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 reliability of mathematical models under such conditions. This study involves examination of two alternative published formulations, one involving the use of circuit theory and a well-mixed fluid assumption, against another formulation, involving the solution to Laplace's equation, but without convective effects. As expected, the models (and an analytical solution) yield identical results under situations where solid and fluid electrical conductivity are 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 the worst-case scenario in ohmic heating is not necessarily associated with a stationary fluid situation. Under the less likely conditions where the solid is more conductive than the fluid, the LENC approach is more conservative than the CAMF approach. Models are also compared with respect to other features, such as practicality of use, and computational cost.