A Non-Iterative Procedure Based on State Space Model for Inverse Heat Conduction Boundary Estimation
Arindam Das1, Purna Chandra Mishra2,a, Achintya Mukhopadhyay2,b, Dipankar Sanyal2,c and Swarnendu Sen2,d
1Department of Mechanical and Industrial Engineering, University of Illinois at Chicago, Chicago, IL 60607, USA.
das_arindam9@rediffmail.com
2Department of Mechanical Engineering, Jadavpur University, Kolkata 700 032, India.
apcmmech@yahoo.co.in
bamukhopadhyay@mech.jdvu.ac.in
cdsanyal@mech.jdvu.ac.in
ddrssen@mech.jdvu.ac.in
ABSTRACT
The present paper deals with inverse heat conduction boundary estimation using a noniterative Procedure based on state space model for retrieving time- and space-varying heat flux on the surface of a one-dimensional metal slab with temperature-dependent thermophysical properties. The estimation is based on transient temperature measurements taken by a thermocouple on the down surface of the metal slab on which the air jet impingement occurs. The inverse problem is solved as an optimization problem in which a squared residue functional is minimized with the conjugate gradient method. Effects of the time step size and pulse duration of the heat flux variation and the measured noise levels on the inverse solution are investigated through the choice of step type and triangular type heat fluxes. A prospective application of the method can be found in the heat treatment of steel makings, where it is desired to monitor the metallurgical features of the steel sheets based on measurement of its internal state. The results show that good estimation of the surface conditions can be obtained from the present inverse scheme in conjunction with knowledge of temperature recordings inside the test material.
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