The role of thermal effusivity on the incipient growth of the surface temperature in a semi-infinite region absorbing heat flux at the surface

Abstract

Heat conduction theory stipulates that two thermo-physical properties of materials: the thermal conductivity “k” and the thermal diffusivity “ ” influence the temperature evolution in regular and irregular bodies as a response to various cooling/heating conditions. The traditional statement involving the two thermo-physical properties is examined at length in the present study for the case of a semi-infinite region. The primary objective of the present study is to investigate the influence of the less known thermo-physical property called the thermal effusivity “e” on the incipient surface temperature raise in a semi-infinite body affected by uniform surface heat flux. The secondary objective of the study is to identify a key figure-of-merit named the dimensionless threshold time that separates the incipient temperature elevation in a semi-infinite region from the incipient temperature elevation in a large wall of finite thickness under the same uniform surface heat flux. The outcome of the methodical analysis suggests that the accurate estimate for the dimensionless threshold time  in the semi-infinite region should be 0.10.