Coupled Zero-Dimensional/One-Dimensional Model for Hybrid Heat Transfer Measurements

This paper covers the application of an improved model to address errors associated with transient heat transfer experiments, which also include the application of lumped capacitance. Using transient thermochromic liquid crystals techniques, and applying thermochromic liquid crystals underneath lumpable features, it is possible to calculate the heat transfer using a lumped heat capacitance approach. In previous studies using the classical lumped capacitance model, the heat loss into the surface underneath the lumped features was not accounted for. In this paper, an exact, closed-form analytical solution to the enhanced lumped capacitance model is derived for discrete bodies for the case of perfect thermal contact. To validate the model and its exact solution, the transient heat conduction in a representative two-dimensional ribbed surface is simulated numerically using the finite volume method. The modeled behavior of the coupled zero-dimensional/one-dimensional model has reasonable agreement with the numerical simulation. The solution for perfect contact can also be extended for imperfect contact.