Craig Somerton

Exact Solution for Nonlinear Thermal Diffusion and Its Use for Verification

An analytical solution is provided to the nonlinear diffusion equation, with the thermal conductivity given as a linear function of temperature. The derivation of the solution, and implications of it, are presented. The boundary and initial conditions associated with the solution provide applicability to specific cases. The solution is useful for verifying numerical (computer) solutions to thermal diffusion with temperature-dependent thermal conductivity. The (nonlinear) analytical solution is compared to a numerical solution from a finite element code to verify the accuracy of the code and to establish the order of convergence for the spatial discretization error

Model building using the f-test and parameter estimation of model coefficients with application in porous media

Flow in porous media is typically described by Darcys Law, which states that a linear proportionality exists between flow rate and the pressure drop through the media. The constant of proportionality is known as the permeability, K, and is a function of the properties of the porous media. In a high flow rate situation the relationship between flow rate and pressure drop is not necessarily linear. The Forchheimer extension to Darcys law attempts to account for this non-linearity by representing the relationship as quadratic in nature. The Forchheimer coefficient, M, is part of the extension to Darcys Law and is also a function of the properties of the porous media. In an attempt to numerically determine the values of the permeability and the Forchheimer coefficient using various estimation methods, the possibility has arisen that the exponent, n, associated with the Forchheimer extension is not exactly two, and may also be a function of the properties of the media. Using the Forchheimer extension to Dar...