A. Maciag et Mj. Al-khatib, Stability of solutions of the overdetermined inverse heat conduction problems when discretized with respect to time, INT J N M H, 10(2-3), 2000, pp. 228-244
Citations number
13
Categorie Soggetti
Mechanical Engineering
Journal title
INTERNATIONAL JOURNAL OF NUMERICAL METHODS FOR HEAT & FLUID FLOW
The inverse heat conduction problem with many intend responses is considere
d After discretization with respect to time, the problem is described by a
system of the Helmholtz equations in a recurrent form An approximate soluti
on of a heat conduction problem in an integral form is shown Then, an appro
ximate solution of an inverse heat conduction problem in a flat slab is pre
sented for many internal temperature responses. Stability of the solution w
ith respect to the internal response errors is investigated for hco casts:
when the integrals ave calculated with the use of the average value theorem
and when they ave calculated numerically. Analysts of the norm of a matrix
that is essential for the solution stability shows that in the case of thr
ee sensors the norm slightly changes with change of the middle sensor locat
ion. If more than three sensors are taken into consideration, thee results
practically uda not change comparing to the case of three sensors The inter
nal temperature response errors ave suppressed if the time step is greater
than a certain critical value.