Main Article Content
Abstract
Estimation of unknown surface conditions using measured temperature time history inside or back wall of a solid body is known as inverse heat conduction problem. The purpose of present paper is to solve inverse heat conduction problem using iterative method in conjunction with measured thermocouple data. Exact solution of one-dimensional heat conduction equation is obtained to calculate temperature distribution inside a finite slab. An analytical expression of the sensitive coefficient is derived for constant wall heat flux. It is observed that the sensitive coefficient varies linearly with wall heat flux. Experiments were conducted in Kinetic Heating Facility to obtain temperature-time data. The facility works employing with close loop feed-back system with thyristor controlled thermac. Experimental results are compared with the estimated values and are found in good agreement. The Kinetic Heating Facility can easily be adopted to estimate the thermal diffusivity of material.
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References
- Stolz, G., "Numerical Solutions of an Inverse Problem of Heat Conduction for Simple Shapes", Journal of Heat Transfer, 82 (1), 1960, pp.20-25.
- Monde, M., "Analytical Method in Inverse Heat Transfer Problem Using Laplace Transform Technique", International Journal of Heat Transfer, 43 (21), 2000, pp.3965-3975.
- Mehta, R. C. and Tiwari, S. B., "Controlled Random Search Technique for Estimation of Convective Heat Transfer Coefficient", Heat and Mass Transfer, 43, 2007, pp.1171-1177.
- Beck, J. V., "Nonlinear Estimation Applied to the Nonlinear Inverse Heat Conduction Problem", International Journal of Heat and Mass Transfer, Vol.13, 1970, pp.703-718.
- Mehta, R. C., "Solution of Inverse Conduction Problem", AIAA Journal, No.9, 1977, pp.1355-1356.
- Bass, B. R., "Application of the Finite Element Method to the Nonlinear Inverse Heat Conduction Problem Using Becks Second Method", Journal of Applied Mechanics, Vol.22, May 1980.
- Mehta, R. C., "Estimation of Heating Rate Using a Calorimetric Probe", Review of Scientific Instrumentation, Vol.52, No.11, 1981.
- Mehta, R. C., "Estimation of Heat Transfer Coefficient in a Rocket Nozzle", AIAA Journal, Vol.19, No.8, 1981, pp.1085.
- Beck, J. V., Litkouhi, B. and St. Clair, Jr. C. R., "Efficient Sequential Solution of the Nonlinear Inverse Heat Conduction Problem", Numerical Heat Transfer, Vol.5, 1982, pp.275-286.
- Rayaund, M., "Some Comments on the Sensitivity to Sensor Location of Inverse Heat Conduction Problems Using Becks Method", International Journal of Heat and Mass Transfer, Vol.29, No.5, 1986, pp.815-817.
- Mehta, R. C. and Jayachandran, T., "Deforming Finite Elements for the Numerical Solution of the Nonlinear Inverse Heat Conduction Problem", Communication in the Applied Numerical Methods, Vol.3, 1987, pp.167-172.
- Mehta, R. C. and Jayachandran, T., "Determination of Heat Transfer Coefficient Using Transient Response Chart", Warme-und Stoffubertragung, Vol.26, 1990, pp.1-5.
- Sacadura, J. F. and Osman, T. T., "Emissivity Estimation Through the Solution of an Inverse Heat Conduction Problem", Journal of Thermo-physics, Vol.4, No.1, 1990.
- Monte, F. D., Beck, J. V. and Amos, D. E., "Optimum Design of Complementary Transient Experiments for Estimating Thermal Properties", 9th International Conference on Inverse Problems in Engineering, IOP Conference, Journal of Physics, Conference Series, 1047 (2018), 2002. doi:10.1088/1742-6596/1047/1/012202.
- McMasters, R. L., de Monte, F. and Beck, J. V., "Estimating Two Heat Conduction Parameters from Two Complementary Transient Experiments", ASME Journal of Heat Transfer, 2018. doi:10.1115/1.4038855.
- Cole, K. D., Beck, J. V., Woodbury, K. A. and de Monte F., "Intrinsic Verification and a Heat Conduction Database", International Journal of Thermal Sciences, 78, 2014, pp.36-47.
- D’Alessandro, G. and de Monte F., "Intrinsic Verification of an Exact Analytical Solution in Transient Heat Conduction", Computational Thermal Sciences, 10 (3), 2018, pp.251-272.
- Beck, J. V., Blackwell, B. and St. Clair, C. R., "Inverse Heat Conduction: Ill-Posed Problem", John Wiley and Sons, 1985.
- Alifanov, O. M., "Inverse Heat Transfer Problem", Springer Verlag, New York, 1994.
- Karnal, M., "High Temperature Measurements at the Internal Nozzle Wall of the Zephyr", M.S. Thesis, Department of Computer Science, Electrical and Space Engineering, Lulea University of Technology, September 2014.
- Zmywaczyk, J., Koniorczyk, P., Preiskorn, M. and Machowski, B., "An Inverse Approach to Estimate Heat Transfer Coefficients of 122 mm Medium-range Missile During Correction Engine Operation", Problems of Mechatronics, Armament, Aviation, safety Engineering, ISSN-2081-5891, 5, 1 (15), 2014, pp.25-4.
- de Monte, F., Beck, J. V. and Amos, D. E., "A Heat Flux Based Building Block Approach for Solving Heat Conduction Problems", International Journal of Heat and Mass Transfer, 54, 2011, pp.2789-2800.
- Mehta, R. C., "Influence of Input Parameters on the Solution of Inverse Heat Conduction Problem", InTech Open, Croatia, 2020.
- Carslaw, H. D. and Jaeger, J. C., "Conduction of Heat in Solids", Oxford University Press, London, 1959.
- Scarborough, J. B., "Numerical Mathematical Analysis", Oxford and IBH Publishing Co., New Delhi, 1968, pp.208-211.
- Touloukian, Y. S., "Thermophysical Properties of High Temperature Solid Materials", Macmillan, New York, 1967, pp.329.
References
Stolz, G., "Numerical Solutions of an Inverse Problem of Heat Conduction for Simple Shapes", Journal of Heat Transfer, 82 (1), 1960, pp.20-25.
Monde, M., "Analytical Method in Inverse Heat Transfer Problem Using Laplace Transform Technique", International Journal of Heat Transfer, 43 (21), 2000, pp.3965-3975.
Mehta, R. C. and Tiwari, S. B., "Controlled Random Search Technique for Estimation of Convective Heat Transfer Coefficient", Heat and Mass Transfer, 43, 2007, pp.1171-1177.
Beck, J. V., "Nonlinear Estimation Applied to the Nonlinear Inverse Heat Conduction Problem", International Journal of Heat and Mass Transfer, Vol.13, 1970, pp.703-718.
Mehta, R. C., "Solution of Inverse Conduction Problem", AIAA Journal, No.9, 1977, pp.1355-1356.
Bass, B. R., "Application of the Finite Element Method to the Nonlinear Inverse Heat Conduction Problem Using Becks Second Method", Journal of Applied Mechanics, Vol.22, May 1980.
Mehta, R. C., "Estimation of Heating Rate Using a Calorimetric Probe", Review of Scientific Instrumentation, Vol.52, No.11, 1981.
Mehta, R. C., "Estimation of Heat Transfer Coefficient in a Rocket Nozzle", AIAA Journal, Vol.19, No.8, 1981, pp.1085.
Beck, J. V., Litkouhi, B. and St. Clair, Jr. C. R., "Efficient Sequential Solution of the Nonlinear Inverse Heat Conduction Problem", Numerical Heat Transfer, Vol.5, 1982, pp.275-286.
Rayaund, M., "Some Comments on the Sensitivity to Sensor Location of Inverse Heat Conduction Problems Using Becks Method", International Journal of Heat and Mass Transfer, Vol.29, No.5, 1986, pp.815-817.
Mehta, R. C. and Jayachandran, T., "Deforming Finite Elements for the Numerical Solution of the Nonlinear Inverse Heat Conduction Problem", Communication in the Applied Numerical Methods, Vol.3, 1987, pp.167-172.
Mehta, R. C. and Jayachandran, T., "Determination of Heat Transfer Coefficient Using Transient Response Chart", Warme-und Stoffubertragung, Vol.26, 1990, pp.1-5.
Sacadura, J. F. and Osman, T. T., "Emissivity Estimation Through the Solution of an Inverse Heat Conduction Problem", Journal of Thermo-physics, Vol.4, No.1, 1990.
Monte, F. D., Beck, J. V. and Amos, D. E., "Optimum Design of Complementary Transient Experiments for Estimating Thermal Properties", 9th International Conference on Inverse Problems in Engineering, IOP Conference, Journal of Physics, Conference Series, 1047 (2018), 2002. doi:10.1088/1742-6596/1047/1/012202.
McMasters, R. L., de Monte, F. and Beck, J. V., "Estimating Two Heat Conduction Parameters from Two Complementary Transient Experiments", ASME Journal of Heat Transfer, 2018. doi:10.1115/1.4038855.
Cole, K. D., Beck, J. V., Woodbury, K. A. and de Monte F., "Intrinsic Verification and a Heat Conduction Database", International Journal of Thermal Sciences, 78, 2014, pp.36-47.
D’Alessandro, G. and de Monte F., "Intrinsic Verification of an Exact Analytical Solution in Transient Heat Conduction", Computational Thermal Sciences, 10 (3), 2018, pp.251-272.
Beck, J. V., Blackwell, B. and St. Clair, C. R., "Inverse Heat Conduction: Ill-Posed Problem", John Wiley and Sons, 1985.
Alifanov, O. M., "Inverse Heat Transfer Problem", Springer Verlag, New York, 1994.
Karnal, M., "High Temperature Measurements at the Internal Nozzle Wall of the Zephyr", M.S. Thesis, Department of Computer Science, Electrical and Space Engineering, Lulea University of Technology, September 2014.
Zmywaczyk, J., Koniorczyk, P., Preiskorn, M. and Machowski, B., "An Inverse Approach to Estimate Heat Transfer Coefficients of 122 mm Medium-range Missile During Correction Engine Operation", Problems of Mechatronics, Armament, Aviation, safety Engineering, ISSN-2081-5891, 5, 1 (15), 2014, pp.25-4.
de Monte, F., Beck, J. V. and Amos, D. E., "A Heat Flux Based Building Block Approach for Solving Heat Conduction Problems", International Journal of Heat and Mass Transfer, 54, 2011, pp.2789-2800.
Mehta, R. C., "Influence of Input Parameters on the Solution of Inverse Heat Conduction Problem", InTech Open, Croatia, 2020.
Carslaw, H. D. and Jaeger, J. C., "Conduction of Heat in Solids", Oxford University Press, London, 1959.
Scarborough, J. B., "Numerical Mathematical Analysis", Oxford and IBH Publishing Co., New Delhi, 1968, pp.208-211.
Touloukian, Y. S., "Thermophysical Properties of High Temperature Solid Materials", Macmillan, New York, 1967, pp.329.