Local sensitivity analysis for the heat flux-temperature integral relationship in the half-space

This paper presents insight into the heat flux-temperature (q″ − T) integral relationship based on constant thermophysical properties. This relationship is often used in one-dimensional, transient heat transfer studies involving null-point calorimetry and heat flux investigations. This study focuses on a short transient studies where energy has not fully penetrated the body as the result of an imposed surface heating condition. A full nonlinear heat transfer model is developed involving a half-space planar region. Temperature results are then introduced into the constant property integral relationship and a newly derived Kirchoff integral relationship for retrieving the local heat flux. Good agreement is observed between the fully nonlinear results and locally linearized system. Additionally, a sensitivity study is presented which involves perturbing the average thermophysical properties of thermal conductivity and heat capacity.