Inverse conduction method using finite difference method

Abstract

A numerical method is used to solve an inverse heat conduction problem using finite difference method and one-dimensional Newton-Raphson optimization technique. A thermocouple placed anywhere on the one-dimensional rod will read the temperature at that point, this temperature when fed into the FORTRAN code can predict the heat flux subjected onto the rod. The code has been further modified to predict variable heat flux (with time) as well. Error contribution of distance of thermocouple from source and time is demonstrated. Accurate prediction of heat flux variable with time has also been validated. First, a FORTRAN code was written to simulate and solve a transient model of a rod subjected to constant temperatures on both sides using Finite Difference Method. Next, a FORTRAN code was written to solve a steady state, and consequently a transient, model of a rod subjected to heat flux from one side using FDM and is tested to measure temperature at any node on the rod. Further, this code was modified to predict heat flux based on temperature data provided using Newton-Raphson optimization technique.