Parallel computations of the step response of a floor heater with the use of a graphics processing unit. Part 1: models and algorithms

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The article presents a method of computing the step response of an air floor heater. The method implements parallel algorithms on a graphics processing unit. In the analyzed concrete slab heating ducts are placed. Hot air is transferred through them, thanks to which the heat penetrates into the slab. Heat transfer into the environment takes place on the top surface of the floor by natural convection and radiation. The bottom surface of the slab is thermally insulated. A two-dimensional heat equation was discretized with the use of the implicit finite difference method. In order to solve the obtained system of equations, the conjugate gradient method was used. Moreover, in order to examine the possibility of shortening the computations time, the algorithm of this method was implemented on a graphics processing unit. A computer program, using the CUDA parallel computing platform and linear algebra libraries CUBLAS and CUSPARSE, was developed

[1] M. Żukowski, Floor Heating, Bialystok University of Technology Publishing House, Bialystok, 2009, (in Polish).

[2] J. Gołębiowski, S. Kwiećkowski, M. Zaręba, and R.P. Bycul, Analysis of the Transient Thermal Field in Electrical Floor Heaters and DC Cables, Bialystok University of Technology Publishing House, Warsaw, 2010, (in Polish).

[3] K.T. Januszkiewicz, Electrical Storage Heating of Rooms, Information Center “The Installation Technique in Building Engineering”, Warsaw, 1998, (in Polish).

[4] R. Rabjasz and M. Dzierzgowski, Floor Heating. Guide, Central Information Center of Construction, Warsaw, 1995, (in Polish).

[5] J. Gołębiowski and S. Kwiećkowski, “Dynamics of threedimensional temperature field in electrical system of floor heating”, Int. J. Heat Mass Tran. 45 (12), 2611-2622 (2002).

[6] R. Holopainen, P. Tuomaala, and J. Piippo, “Uneven gridding of thermal nodal networks in floor heating simulations”, Energy and Buildings 39 (10), 1107-1114 (2007).

[7] S.F. Larsen, C. Filipp´ın, and G. Lesino, “Transient simulation of a storage floor with a heating/cooling parallel pipe system”, Building Simulation 3 (2), 105-115 (2010).

[8] X. Jin, X. Zhang, and Y. Luo, “A calculation method for the floor surface temperature in radiant floor system”, Energy and Buildings 42 (10), 1753-1758 (2010).

[9] Y. Liu, D. Wang, and J. Liu, “Study on heat transfer process for in-slab heating floor”, Building and Environment 54, 77-85 (2012).

[10] W. Baade, Elektrische Raumheiztechnik. Installieren, Warten, Pr¨ufen, Verlag Technik, Berlin, 1995.

[11] M. Palic, Elektrische W¨arme-und Heiztechnik, Expert Verlag, Ehningen bei B¨oblingen, 1992.

[12] Legalett, “Legallet plate heating foundation”, Creator-Projects Q. 1, 10-13 (2008), (in Polish).

[13] B.D. Howard, “The CMU air-core passive hybrid heat storage system”, Proc. Renewable and Advanced Energy Systems 21stCentury 1, CD-ROM (1999).

[14] O. Bozkir and S. Canbazo˘glu, “Unsteady thermal performance analysis of a room with serial and parallel duct radiant floor heating system using hot airflow”, Energy and Buildings 36 (6), 579-586 (2004).

[15] F. Incropera, D. De Witt, T. Bergman, and A. Lavine, Introduction to Heat Transfer, John Wiley&Sons, Hoboken, 2007.

[16] K.T. Januszkiewicz, “The dynamical properties of electrically heated rooms”, Electrical Review 3, 85-87 (2007), (in Polish).

[17] J.V. Beck, K.D. Cole, A. Haji-Sheikh, and B. Litkouhi, Heat Conduction Using Green’s Functions, Hemisphere Publishing Corporation, London, 1992.

[18] D.B. Kirk and W.W. Hwu, Programming Massively Parallel Processors: a Hands-on Approach, Morgan Kaufmann, Burlington, 2010.

[19] J. Szargut, R. Białecki, A. Fic, K. Kurpisz, A. Nowak, Z. Rudnicki, and J. Skorek, Numerical Modelling of Temperature Fields, WNT, Warsaw, 1992, (in Polish).

[20] J. Taler and P. Duda, Solving Direct and Inverse Heat Transfer Problems, WNT, Warsaw, 2003, (in Polish).

[21] J.D. Hoffman, Numerical Methods for Engineers and Scientists, Marcel Dekker, Inc., New York, 2001.

[22] J.R. Shewchuk, “An introduction to the conjugate gradient method without the agonizing pain”, in Technical Report, Carnegie Mellon University, Pittsburgh, 1994.

[23] R. Barrett, M. Berry, T.F. Chan, J. Demmel, J.M. Donato, J. Dongarra, V. Eijkhout, R. Pozo, Ch. Romine, and H. Van der Vorst, Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods, SIAM, Philadelphia, 1994.

[24] K. Gnidzińska, G. De Mey, and A. Napieralski, “Heat dissipation and temperature distribution in long interconnect lines”, Bull. Pol. Ac.: Tech. 58 (1), 119-124 (2010).

[25] Compute Unified Device Architecture (CUDA), (2012).

[26] J. Sanders and E. Kandrot, CUDA by Example. An introduction to General-Purpose GPU Programming, Addison-Wesley, Upper Saddle River, 2010.

[27] CUDA CUBLAS Library, NVIDIA Corporation, Santa Clara, CA, 2010.

[28] CUDA CUSPARSE Library, NVIDIA Corporation, Santa Clara, CA, 2010.

Bulletin of the Polish Academy of Sciences Technical Sciences

The Journal of Polish Academy of Sciences

Journal Information

IMPACT FACTOR 2016: 1.156
5-year IMPACT FACTOR: 1.238

CiteScore 2016: 1.50

SCImago Journal Rank (SJR) 2016: 0.457
Source Normalized Impact per Paper (SNIP) 2016: 1.239


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