A SPLINE-BASED METHOD FOR SOLVING THE INVERSE HEAT CONDUCTION PROBLEM IN SLABS AND THICK-WALLED CYLINDERS UNDER COMPLEX THERMAL LOADING
Open Access
Author:
Klinger, Grant
Graduate Program:
Engineering Science and Mechanics
Degree:
Master of Science
Document Type:
Master Thesis
Date of Defense:
April 03, 2023
Committee Members:
Albert Segall, Program Head/Chair Matt Lear, Thesis Advisor/Co-Advisor Corina Stefania Drapaca, Committee Member
Keywords:
Inverse Heat Conduction Problem Spline Piecewise Plate/Slab Cylinder
Abstract:
A spline solution to the inverse heat conduction problem using a thermal spline is explored for a finite plate/slab and a thick-walled cylinder with axial symmetry undergoing thermal loading at a surface. The surface thermal loading is assumed to take the form of a cubic polynomial with four unknown coefficients, with convection allowed to occur on the opposite surface where no thermal loading is applied. A direct heat conduction solution is defined as a function of time in terms of the cubic polynomial surface excitation and unit response solution using Duhamel's integral. Response temperatures were then theoretically constructed at a point on the convective surface of the slab and cylinder at discrete times. The direct thermal solution was substituted into the cubic spline process to fit the data by finding the four coefficients of the inverse solution between each set of data points. An inverse solution was then constructed piecewise for each interval with these four coefficients, allowing for much higher accuracy than that of the least squares method. Furthermore, response data that oscillates can easily be modeled by the thermal spline and produces a dependable inverse solution, whereas the least squares method is not capable of modeling such complex data.
