Analytic Solution of Governing Equations of Heat and Moisture Transfer in a CapillaryPorous Body with Dirichlet Boundary Conditio

Document Type : Research Article

Author

Mechanical Engineering Department, Imam Khomeini International University, Qazvin,Iran

Abstract

In this research, a new analytical solution of one dimensional coupled equations of moisture and heat transfer in a capillary-porous body is presented. These equations are known as the Luikov system of equations. These partial differential equations are coupled and non-homogenous, that could be considered linear with the assumption that the coefficients of the equations are independent of space, time, and (every) dependent variables. In the innovative method of this survey, at the first, it is assumed that the system of equations is independent of each other, it has been resulted in a general answer for equations by using the method of separation of variables. Next, the special answers will be obtained by considering coupled equations and using the Laplace transform method. In this survey, it has been studied the effect of dimensionless coefficients such as Luikov number, Fourier number, and phase change coefficient on the rate of heat and moisture transfer. The result shows the coupling important effect of Luikov number on the rate of heat and moisture transfer of capillary-porous body equations. It has also resulted that the phase change coefficient has a minor effect on moisture transfer which was also reported in the study of Luikov.

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References

[1] A. V. Luikov, Y. A. Mikhailov, Theory of  energy and mass Transfer, Pergamon Press, 1966.
[2] A.V. Luikov, Heat and mass transfer in capillary- porous bodies, Pergamon Press,Oxford, 233– 303,1966
[3] M.D. Mikhailov, M.N. Özisik, Unified  Analysis and Solutions of Heat and Mass Diffusion, Wiley, 1984.
[4] P.D.C. Lobo, M.D. Mikhailov, M.N. Özisik, On the complex eigenvalues of Luikov system of equations, Drying Technology 5 (2) 273–286,1984.
[5] R.N. Pandey, S.K. Srivastava, M.D. Mikhailov, Solutions of Luikov equations of heat and mass transfer in capillary porous bodies through matrix calculus: a new approach, International journal of heat and mass transfer 42 (14( 2649–2660, 1999.
[6] Ribeiro, J. W., R. M. Cotta, and M. D. Mikhailov. "Integral transform solution of Luikov's equations for heat and mass transfer in capillary porous media." International journal of heat and mass transfer 36, no. 18 4467-4475,1993.
[7] M. Qin, R. Belarbi, A. Aït-Mokhtar, A. Seigneurin, An analytical method to calculate  the  coupled  heat and moisture transfer in building materials, International Communications in Heat and Mass Transfer, 33 (3( 39–48,2006.
[8] Liu, Jen Y., and Cheng Shun. "Solutions of Luikov equations of heat and mass transfer in capillary- porous bodies." International Journal of Heat and Mass Transfer 34, no. 7: 1747-1754,1991.
[9] R.W Lewis, W. J. Ferguson, A partially nonlinear finite element analysis of  heat and  mass transfer  in  a  capillary-porous  body under  the  influence  of a pressure gradient, Applied mathematical modelling, 17, 15-24,1993.
[10] Comini, G., and R. W. Lewis. "A numerical solution of two-dimensional problems involving heat and mass transfer." International journal of heat and mass transfer 19, no. 12 : 1387-1392, 1976.
[11] Zhang, Hongwei, and Qingying Hu. "Analytical Solutions to Coupled Partial Differential Equations Governing Heat and Mass Transfer During Food Drying." Advances in Information Sciences and Service Sciences 5, no. 5 : 387,2013.
[12] Dantas, L. B., H. R. B. Orlande,  and  R.  M. Cotta. "Estimation  of  dimensionless  parameters  of Luikov's system for heat and mass transfer in capillary porous media." International Journal of Thermal Sciences 41, no. 3: 217-227,2012.
[13] Santos, MJ Nascimento, João MPQ Delgado, Antonio Gilson Barbosa de Lima, and I.  R. Oliveira. "Liquid injection  molding  process  in  the manufacturing of fibrous composite materials: Theory, advanced modeling and engineering applications." In Transport Phenomena in Multiphase Systems, pp. 251-272. Springer, Cham, 2018.
[14] Yu, Chenxu, and Joseph Irudayaraj. "Multiplex biosensor using gold nanorods." Analytical chemistry 79, no. 2: 572-579, 2007.
[15] Yang, Yanmei, Qing Shao, Renren Deng, Chao Wang, Xue Teng, Kai Cheng, Zhen Cheng et al. "In vitro and in vivo uncaging and bioluminescence imaging by using photocaged upconversion nanoparticles." Angewandte Chemie International Edition 51, no. 13: 3125-3129, 2012.
[16] D. Kulasiri, I.  Woodhead,  Analytical  solutions to coupled partial differential equations governing heat and moisture transfer, Hindawi publishing corporation, Mathematical problems in engineering, 2005:3 (2005( 275–291.
[17] Volpicelli, Giovanni, Mahmoud Elbarbary, Michael Blaivas, Daniel A. Lichtenstein, Gebhard Mathis, Andrew W. Kirkpatrick, Lawrence Melniker et al. "International evidence-based  recommendations for point-of-care lung ultrasound." Intensive care medicine 38, no. 4 577-591,2012.
Amirkabir Journal of Mechanical Engineering
Volume 52, Issue 2
May 2020
Pages 465-476

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