Analytical and numerical investigation of water diffusion through Raffia vinifera pith

References

• Abu, A. K., P. P. Kofi Yalley, and F. Adogla. 2016. The use of raffia palm (raffia hookeri) piassava fibres as reinforcement of concrete. The International Journal of Ingineering and Science 5 (6):1–17.
   Google Scholar
• Bakhtiyor, K., M. Jabbor, I. Gafurjan, M. A. Fadzilah, and F. Bekzodjon. 2020. Solute transport in the element of fractured porous medium with an inhomogeneous porous block. symmetry 12 (6):1–13. doi:10.3390/sym12061028.
   Google Scholar
• Berthelot, J. M. 2010. Mécanique des Matériaux et Structures Composites. France: Le Mans.
   Google Scholar
• Carr, E. J. 2018. Characteristic time scales for diffusion processes through layers and across interfaces. Physical Review E 97 (4):1–15. doi:10.1103/PhysRevE.97.042115.
   Web of Science ®Google Scholar
• Carr, E. J., and N. G. March. 2018. Semi-analytical solution of multilayer diffusion problems with time-varying boundary conditions and general interface conditions. Applied Mathematics and Computation 333:286–303. doi:10.1016/j.amc.2018.03.095.
   Web of Science ®Google Scholar
• Carr, E. J., and G. Pontrelli. 2018. Modelling mass diffusion for a multi-layer sphere immersed in a semi-infinite medium: Application to drug delivery. Mathematical Biosciences 303:1–9. doi:10.1016/j.mbs.2018.04.004.
   PubMed Web of Science ®Google Scholar
• Carr, E. J., and I. W. Turner. 2016. A semi-analytical solution for multilayer diffusion in a composite medium consisting of a large number of layers. Applied Mathematical Modelling 40 (15–16):7034–50. doi:10.1016/j.apm.2016.02.041.
   Web of Science ®Google Scholar
• Carslaw, H. S., and J. C. Jaeger. 1959. Conduction of heat in solids. Second ed. London: Oxford at the Clarendon press.
   Google Scholar
• Castiglione, P., B. P. Mohanty, P. J. Shouse, J. Simunek, M. Th van Genuchten, and A. Santini. 2003. Lateral water diffusion in an artificial macroporous system: modeling and experimental evidence. Vadose Zone Journal 2 (2):212–21. doi:10.2113/2.2.212.
   Web of Science ®Google Scholar
• Crank, J. 1995. The mathematics of diffusion. second ed. London, W.I: Oxford University Press.
   Google Scholar
• Dahlquist, G. A. B. 2008. Numerical methods in scientific computing, Vol. 2. Philadelphia: SIAM.
   Google Scholar
• Dahlquist, G., and A. Björck. 2007. Numerical methods in scientific computing, Vol. 1. Philadelphia: SIAM.
   Google Scholar
• Dejam, M., H. Hassanzadeh, and Z. Chen. 2016. Shear dispersion in a capillary tube with a porous wall. Journal of Contaminant Hydrology 185-186:87–104. doi:10.1016/j.jconhyd.2016.01.007.
   PubMed Web of Science ®Google Scholar
• Delouei, A. A., M. H. Kayhani, and M. Norouzi. 2012. Exact analytical solution of unsteady axi-symmetric conductive heat transfer in cylindrical orthotropic composite laminates. International Journal of Heat and Mass Transfer 55:4427–36. doi:10.1016/j.ijheatmasstransfer.2012.04.012.
   Web of Science ®Google Scholar
• Elenga, R. G., G. F. Dirras, J. G. Maniongui, P. Djemia, and M. P. Biget. 2009. On the microstructure and physical properties of untreated raffia textilis fiber. Composites Part A, Applied Science and Manufacturing 40 (4):418–22. doi:10.1016/j.compositesa.2009.01.001.
   Web of Science ®Google Scholar
• Elenga, R. G., G. F. Dirras, J. G. Maniongui, and B. Mabiala. 2011. Thin-layer drying of raffia textilis fiber. BioRessurces 6 (4):4135–44.
   Web of Science ®Google Scholar
• Elenga, R. G., P. Djemia, M. P. Biget, J. G. Maniongui, and G. Dirras. 2006. Microstructure et Propriétés Physico-Mécaniques de la fibre brute de Raphia. Researchgate 1–9.
   Google Scholar
• Elenga, R. G., P. Djemia, D. Tingaud, T. Chauveau, J. G. Maniongui, and G. Dirras. 2013. Effects of alkali traitement on the microstructure, composition, and properties of raffia textillis fiber. BioRessurces 8 (2):2934–49. doi:10.15376/biores.8.2.2934-2949.
   Web of Science ®Google Scholar
• Elenga, R. G., G. Tsiba, J. G. Maniongui, J. M. Ouamba, and J. M. Bessière. 2011. Effects of drying methods on the drying kinetics and the essential oil of “Lippia multiflora” moldenke leaves. Research Journal of Applied Sciences, Engineering and Technology 3 (10):1135–41.
   Google Scholar
• Epelde, G. M. 2015. Bessel functions and equations of mathematical physics. Leioa: Final Degree Dissertation, Universidad del Pais Vasco.
   Google Scholar
• Foadieng, E., M. Fogue, A. G. L. Gbaguidi, P. K. Talla, F. B. Pelap, A. Foudjet, A. F. Sinju, G. N. Bawe, and S. T. Mabekou. 2012. Effect of the span length on the deflection and the creep behaviour of Raphia vinifera l. arecacea beam. International Journal of Materials Science 7 (2):153–67.
   Google Scholar
• Foadieng, E., P. K. Talla, and M. Fogue. 2019. Study of the mechanical properties of raffia bamboo Vinifera L. Arecaceae. Revue Scientifique et Technique Forêt et Environnement du Bassin du Congo 12:12–21. doi:10.5281/zenodo.2610534.
   Google Scholar
• Foadieng, E., P. K. Talla, M. Fogue, S. Mabekou, and A. F. Sinju. 2014. Contribution à l’étude de l’anatomie et des propriétés physiques du bambou de Raphia vinifera (arecaceae. Revue Scientifique et Technique Forêt et Environnement du Bassin du Congo 3:9–18.
   Google Scholar
• Foadieng, E., P. K. Talla, G. B. Nkamgang, and M. Fogue. 2017. Study of the thermal properties of Raffia Bamboo Vinifera L. Arecaceae,advances in materials science and engineering. Advances in Materials Science and Engineering 2017:1–10. doi:10.1155/2017/9868903.
   Web of Science ®Google Scholar
• Gilli, M. 2015. Méthodes numériques. Suisse: Département d’économétrie, Université de Genève.
   Google Scholar
• Hahn, D. W., and M. N. Özisik. 2012. Heat conduction. Third ed. Hoboken, New Jersey: John Wiley & Sons.
   Google Scholar
• Hickson, R. I., S. I. Barry, and G. N. Mercer. 2009. Critical times in multilayer diffusion. Part 1: Exact solutions. International Journal of Heat and Mass Transfer 52 (26):5776–83. doi:10.1016/j.ijheatmasstransfer.2009.08.013.
   Web of Science ®Google Scholar
• Ismail, M. F., M. T. H. Sultan, A. Hamdan, A. U. M. Shah, and M. Jawaid. 2019. Low velocity impact behaviour and post-impact characteristics of kenaf/glass hybrid composites with various weight ratios. Journal of Materials Research and Technology 8 (3):2662–73. doi:10.1016/j.jmrt.2019.04.005.
   Google Scholar
• Jain, P. K., S. Suneet, and R. U. Rizwan-Uddin. 2009. Analytical solution to transient asymmetric heat conduction in a multilayer annulus. Journal of Heat Transfer 131 (1):1–7. doi:10.1115/1.2977553.
   Web of Science ®Google Scholar
• Kaoui, B., M. Lauricella, and G. Pontrelli. 2018. Mechanistic modelling of drug release from multi-layer capsules. Computers in Biology and Medicine 93:149–57. doi:10.1016/j.compbiomed.2017.12.010.
   PubMed Web of Science ®Google Scholar
• LaBolle, E. M., J. Quastel, and G. E. Fogg. 1998. Diffusion theory for transport in porous media: Transitionprobability densities of diffusion processes corresponding to advection-dispersion equations. Water Resources Research 34 (7):1685–93. doi:10.1029/98WR00319.
   Web of Science ®Google Scholar
• Lerner, N. 2015. Fonctions spéciales, Cours de master 1. Paris: Université Pierre et Marie Curie.
   Google Scholar
• Lubin, T. 2017. Equations aux dérivées partielles (EDP), Méthode de résolution des EDP par séparation de variables; Applications. Université de Lorraine - Faculté des Sciences et Technologies - Nancy, France.
   Google Scholar
• Matthews, F. L., G. A. O. Davies, D. Hitchings, and C. Soutis. 2000. Finite element modelling of composite materials and structures. Cambridge England: Woodhead Publishing Limited.
   Google Scholar
• Mbou, E. T., E. Njeugna, A. Kemajou, N. R. T. Sikame, and D. Ndapeu. 2017. Modelling of the water absorption kinetics and determination of the water diffusion coefficient in the pith of Raffia vinifera of Bandjoun, Cameroon. Advances in Materials Science and Engineering 1–12. doi:10.1155/2017/1953087.
   Web of Science ®Google Scholar
• Michel, P., and H. Antoine. 2014. Analyse Numérique, Ecole des Mines de Nancy - Campus Artem - 54 042 Nancy Cedex.
   Google Scholar
• Monte, F. 2000. An analytic approach to the unsteady heat conduction processes in one-dimensional composite media. International Journal of Heat and Mass Transfer 45 (6):1333–43. doi:10.1016/S0017-9310(01)00226-5.
   Web of Science ®Google Scholar
• Naveen, J., M. Jawaid, E. S. Zainudin, M. T. H. Sultan, R. Yahaya, and M. S. Abdul Majid. 2019. Thermal degradation and viscoelastic properties of Kevlar/Cocos nucifera sheath reinforced epoxy hybrid composites. Composite Structures 219:194–202. doi:10.1016/j.compstruct.2019.03.079.
   Web of Science ®Google Scholar
• Nayak, S. Y., M. T. H. Sultan, S. B. Shenoy, C. R. Kini, R. Samant, A. U. M. Shah, and P. Amuthakkannan. 2020. Potential of natural fibers in composites for ballistic applications–a review. Journal of Natural Fibers 19:1–11. doi:10.1080/15440478.2020.1787919.
   Web of Science ®Google Scholar
• Neto, J. S. S., H. F. M. de Queiroz, R. A. A. Aguiar, and M. D. Banea. 2021. A review on the thermal characterisation of natural and hybrid fiber composites. Polymers 4425 (13):1–28. doi:10.3390/polym13244425.
   Google Scholar
• Nimjieu, T. H., N. R. T. Sikame, P. R. T. Nwagoum, M. Fogue, and E. Njeugna. 2021. Modeling of hygro-mechanical behaviour through raffia vinifera fiber during the water diffusion phenomenon. Mathematical Problems in Engineering 1-2:1–12. doi:10.1155/2021/9354878.
   Google Scholar
• Nimjieu, T. H., T. N. R. Sikame, T. P. R. Nwagoum, R. Tapimo, M. Fogue, and E. Njeugna. 2022. Analytical and numerical modeling and simulation of heat transfer through raffia vinifera bamboo. Alexandria Engineering Journal 61:12463–74. doi:10.1016/j.aej.2022.06.032.
   Web of Science ®Google Scholar
• Njeugna, E., T. N. R. Sikame, J. -Y. Drean, D. Fokwa, and O. Harzallah. 2012. Mechanical characterization of Raffia fibres from “raphia viniferaa. International Journal of Mechanics Structural 3 (1):1–17.
   Google Scholar
• Nouri, M., M. Tahlaiti, A. Meroufel, and F. Grondin. 2021. Enhanced modeling of water diffusion in natural fibers: Application to diss fibers. Journal of Natural Fibers 19:9259–68. doi:10.1080/15440478.2021.1982817.
   Web of Science ®Google Scholar
• Obahiagbon, F. I. 2009. A review of the origin, morphology, cultivation, economic products, health and physiological implications of raphia palm. African Journal of Foods Science 3 (13):447–53.
   Google Scholar
• Ohimain, E. I., I. R. Inyan, and G. U. Osai. 2015. The effects of raffia palm mesocarp on heamatological parameters of clarias gariepinus, a common Niger delta wetland fish. Annual Research & Review in Biology 8:1–7. doi:10.9734/ARRB/2015/19065.
   Google Scholar
• Oliveira Filho, E. G. D., F. Santos da Luz, R. T. Fujiyama, A. C. Rios da Silva, V. S. Candido, and S. N. Monteiro. 2020. Effect of chemical treatment and length of raffia fiber (Raphia vinifera) on mechanical stiffening of polyester composites. Polymers 12:1–17. doi:10.3390/polym12122899.
   Web of Science ®Google Scholar
• Özisik, N. M. 1993. Heat conduction. Second ed. New York: John Wiley & Sons, Inc.
   Google Scholar
• Quarteroni, A., R. Sacco, and F. Saleri. 2004. Méthodes Numériques Algorithmes, analyse et applications. Springer. doi:10.1007/978-88-470-0496-2.
   Google Scholar
• Rober, J. J. T., and T. Shedrack. 2016. Investigation of thermal conductivity of raphia fibre (Piassava) from raphia hookeri. International Journal of Applied Science and Mathematical Theory 2:11–17.
   Google Scholar
• Rodrigo, M. R., and A. L. Worthy. 2016. Solution of multilayer diffusion problems via the Laplace transform. Journal of Mathematical Analysis and Applications 444 (1):475–502. doi:10.1016/j.jmaa.2016.06.042.
   Web of Science ®Google Scholar
• Safri, S. N. A., M. T. H. Sultan, N. Saba, and M. Jawaid. 2018. Effect of benzoyl treatment on flexural and compressive properties of sugar palm/glass fibres/epoxy hybrid composites. Polymer Testing 71:362–69. doi:10.1016/j.polymertesting.2018.09.017.
   Web of Science ®Google Scholar
• Sikame, N. R. T., N. Ebénézer, N. Dieunedort, F. Didier, M. Fogue, J. Y. Drean, and O. Harzallah. 2017. Investigation of the physical and mechanical properties of Raffia vinifera fibers along the stem. Journal of Natural Fibers 14 (5):621–33. doi:10.1080/15440478.2016.1250025.
   Web of Science ®Google Scholar
• Sikame, T. N. R., T. E. Mbou, O. Harzallah, D. Ndapeu, W. Huisken, D. Nkemaja, E. Njeugna, M. Fogue, and J. -Y. Drean. 2020. Physicochemical and mechanical characterization of Raffia vinifera pith. Advances in Materials Science and Engineering 2020:1–10. doi:10.1155/2020/8895913.
   Web of Science ®Google Scholar
• Sikame, N. R. T., D. Ndapeu, D. Nkemaja, G. Tchemou, D. Fokwa, W. Huisken, O. Harzallah, M. Fogue, J. -Y. Drean, and O. Harzallah. 2018. Study of the viscoelastic behaviour of the Raffia vinifera fibres. Industrial Crops and Products 124:572–81. doi:10.1016/j.indcrop.2018.07.077.
   Web of Science ®Google Scholar
• Sikame, T. N. R., E. Njeugna, M. Fogue, J. Y. Drean, and D. Fokwa. 2013. Study of water diffusion through Raffia Vinifera fibres of the stem from Bandjoun Cameroon: Case of drying kinetics. Research Journal of Applied Sciences, Engineering and Technology 6 (19):3547–58. doi:10.19026/rjaset.6.3559.
   Google Scholar
• Sikame, N. R. T., E. Njeugna, M. Fogue, J. Y. Drean, A. Nzeukou, and D. Fokwa. 2014. Study of water absorption in Raffia vinifera fibres from Bandjoun,Cameroon. ScientificWorldjournal 2014:1–12. doi:10.1155/2014/912380.
   Google Scholar
• Silva, E. G. D. 2007. Méthodes et Analyse Numériques”. Engineering School Institut Polytechnique de Grenoble 99.
   Google Scholar
• Sultan, M. T. H., K. Worden, W. J. Staszewski, S. G. Pierce, J. M. Duliue-Barton, and A. Hodzic. 2009. Impact damage detection and quantification in CFRP laminates: A precursor to machine learning. Structural Health Monitoring 2009: From System Integration to Autonomous Systems - Proceedings of the 7th International Workshop on Structural Health Monitoring, IWSHM 2009:1528–37.
   Google Scholar
• Talla, P. K., A. Fomethe, M. Fogue, A. Foudjet, and G. N. Bawe. 2010. Time-temperature equivalency of Raphia vinifera L. (Arecaceae) under compression. International Journal of Mechanics & Solids 5 (1):27–33.
   Google Scholar
• Talla, P. K., A. Foudjet, and M. Fogue. 2005. Statistical model of strength in flexion and size effect on the failure of Raphia vinifera L. (Arecacea. Journal of Bamboo and Rattan 4 (4):335–42. doi:10.1163/156915905775008435.
   Google Scholar
• Talla, P. K., F. B. Pelap, M. Fogue, A. Fomethe, G. N. Bawe, E. Foadieng, and M. H. Kadivar. 2007. Nonlinear creep behavior of Raphia vinifera L.(Arecacea)”. International Journal of Mechanics and Solids 2 (1):1–11.
   Google Scholar
• Talla, P. K., J. R. Tekougnening, E. Tangka, A. Foudjet, 2004. Statistical model of strength in compression of Raphia vinifera L. (Arecacea). Journal of Bamboo and Rattan 3 (3):229–35. doi:10.1163/1569159041765290.
   Google Scholar
• Tamene, Y., C. Bougriou, and R. Bessaïh. 2006. Thermal behaviour of a composite cylinder in transient regime. International Journal of Theoretical and Applied Mechanics 1 (1):1–12.
   Google Scholar
• Tido, T. S., G. C. Komadja, Y. R. Nafu, A. A. Mahamat, P. W. H. Mejouyo, J. F. Tendo, E. Njeugna, P. A. Onwualu, and H. S. Junior. 2022. Potential of raffia nanofibrillated cellulose as a reinforcement in extruded earth-based materials. Case Studies in Construction Materials 16 (2022):1–11. doi:10.1016/j.cscm.2022.e00926.
   Google Scholar
• Watson, G. N. 1922. A treatise on the theory of bessel functions. Cambridge: Cambridge at the university press.
   Google Scholar
• Zakharov, V. 2009. Bessel functions and their applications to solutions of partial differential equations. Lecture Notes.
   Google Scholar