Ohmic heating of solid-liquid mixtures: A comparison of mathematical models under worst-case heating conditions

A critical issue in the modeling of ohmic heating of solid-liquid mixtures is the understanding of worst-case scenarios, and in particular, the reliab ility of mathematical models under such conditions. This study involves exa mination of two alternative published formulations, one involving the use o f circuit theory and a well-mixed fluid assumption, against another formula tion, involving the solution to Laplace's equation, but without convective effects. As expected, the models (and an analytical solution) yield identic al results under situations where solid and fluid electrical conductivity a re equal. However, when the solid is of lower electrical conductivity than the fluid, the Circuit Analogy, Mixed Fluid (CAMF) approach is shown to be more conservative than the Laplace Equation, No Convection (LENC) approach. This prediction is borne out by experimental studies, which confirm that t he worst-case scenario in ohmic heating is not necessarily associated with a stationary fluid situation. Under the less likely conditions where the so lid is more conductive than the fluid, the LENC approach is more conservati ve than the CAMF approach. Models are also compared with respect to other f eatures, such as practicality of use, and computational cost.