|
The present study introduces a numerical method to analyze
inverse heat conduction problem concerning the prediction of the
surface behavior. The numerical algorithm combines the Laplace
transform technique and the finite difference method in
conjunction with the least square scheme. Time-dependent terms
in the governing equation are removed by using the Laplace
transform technique, and then the resulting differential
equation are solved by using the finite difference method.
Temperature distributions in the domain are obtained by using
the numerical inversion of Laplace transform. Due to the
application of the Laplace transform technique, the temperature
can be calculated at a specific time without step-by-step
computation in the time domain. By using the least square
scheme, the convergence of iteration is fast and stable. In the
estimation of the unknown boundary temperature, various examples
are illustrated to show the applicability and efficiency of the
present numerical method. The influences of measurement time
intervals and thermocouple locations are investigated. It can be
seen from various illustrated examples that the present
numerical method can accurately and efficiently estimate the
unknown boundary temperature and the thermocouple can be located
far from the estimated surface. In addition, the effect of the
measurement error and noises on measurements will be
investigated. It is fount that the present numerical method can
also estimate the boundary surface well while the measurement
error and noises are considered. Thus, it can be concluded that
the present numerical method can successfully be to analyze
inverse heat conduction problem applied.
|