Initial surface fluxes in transient heat conduction

In the heat transfer literature, it appears that numerical analyses focusing on surface heat fluxes in the initial phase for transient heat-conduction systems, i.e., qx at x = 0 and t=Δtt=Δt, have not been sufficiently reported. Due to this scarcity, some results may need to be re-examined for their accuracies or even their validities. The objective of the present study is twofold. First, we have identified two specific cases that may call for the awareness of the heat transfer community. Second, after such identification, we have further developed and proposed a technique, called the surface cubic-spline method, to help improve accuracies of heat-flux solutions. An effort is made to render the implementation of this method easy for interested readers, along with a MATLAB code offered in the appendix for them to directly cut and paste. Finally, some discussions of the second law of thermodynamics are presented, as they are related to transient heat conduction processes, and none of these essential ideas has been adequately reported in the literature.