A. S. Y. Nana - Department of Mathematics, University of Yaounde I, Cameroon. K. M. Malloum - Department of Mathematics, University of Ndjamena, Chad. M. S. D. Haggar - Department of Mathematics, University of Ndjamena, Chad. M. Mbehou - Department of Mathematics, University of Yaounde I, Cameroon.
The study of heat and moisture transfer in fibrous insulation materials is crucial for optimizing thermal performance and ensuring durability in various applications. This paper presents a comprehensive analysis of the linearized Crank-Nicolson finite element method (FEM) as applied to the coupled heat and moisture transfer equations in fibrous insulation. The Finite Element Method (FEM) is particularly well-suited for solving complex, nonlinear problems like heat and moisture transfer in fibrous insulation materials. FEM allows for the accurate modeling of complex geometries and nonlinear material properties, which is crucial for simulating the behavior of fibrous insulation materials. Compared to other finite methods, FEM provides a flexible framework for handling coupled heat and moisture transfer equations, allowing for the accurate prediction of temperature and moisture distributions within the material. The semi-discrete formulation is presented using FEM and optimal error estimates for \(L^2\) and energy norms are established. For the fully discrete scheme, the stability and optimal error estimates for the numerical solution are also derived for the same norms, highlighting the method's convergence properties and accuracy. The analysis considers various factors influencing the transfer processes, including fiber orientation, density, and environmental conditions.
A. S. Y. Nana, K. M. Malloum, M. S. D. Haggar, M. Mbehou, Numerical analysis for heat and moisture transfer in fibrous insulation, Journal of Mathematics and Computer Science, 42 (2026), no. 1, 1--20
Nana A. S. Y., Malloum K. M., Haggar M. S. D., Mbehou M., Numerical analysis for heat and moisture transfer in fibrous insulation. J Math Comput SCI-JM. (2026); 42(1):1--20
Nana, A. S. Y., Malloum, K. M., Haggar, M. S. D., Mbehou, M.. "Numerical analysis for heat and moisture transfer in fibrous insulation." Journal of Mathematics and Computer Science, 42, no. 1 (2026): 1--20
