A spectral method for solving heat and moisture transfer through consolidated porous media

This work presents an efficient numerical method based on spectral expansions for simulation of heat and moisture diffusive transfers through multilayered porous materials. Traditionally, by using the finite-difference approach, the problem is discretized in time and space domains (Method of lines) to obtain a large system of coupled Ordinary Differential Equations (ODEs), which is computationally expensive. To avoid such a cost, this paper proposes a reduced-order method that is faster and accurate, using a much smaller system of ODEs. To demonstrate the benefits of this approach, tree case studies are presented. The first one considers nonlinear heat and moisture transfer through one material layer. The second case - highly nonlinear - imposes a high moisture content gradient - simulating a rain like condition - over a two-layered domain, while the last one compares the numerical prediction against experimental data for validation purposes. Results show how the nonlinearities and the interface between materials are easily and naturally treated with the spectral reduced-order method. Concerning the reliability part, predictions show a good agreement with experimental results, which confirm robustness, calculation efficiency and high accuracy of the proposed approach for predicting the coupled heat and moisture transfer through porous materials.

[1]  Weidong Guo,et al.  The Application of the Chebyshev-Spectral Method in Transport Phenomena , 2013 .

[2]  Ben-Wen Li,et al.  Iterative and direct Chebyshev collocation spectral methods for one-dimensional radiative heat transfer , 2008 .

[3]  Philip S. Beran,et al.  Reduced-order modeling - New approaches for computational physics , 2001 .

[4]  C. Herzet,et al.  Model Reduction from Partial Observations , 2016 .

[5]  Roland W. Lewis,et al.  A fully nonlinear analysis of heat and mass transfer problems in porous bodies , 1980 .

[6]  Ben-Wen Li,et al.  Chebyshev collocation spectral method for solving radiative transfer with the modified discrete ordinates formulations , 2015 .

[7]  Jan Carmeliet,et al.  Assessment Method of Numerical Prediction Models for Combined Heat, Air and Moisture Transfer in Building Components: Benchmarks for One-dimensional Cases , 2004 .

[8]  Nathan Mendes,et al.  Numerical methods for diffusion phenomena in building physics: A practical introduction , 2017 .

[9]  Yaowen Yang,et al.  Collocation methods for uncertain heat convection-diffusion problem with interval input parameters , 2016 .

[10]  S. Motsa.  On the New Bivariate Local Linearisation Method for Solving Coupled Partial Differential Equations in Some Applications of Unsteady Fluid Flows with Heat and Mass Transfer , 2015 .

[11]  Nathan Mendes,et al.  Solving nonlinear diffusive problems in buildings by means of a Spectral reduced-order model , 2017, 1704.07607.

[12]  Nathan Mendes,et al.  Stable explicit schemes for simulation of nonlinear moisture transfer in porous materials , 2017, 1701.07059.

[13]  Ben-Wen Li,et al.  Spectral collocation method for natural convection in a square porous cavity with local thermal equilibrium and non-equilibrium models , 2016 .

[14]  Thermal radiation heat transfer in one- and two-dimensional enclosures using the spectral collocation method with full spectrum k-distribution model , 2014 .

[15]  Nathan Mendes,et al.  Advanced Reduced-Order Models for Moisture Diffusion in Porous Media , 2017, Transport in Porous Media.

[16]  T. A. Zang,et al.  Spectral Methods: Fundamentals in Single Domains , 2010 .

[17]  J. R. Philip,et al.  Moisture movement in porous materials under temperature gradients , 1957 .

[18]  W. Gautschi.  Orthogonal Polynomials: Computation and Approximation , 2004 .

[19]  J.-L. Auriault,et al.  Heat and mass transfer in wet porous media in presence of evaporation—condensation , 1998 .

[20]  Xiaoshu Lü,et al.  Modelling of heat and moisture transfer in buildings: I. Model program , 2002 .

[21]  W. Kahan,et al.  On a proposed floating-point standard , 1979, SGNM.

[22]  A. Luikov.  Heat and Mass Transfer in Capillary-Porous Bodies , 2014 .

[23]  Catherine Buhé,et al.  Factors governing the development of moisture disorders for integration into building performance simulation , 2015 .

[24]  J. Roux,et al.  Influence of concrete fracture on the rain infiltration and thermal performance of building facades , 2013 .

[25]  Claudio Canuto,et al.  Spectral Methods: Evolution to Complex Geometries and Applications to Fluid Dynamics (Scientific Computation) , 2007 .

[26]  L. Trefethen.  Spectral Methods in MATLAB , 2000 .

[27]  L. Trefethen.  Finite Difference and Spectral Methods for Ordinary and Partial Differential Equations , 1996 .

[28]  Simultaneous transport of heat and moisture in a partially saturated porous media , 1990 .

[29]  P. Perré,et al.  Vers une méthode de conception HYGRO-thermique des BATiments performants : démarche du projet HYGRO-BAT , 2014 .

[30]  Monika Woloszyn,et al.  Identification of the hygrothermal properties of a building envelope material by the covariance matrix adaptation evolution strategy , 2016 .

[31]  Hywel Rhys Thomas,et al.  The influence of soil moisture content variations on heat losses from earth-contact structures: an initial assessment , 2001 .

[32]  Vasco Peixoto De Freitas,et al.  Moisture migration in building walls—Analysis of the interface phenomena , 1996 .

[33]  Z. Bai.  Krylov subspace techniques for reduced-order modeling of large-scale dynamical systems , 2002 .

[34]  H. Sadrnia,et al.  Spectral method for simulating 3D heat and mass transfer during drying of apple slices , 2017 .

[35]  A. V. Luikov,et al.  CHAPTER 6 – HEAT AND MASS TRANSFER IN CAPILLARY-POROUS BODIES , 1966 .

[36]  Monika Woloszyn,et al.  Proper generalized decomposition for solving coupled heat and moisture transfer , 2015 .

[37]  Sandile Sydney Motsa,et al.  A spectral relaxation method for linear and non-linear stratification effects on mixed convection in a porous medium , 2015, Appl. Math. Comput..

[38]  Nathan Mendes,et al.  A method for predicting heat and moisture transfer through multilayered walls based on temperature and moisture content gradients , 2005 .

[39]  M. Deru.  Model for Ground-Coupled Heat and Moisture Transfer from Buildings , 2003 .

[40]  Seckin Gokaltun,et al.  Constrained reduced-order models based on proper orthogonal decomposition , 2017 .

[41]  Bengt Fornberg,et al.  A practical guide to pseudospectral methods: Introduction , 1996 .

[42]  Jintu Fan,et al.  An improved model of heat and moisture transfer with phase change and mobile condensates in fibrous insulation and comparison with experimental results , 2004 .

[43]  R. Peyret.  Spectral Methods for Incompressible Viscous Flow , 2002 .

[44]  J. Berger,et al.  Comparison of model numerical predictions of heat and moisture transfer in porous media with experimental observations at material and wall scales: An analysis of recent trends , 2018, Drying Technology.

[45]  Nathan Mendes,et al.  Combined Heat, Air and Moisture (HAM) Transfer Model for Porous Building Materials , 2009 .

[46]  Wha Wil Schilders,et al.  Introduction to model order reduction , 2008 .