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Stochastic modelling of the heat and moisture transfer in a porous medium

机译：多孔介质中热量和水分传递的随机模型

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摘要

A multi-phase and multi-component flow model with inherent stochastic terms is derived and is used to study the heat and moisture transfer in a fibrous porous medium. The materials' porosity, velocity derived from Darcy's law and ambient temperature at the external boundary are treated as white Gaussian noises. An effective multistep implicit splitting finite difference method (FDM) is adopted to solve the strongly coupled non-linear water, energy, vapour and air equations. The existence of a unique solution is analysed through the Lipschitz, monotonicity, growth, hemicontinuity and coercivity conditions. The notion of better thermal comfort arises from the results, as fluctuations are seen to dissipate on approaching the inner boundary (human body). Also, attention is drawn to the significance of considering all necessary uncertain variables in the system of equations. Four scenarios are considered in order to investigate the degree of contribution of the fluctuating terms. Clearly, ignoring certain vital stochastic elements can influence the results. Consequently, a combination of the stochastic porosity, velocity and ambient temperature incorporated into the same multi-phase and multi-component flow model is expected to provide more realistic results.
机译：推导了具有固有随机项的多相多组分流动模型，该模型用于研究纤维状多孔介质中的热量和水分传递。材料的孔隙率，根据达西定律得出的速度和外部边界处的环境温度被视为高斯白噪声。采用有效的多步隐式分裂有限差分法（FDM）求解强耦合非线性水，能量，蒸气和空气方程。通过Lipschitz，单调性，增长，半连续性和矫顽力条件分析了唯一解决方案的存在。结果显示出更好的热舒适性，因为随着接近内边界（人体），波动逐渐消失。同样，提请注意考虑方程组中所有必需的不确定变量的重要性。为了研究波动项的贡献程度，考虑了四种方案。显然，忽略某些重要的随机因素会影响结果。因此，将随机孔隙率，速度和环境温度结合到同一多相和多组分流动模型中，有望提供更实际的结果。

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