional model attempted to predict the transient temperature, the velocity, and the heat transfer rate profiles at any domain. The values obtained from the model calculation were then compared with the actual results from the experiments. The experiment showed that the time required to attain a steady state (where transient temperature is constant) was reasonably consistent with the model. The working fluid r134a (tetrafluoroethane) was the quickest to reach the steady state and transferred the greatest amount of heat