Estimation of Heat Shocks in Inverse Heat Transfer Problems using Kalman Filtering

Document Type : Original Article

Authors

• Mahdi Molavi ¹
• Ahmad Sedaghat ²
• Mohamad Reza Salimpour ²

¹ -

² Isfahan University of Technology

10.22067/fum-mech.v26i2.25532

Abstract

In this paper, the heat shocks in the heat flux profile are estimated with known temperature distribution using Kalman filtering. For this task, the temperature distribution is calculated and artificial noise is added to adequately simulate the real temperature measurements. Next by using Kalman filtering, estimation of online heat flux is assessed which appears as heat shocks in the discussed problem. Results indicate that the present method can accurately estimate jumps in the heat flux.

Keywords

• Inverse Heat Transfer Problem
• Estimation of Heat Flux
• Online Estimation Method
• Kalman Filtering

---

References

1. J. Hadamard, J., "Lectures on Cauchy’s Problem in Linear Partial Differential Equations", Yale University Press, New Haven, CT, (1923).

2. Tikhonov, A.N., Arsenin, V.Y., "Solution of Ill-Posed Problem", Winston and Sons, Washington, DC, (1977).

3. Alifanov, O. M., "Solution of an Inverse Problem of Heat Conduction by Iteration Methods", J. Eng. Phys., vol. 26, no. 4, pp. 471-475, (1974).

4. Alifanov, O.M., "Inverse Heat Transfer Problems", Springer-Verlag, New York, (1994).

5. Beck, J.V., Blackwell, B. and Clair, C.R.St., "Inverse Heat Conduction: Ill-Posed Problems", Wiley Interscience, New York, (1985).

6. Stolz, G.Jr., "Numerical Solutions to an Inverse Problem of Heat Conduction for Simple Shapes", Journal Heat Transfer, 82, pp. 20-26, (1960).

7. Mirsepassi, T.J., "Heat-Transfer Charts for Time-Variable Boundary Conditions", British Chemical Engineering. 4, pp. 130-136, (1959).

8. Shumakov, N.V., "A Method for the Experimental Study of the Process of Heating a Solid Body", Soviet Physics Technical Physics (Translated by American Institute of Physics), 2, pp. 771-780, (1957).

9. Beck, J.V. and Arnold, K.J., "Parameter Estimation in Engineering and Science", Wiley: New York, (1977).

10. Kalman, R.E., "A New Approach to Linear Filtering and Prediction Problems", ASME Journal of Basic Engineering, 82, pp. 35–45, (1960).

11. Kalman, R.E. and Bucy, R.S., "New Results in Linear Filtering and Prediction Theory", ASME Journal of Basic Engineering, 83, pp. 95-108, (1961).

12. Molavi, H., Hakkaki-Fard, A., Rahmani, R.K., Ayasoufi, A. and Molavi, M., "A Novel Methodology for Combined Parameter and Function Estimation Problems", ASME Journal of Heat Transfer, 132, No. 12, p. 121301, (2010).

13. Molavi, H., Hakkaki-Fard, A., Molavi, M., Rahmani, R.K., Ayasoufi, A. and Noori. S., "Estimation of Boundary Conditions in the Presence of Unknown Moving Boundary Caused by Ablation", International Journal of Heat and Mass Transfer, 54, pp. 1030-1038, (2011).

14. Kowsari, F. and Nazari, M., "A Feasibility Study of Employing Sequential Function Specification Method for Estimation of Transient Heat Flux in a Non-Thermal Equilibrium Porous Channel", Journal of Porous Media, 14(5), (2010).

15. Nazari, M., Farahani, S. D. and Kowsary, F., "Comparison of the Mollification and Wavelet Prefiltering of Temperature Data in an Ill-Posed Inverse Heat Conduction Problem, Application: Nonthermal Equilibrium Porous Medium", Heat Transfer Engineering, 33(8), 704-711, (2012).

16. Lebreux, M., Desilets, M., Lacroix, M. "An unscented Kalman filter inverse heat transfer method for the prediction of the ledge thickness inside high- temperature metallurgical reactors", International Journal of Heat and Mass Transfer, 57, pp. 265-273, (2013).

17. Franklin, G.F., Powell, J.D. and Workman, M.I., "Digital Control of Dynamic Systems", 2nd ed. Addision Wesley, Reading, MA, (1990).