Article
Full entry |
PDF
(0.7 MB)
Feedback
PDF
(0.7 MB)
Feedback
Keywords:
building heat transfer; PDEs of evolution; inverse problems; Fourier method; Newton iterations; incertainties in laboratory measurements
building heat transfer; PDEs of evolution; inverse problems; Fourier method; Newton iterations; incertainties in laboratory measurements
Summary:
Modelling of building heat transfer needs two basic material characteristics: heat conduction factor and thermal capacity. Under some simplifications these two factors can be determined from a rather simple equipment, generating heat from one of two aluminium plates into the material sample and recording temperature on the contacts between the sample and the plates. However, the numerical evaluation of both characteristics leads to a non-trivial optimization problem. This article suggests an efficient numerical algorithm for its solution, based on the weak formulation of certain initial and boundary problem for the heat transfer equation, on the classical Fourier analysis and on the Newton iterative method, and demonstrates its practical application.
References:
[1] Barták J., Herrmann L., Lovicar, V., Vejvoda O.: Partial Differential Equations of Evolution. Ellis Horwood, 1991 MR 1112789 | Zbl 0726.35001
[2] Bryant R., Johnsson E., Ohlemiller, T., Womeldorf C.: Estimates of the uncertainty of radiative heat flux calculated from total heat flux measurements. In: Proc. 9th Interflam Conference in Edinburgh, Interscience Communications London, 2001, pp. 605–616
[3] Carslaw H. S., Jaeger J. C.: Conduction Heat in Solids. Clarendon Press, Oxford 1959 MR 0959730
[4] Davies M. G.: Building Heat Transfer. Wiley, New York 2004
[5] Ellison S. R. L., Rosslein M., (eds.) A. Williams, al.: Quantifying Uncertainty in Analytical Measurements. EURACHEM/CITAC Guide CG4 (2000), available at http://www.measurementuncertainty.org/mu/QUAM2000-1.pdf
[6] Fasshauer G. E.: Meshfree Methods. Handbook of Theoretical and Computational Nanotechnology (M. Rieth and W. Schommers, eds.), American Scientific Publishers, 2006, pp. 33–97; preprint available at http://amadeus.math.iit.edu/ fass/MeshfreeNano.pdf MR 2235818
[7] Ferziger J. H., Perić M.: Computational Methods for Fluid Dynamics. Springer–Verlag, Berlin 2002 MR 1384758 | Zbl 0998.76001
[8] Fiedler J.: Special Matrices and Their Application to Numerical Mathematics. SNTL, Prague 1981. In Czech
[9] Greguš M., Švec, M., Šeda V.: Ordinary Differential Equations. Alfa, Bratislava 1985. In Slovak
[10] Kolmogorov A. N., Fomin S.: Elements of the Theory of Functions and Functional Analysis. Nauka, Moscow 1989. In Russian MR 1025126 | Zbl 0672.46001
[11] Kmínová H., Šastník S.: Analysis of uncertainties in measurements of thermal technical properties of building materials. In: Proc. 4th Mathematical Workshop in Brno, Brno University of Technology, 2005, pp. 65–66. In Czech
[12] Kuneš J.: Modelling of Thermal Processes. SNTL, Prague 1989. In Czech
[13] Lindberg V.: Uncertainties, Graphing, the Vernier Caliper. Rochester Institute of Technology 2000, available at http://www.rit.edu/
[14] Ralston A.: A First Course in Numerical Analysis. Academia, Prague 1973. In Czech
[15] Rektorys K.: Method of Discretization in Time and Partial Differential Equations. SNTL, Prague 1985. In Czech
[16] Riečan B., Lamoš, F., Lenárt C.: Probability and Mathematical Statistics. Alfa, Bratislava 1987. In Slovak
[17] Vala J.//Linear Spaces, Operators: Educational supports of the Faculty of Civil Engineering, Brno University of Technology 2004, available at ftp:. ftp.fce.vutbr.cz/.StudijniOpory_SI/R1S1_BA01_Matematika-I/BA01_M02.pdf In Czech
[18] Vala J., Šastník S.: On the modelling of heat propagation in buildings. Building Research Journal 52 (2004), 31–56
Search
Partner of
