# Numerical Analysis of Coupled Heat and Mass Transfer Phenomena in Concrete at Elevated Temperatures

- 33 Downloads

## Abstract

Based on well-established physical laws, a one-dimensional model that describes coupled heat and mass transfer phenomena in heated concrete has been developed. The mathematical model is based on the fully implicit finite difference scheme. The control volume approach was employed in the formulation of the finite difference equations. The primary variables considered in the analysis are temperature, vapor density, and pore pressure of the gaseous mixture. Several phenomena have been taken into account, such as evaporation, condensation, and dehydration processes. Temperature-, pressure-, and moisture content-dependent properties of both gaseous and solid phases were also considered. Numerical case studies that deal with extremely rapid heating of concrete are validated against experimental results with good agreement in spatial and temporal trends for temperature and pressure. Outputs from the numerical model demonstrated the influence of the coupling relationship between heat and mass transfer phenomena on temperature, vapor, and pressure distributions. Furthermore, it was noted that the temperature distribution trends are significantly affected by the vapor migration phenomenon; such an effect becomes more pronounced when moving deeper toward the concrete core.

### Keywords

Control volume Fire Evaporation Dehydration Finite difference## Notes

### Acknowledgements

The first author would like to acknowledge the support of the Higher Committee for Education Development in Iraq (HCED).

### References

- Abdel-Rahman, A.K., Ahmed, G.N.: Computational heat and mass transport in concrete walls exposed to fire. Numer. Heat Transf. Part A Appl.
**29**(4), 373–395 (1996)CrossRefGoogle Scholar - Ahmed, G.N., Hurst, J.P.: An analytical approach for investigating the causes of spalling of high-strength concrete at elevated temperatures. In: International Workshop on Fire Performance of High-Strength Concrete, pp. 13–14 (1997)Google Scholar
- American Society for Testing and Materials : ASTM E119-16a. Standard test methods for fire tests of building construction and materials. ASTM International, West Conshohocken, PA. www.astm.org (2001)
- Atkinson, A., Nickerson, A.: The diffusion of ions through water-saturated cement. J. Mater. Sci.
**19**(9), 3068–3078 (1984)CrossRefGoogle Scholar - Baggio, P., Bonacina, C., Strada, M.: Trasporto di calore e massa nel calcestruzzo cellulare. Termotecnica
**47**(12), 53–59 (1993)Google Scholar - Baggio, P., Majorana, C.E., Schrefler, B.A.: Thermo-hygro-mechanical analysis of concrete. Int. J. Numer. Methods Fluids
**20**(6), 573–595 (1995)CrossRefGoogle Scholar - Bazant, Z.P., Kaplan, M.F.: Concrete at High Temperatures: Material Properties and Mathematical Models. Longman Group Limited, Harlow (1996)Google Scholar
- Bazant, Z.P., Thonguthai, W.: Pore pressure and drying of concrete at high temperature. J. Eng. Mech. Div.
**104**(5), 1059–1079 (1978)Google Scholar - Bažant, Z.P., Thonguthai, W.: Pore pressure in heated concrete walls: theoretical prediction. Mag. Concr. Res.
**31**(107), 67–76 (1979)CrossRefGoogle Scholar - Bejan, A.: Convection Heat Transfer. Wiley, New York (2013)CrossRefGoogle Scholar
- Bratina, S., Planinc, I., Saje, M., Turk, G.: Non-linear fire-resistance analysis of reinforced concrete beams. Struct. Eng. Mech.
**16**(6), 695–712 (2003)CrossRefGoogle Scholar - Broyden, C.G.: A class of methods for solving nonlinear simultaneous equations. Math. Comput.
**19**, 577–593 (1965)CrossRefGoogle Scholar - Capua, D.D., Mari, A.R.: Nonlinear analysis of reinforced concrete cross sections exposed to fire. Fire Saf. J.
**42**(2), 139–149 (2007)CrossRefGoogle Scholar - Cengel, Y.A., Hernán Pérez, J.: Heat Transfer: A Practical Approach. Transferencia de Calor. McGraw-Hill, México (2004)Google Scholar
- Cheng, P.: Heat transfer in geothermal systems. Adv. Heat Transf.
**14**, 1–105 (1979)CrossRefGoogle Scholar - Davie, C., Pearce, C., Bićanić, N.: Aspects of permeability in modelling of concrete exposed to high temperatures. Transp. Porous Media
**95**, 1–20 (2012)CrossRefGoogle Scholar - Davie, C.T., Pearce, C.J., Bićanić, N.: Coupled heat and moisture transport in concrete at elevated temperatures—effects of capillary pressure and adsorbed water. Numer. Heat Transf. Part A Appl.
**49**(8), 733–763 (2006)CrossRefGoogle Scholar - Dwaikat, M.B., Kodur, V.: Hydrothermal model for predicting fire-induced spalling in concrete structural systems. Fire Saf. J.
**44**(3), 425–434 (2009)CrossRefGoogle Scholar - Eurocode, : 2, Design of Concrete Structures, Part 1–2: General Rules–Structural Fire Design. European Committee for Standardization, Brussels, Belgium (2004)Google Scholar
- Faires, V.M.: Applied Thermodynamics. Macmillan Co, Basingstoke (1950)Google Scholar
- Forsyth, P.A., Simpson, R.: A two-phase, two-component model for natural convection in a porous medium. Int. J. Numer. Methods Fluids
**12**(7), 655–682 (1991)CrossRefGoogle Scholar - Gawin, D., Majorana, C., Schrefler, B.: Numerical analysis of hygro-thermal behaviour and damage of concrete at high temperature. Mech. Cohesive Frict. Mater.
**4**(1), 37–74 (1999)CrossRefGoogle Scholar - Gawin, D., Pesavento, F., Schrefler, B.: Modelling of hygro-thermal behaviour of concrete at high temperature with thermo-chemical and mechanical material degradation. Comput. Methods Appl. Mech. Eng.
**192**(13), 1731–1771 (2003)CrossRefGoogle Scholar - Gawin, D., Pesavento, F., Schrefler, B.A.: What physical phenomena can be neglected when modelling concrete at high temperature? a comparative study. Part 1: physical phenomena and mathematical model. Int. J. Solids Struct.
**48**(13), 1927–1944 (2011a)CrossRefGoogle Scholar - Gawin, D., Pesavento, F., Schrefler, B.A.: What physical phenomena can be neglected when modelling concrete at high temperature? a comparative study. Part 2: comparison between models. Int. J. Solids Struct.
**48**(13), 1945–1961 (2011b)CrossRefGoogle Scholar - Harmathy, T.Z.: Effect of moisture on the fire endurance of building elements. ASTM Spec. Tech. Publ.
**385**, 74–95 (1965)Google Scholar - Kalifa, P., Menneteau, F.D., Quenard, D.: Spalling and pore pressure in hpc at high temperatures. Cem. Concr. Res.
**30**(12), 1915–1927 (2000)CrossRefGoogle Scholar - Lewis, R.W., Schrefler, B.A.: The Finite Element Method in the Static and Dynamic Deformation and Consolidation of Porous Media. Wiley, New York (1998)Google Scholar
- Lie, T.T., Woollerton, J.: Fire resistance of reinforced concrete columns. Technical report, National Research Council of Canada (1988)Google Scholar
- Luckner, L., Van Genuchten, M.T., Nielsen, D.: A consistent set of parametric models for the two-phase flow of immiscible fluids in the subsurface. Water Resour. Res.
**25**(10), 2187–2193 (1989)CrossRefGoogle Scholar - Luikov, A.: Heat and mass transfer in capillary-porous bodies. Adv. Heat Transf.
**1**, 123–184 (1964)CrossRefGoogle Scholar - Mahmoud, K.A., Abdel-Rahman, A.K.: Two-dimensional thermal and structural modelling of hsc columns exposed to fire. Arab. J. Sci. Eng.
**38**(8), 2009–2022 (2013)CrossRefGoogle Scholar - Nield, D.A.: Convection in Porous Media. Springer, Berlin (2006)Google Scholar
- Ozisik, N.: Finite Difference Methods in Heat Transfer. CRC press, Boca Raton (1994)Google Scholar
- Pont, S.D., Schrefler, B., Ehrlacher, A.: Intrinsic permeability evolution in high temperature concrete: an experimental and numerical analysis. Transp. Porous Media
**60**(1), 43–74 (2005)CrossRefGoogle Scholar - Schaffer, E.: Structural fire protection. In: Lie, T. T. (ed.) Issue 78 of ASCE manuals and reports on engineering practice. Committee on Fire Protection, American Society of Civil Engineers. ISBN0872628884, 9780872628885 (1992)Google Scholar
- Schneider, U., Herbst, H.: Permeabilitaet und porositaet von beton bei hohen temperaturen. Dtsch. Aussch. Fuer Stahlbeton
**403**, 23–52 (1989)Google Scholar - Tenchev, R.T., Li, L., Purkiss, J.: Finite element analysis of coupled heat and moisture transfer in concrete subjected to fire. Numer. Heat Transf. Part A Appl.
**39**(7), 685–710 (2001)CrossRefGoogle Scholar - Ulm, F.J., Acker, P., Lévy, M.: The chunnel fire. II: analysis of concrete damage. J. Eng. Mech.
**125**(3), 283–289 (1999)CrossRefGoogle Scholar - VDI: VDI Heat Atlas (VDI-Buch in German), 2nd edn, 1584 pp. ISBN 978-3-540-77877-6, 978-3-540-79999-3, 978-3-540-77876-9. Springer, Berlin (2010)Google Scholar
- Weber, B.: Heat transfer mechanisms and models for a gypsum board exposed to fire. Int. J. Heat Mass Transf.
**55**(5), 1661–1678 (2012)CrossRefGoogle Scholar - Whitaker, S.: Simultaneous heat, mass, and momentum transfer in porous media: a theory of drying. Adv. Heat Transf.
**13**, 119–203 (1977)CrossRefGoogle Scholar - Xu, Yy, Wu, B.: Fire resistance of reinforced concrete columns with l-, t-, and+-shaped cross-sections. Fire Saf. J.
**44**(6), 869–880 (2009)CrossRefGoogle Scholar - Yuen, R.K., Kwok, W., Lo, S., Liang, J.: Heat and mass transfer in concrete at elevated temperature. Numer. Heat Transf. Part A Appl.
**51**(5), 469–494 (2007)CrossRefGoogle Scholar