Abstract:
In this work, application of the homotopy perturbation method (HPM) and
an inverse solution for estimating unknown thermal parameters such as the
variable thermal conductivity parameter (β), the thermogeometric parameter (K), and the nondimensional coe cient of thermal expansion (χ) in an
annular n subjected to thermal stresses is presented. Initially, to obtain the
nondimensional temperature distribution from the heat equation, the forward
method is employed using an approximate analytical solution based on HPM.
Thereafter, a closed form solution for the temperature-dependent thermal
stresses is obtained using the classical theory of thermoelasticity coupled
with HPM solution containing the temperature distribution. Next, for satisfying
a particular stress criterion which makes relevance in selecting appropriate
congurations for selecting the nned system, unknown thermal parameters
are obtained using an inverse approach based on the Nelder–Mead simplex
search minimization technique. The objective function is taken as the sum
of square of the residuals between the measured stress eld and an initially
guessed value which is updated iteratively. It is found that more than one
type of temperature distribution may yield a given stress distribution, thereby
giving rise to dierent n e ciencies. The agreement between the actual and
the predicted results was found to be satisfactory
