Modelling for Temperature Distribution Calculation using Surface Scattering of Free Electrons in Finite Metal Solid

This study generalizes the temperature distribution equation for finite metal solid, unifying previous separate models for thick and thin plates. Effects of surface scattering of free electrons on heat conduction is taken account. As plate thickness decreases, these scattering events increase, leading to elevated temperatures due to reduction in mean free paths. We propose a prediction model for temperature distribution incorporating these effects onto the existing Rosenthal solution. It exhibits excellent agreement with finite element analysis results across all thicknesses. Furthermore, from an engineering standpoint, two examples of how heat concentration occurs in material with geometry that promotes multiple surface scattering are presented.