Inverse Heat Conduction Estimation Procedures

Sensitivity to measurement errors and damping and lagging of measurement signals resulting from the surface disturbance make the inverse heat conduction problem (IHCP) difficult. Ill-posedness is demonstrated through examination of a classic exact solution which motivates the need for regularization. General features of IHCP solutions are outlined. Sensitivity coefficients are important in IHCP solutions and these coefficients for heat flux, temperature, and heat transfer coefficient disturbance at the surface are presented and discussed. Many IHCP solution techniques for estimating a single heat flux history for the linear IHCP including both sequential and whole-domain approaches are discussed. These include Stolz method (exact matching), function specification method (FSM), Tikhonov regularization (TR), conjugate gradient method (CGM), adjoint method (AM), truncated singular value decomposition (TSVD), and Kalman filtering (KF). The thorough discussions on these solution methods provide the readers with a unique reference to learn about solving IHCPs.