A Higher-Order Numerical Method for Solid Conductive Heat Transfer

Open Access
Author:
Nelson, Cameron Stuart
Graduate Program:
Mechanical Engineering
Degree:
Master of Science
Document Type:
Master Thesis
Date of Defense:
March 24, 2016
Committee Members:
  • John Michael Cimbala, Thesis Advisor
  • Daniel Connell Haworth, Thesis Advisor
Keywords:
  • higher-order
  • finite volume
  • numerical
  • conduction
  • heat transfer
Abstract:
This thesis details the development of a higher-order numerical finite volume method for solid conductive heat transfer. Important thermodynamic and mathematical principles applied are conservation of energy, the heat diffusion equation, Fourier’s Law, the thermal contact resistance concept, Taylor series expansion, and the first-order backward Euler time-differencing method. The higher-order method turns out to be second-order accurate in space and third-order accurate in time with respect to temperature.