An on-line methodology to solve two-dimensional inverse heat conduction problems (IHCP) is presented. A new input estimation approach based on the Kalman filtering technique is developed to estimate the two separate unknown heat flux inputs on the two boundaries in real time. A recursive relation between the observed value of the residual sequence with unknown heat flux and the theoretical residual sequence of the Kalman filter that assumes known heat flux is formulated. A real-time least-squares algorithm is derived that uses the residual innovation sequence to compute the magnitude of heat flux. This recursive approach facilitates practical implementation, and its capabilities are demonstrated in several typical cases with discontinuous and time-varying heat flux inputs.

An input estimation approach to on-line two-dimensional inverse heat conduction problems

A new space-marching finite-difference algorithm is developed to solve the nonlinear inverse heat conduction problem. This algorithm uses interior temperature measurements at future times to estimate the surface heat flux. The results of this method are compared on a test case with four other numerical schemes. The method is as accurate as the method developed by Beck [ 1] and uses a smaller computational time. This scheme is also employed to estimate the effects of different types of experimental errors on the estimation of the surface heat flux. Errors due to temperature measurements, thermocouple locations, and material properties are each investigated.

A new finite-difference method for the nonlinear inverse heat conduction problem

Solution of an inverse dynamics problem using an eigenvalue reduction technique

The one-dimensional nonlinear problem of heat conduction is considered. A noniterative space-marching finite-difference algorithm is developed to estimate the surface temperature and heat flux from temperature measurements at subsurface locations. The trade-off between resolution and variance of the estimates of the surface conditions is discussed quantitatively. The inverse algorithm is stabilized through the use of digital filters applied recursively. The effect of the filters on the resolution and variance of the surface estimates is quantified. Results are presented which indicate that the technique is capable of handling noisy measurement data.

One-dimensional nonlinear inverse heat conduction technique

The surface heat flux at one boundary of a one-dimensional system is computed by using a transient finite-element analysis, given the initial temperature history at on interior node. A technique based on a difference of squares of temperatures is used to determine incremental changes in the surface heat flux. Specifically, two cases are treated. The first case involves an imposed step change in the surface heat flux, and the second involves an imposed surface heat flux that oscillates periodically in the form of a square wave. Comparison of the predicted heat flux with the imposed heat flux provides an evaluation of the inverse technique.

Application of the Finite-Element Method to the Inverse Heat Conduction Problem

Numerical solution of one-dimensional inverse transient heat conduction by finite difference method

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Numerical solution of one-dimensional inverse transient heat conduction by finite difference method