A guide for the use of the function specification method for 2D inverse heat conduction problems

Performance analysis and feasibility study of ant colony optimization, particle swarm optimization and cuckoo search algorithms for inverse heat transfer problems

“…This is due to the fact that results are more sensitive to the noise present in measurement at smaller values of time steps than at higher time step size. It is important to mention here that the smaller value of the time step used (Dt = 1 s) is close to the temporal stability limit [77] defined as aDt e 2 > 0:01 ð19Þ…”

“…Lack of temporal resolution at higher values of time step size is also a major concern. In such situations where it is inevitable to use lower time steps, regularization schemes with suitable hyper-parameters can be used for temporal and spatial regularization [77,78]. This is discussed in the next section.…”

What is the most suitable fixed grid solidification method for handling time-varying inverse Stefan problems in high temperature industrial furnaces?

“…This time delay represents a fraction j of the heat diffusion time through the thermal system, s diff [9,25]. For inverse heat transfer problems, this lagging effect is directly linked to the temporal stability criterion known as [26] …”

“…In practice, the recommended value for n is about 1% and it should be diminished for measurements of high quality [26]. Note that, according to this semi-empirical criterion, s o = ns diff corresponds to the minimum allowable sliding time horizon s o,min .…”

Assessment of Various Methods in Solving Inverse Heat Conduction Problems

“…If such information is available, it should be utilized to improve the estimates. While classical methods, such as the least square regularization method (Beck et al, 1985;Beck et al, 1996), the sequential function specification method (Alifanov, 1995;Beck et al, 1996;Blanc et al, 1998), the space marching method (Al-Khalidy, 1998), conjugate gradient method (Abou khachfe & Jarny, 2001;Huang & Wang, 1999), steepest descent method (Huang et al, 2003), and the model reduction algorithm (Battaglia, 2002;Girault et al, 2003) are vastly studied in the literature, and applied to the problems in thermal engineering (Bass, 1980;Osman, 1190;Kumagai et al, 1995;Louahia-Gualous et al, 2003;Kim & Oh, 2001;Pietrzyk & Lenard, 1990;Alifanov et al, 2004;Gadala & Xu, 2006), there are still some unsolved problems:  The solution often shows some kinds of overshoot and undershoot, which may result in non-physical answers.  Very high heat flux peak values such as those experienced in jet impingement cooling are normally damped and considerably underestimated.…”