General Formulation of Transmission-Line Modeling (TLM) Method Applied to Bio-Energetics of Endotherms

Abstract. Bio-energetics modeling of endotherms allows calculation of energy uptake by feeding and drinking, and the partition of this energy into energy requirement for maintenance and potential energy for production and reproduction purposes at different environmental conditions. The scientific literature contains limited information on 3-D bio-energetic models of endotherms. Most existing models simplify the animal‘s geometry to a cylinder, sphere, etc. In this study, a realistic 3-D cow geometry, acquired through 3-D scanning technology, and use of transmission-line modeling (TLM) method to solve the coupled heat and mass transfer problem is developed. The transient and coupled heat and mass transfer model includes: convection, radiation, metabolic heat generation, cutaneous (skin surface) evaporation, and respiratory evaporation. The main advantage of the TLM method over others numerical methods is that the time-domain of the TLM‘s solution process does not involve any matrix inversion. This approach improves computational time and memory considerably. The TLM method is based on using circuit nodes (with transmission-lines and circuit elements) that represent elementary control volumes (such as squares, triangles, cubes, and tetrahedrons) and the combination of different nodes to represent different properties and geometries of the problem. The partial differential equations in time and space of the problem are solved using linear-system equations of the arrangement of the circuit nodes. The limitation of this approach is that for every differential equation and control volume, a new circuit node must be developed. In this presentation, we will show a new and general formulation of TLM that can be applied to solve any heat and mass transfer problem for any type of biological control volume.