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

## TL;DR

This paper introduces a spectral reduced-order numerical method for efficiently simulating heat and moisture transfer in multilayered porous media, demonstrating high accuracy and computational speed through case studies and experimental validation.

## Contribution

It presents a novel spectral reduced-order approach that simplifies the complex coupled heat and moisture transfer equations, improving efficiency and accuracy over traditional methods.

## Key findings

- Method accurately predicts nonlinear heat and moisture transfer.
- Spectral approach reduces computational cost significantly.
- Validated against experimental data with high reliability.

## Abstract

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.