Solutions of Luikov equations of heat and mass transfer in capillary-porous bodies

Liu, Jen Y.; Cheng, Shan

doi:10.1016/0017-9310(91)90150-d

Cited by 60 publications

(21 citation statements)

References 6 publications

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“…It was observed by Lobo (1987) that the numerical example presented by Mikhailov and Shishedjiev (1975) were not fully converged for smaller values of the time variable because they did not consider the existence of complex eigenvalues. Liu and Cheng (1991) confirmed such values and report numerical efforts in computing them.…”

Section: Introductionsupporting

confidence: 79%

On comparing finite difference schemes applied to a nonlinear multi-region heat and mass transfer problem

Lobo

2002

Computational Mechanics

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A three-time-level scheme is employed to obtain numerical solutions of heat and mass transfer potentials for the nonlinear Luikov system. Relative errors are examined when the numerical solutions are compared to the analytical solutions for a single layer linear problem using different finite difference techniques. As a final example, comparisons also are made when the numerical schemes are used to solve a two-layer multi-region nonlinear approach, considering that the thermal conductivity and mass conductivity of the material are dependent on temperature and moisture transfer potential respectively. List of symbolsBi m Biot number for mass transfer, a m L=k m Bi q Biot number for heat transfer, a q L=k q Fo Fourier number, a q s=L 2 Ki m dimensionless mass flux, Lw m =k m / / Ki q dimensionless heat flux, Lw q =k q t t Ko Kossovitch number, qc m /=c q t Lu Luikov number, a m =a q Pn Posnov number, d t t=c m / / r r dimensionless coordinate, r=L e phase change criterion, where, for the boundary conditions of the second kind t t ¼ t 0 ; / / ¼ / 0 and for the boundary conditions of the third kind t t ¼ t s À t 0 ;/ / ¼ / 0 À / Ã a m diffusion coefficient of moisture, m 2 /s a q thermal diffusivity coefficient, m 2 /s c m specific isothermal mass capacity, 1/ M c q specific heat capacity, kJ/Kg C L half thickness of the layer, m q specific heat of evaporation, kJ/kg t temperature, C r coordinate perpendicular to the surface, m a m mass transfer coefficient, kg/m 2 s M a q heat transfer coefficient, kJ/m 2 s C d thermal gradient coefficient, 1/ C k m moisture conductivity, kg/m s M k q thermal conductivity, kJ/m s C s time, s / moisture transfer potential, M w m mass flux, kg/m 2 s w q heat flux, kg/m 2 s Subscripts 0 initial s surrounds or surface Ã in equilibrium with surroundings j region i space node Superscript n geometry h time level IntroductionThere is a continuously increasing activity in the field of heat and mass transfer in capillary porous media due to its wide research as well industrial applications. Besides its applications as ground water pollution, heat transfer in the ground, drying processes, and multiphase flow under nonisothermal conditions, it is also been used in space research, especially in devices for liquid and energy transfer (heat pipes, heat exchangers, insulation of highly conducting wire nets, etc.) due to the fact that the performance of capillary porous materials does not depend on a gravitational field (Pandey et al., 1999). Because of the complexities of the mechanism involved, it is very difficult to model the process. The phenomena appropriate for moisture, pressure and enthalpy distributions are coupled. The transport of associated matter of all phases and the transfer of enthalpy must be considered simultaneously. Luikov (1965Luikov ( , 1966Luikov ( , 1975) developed a uniquely model for a simultaneous heat and moisture transfer in capillary porous materials, which is based on non-equilibrium thermodynamics of irreversible transfer processes. This model is applicable for both ...

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Section: Introductionsupporting

confidence: 79%

On comparing finite difference schemes applied to a nonlinear multi-region heat and mass transfer problem

Lobo

2002

Computational Mechanics

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“…The proposed computational scheme for evaluating more than 40 roots within the accuracy of seven decimal places has been implemented on the IBM-compatible PC=AT 386, which computes real as well as complex eigenvalues and takes less than 42 seconds of CPU time to compute these roots. This technique is entirely di erent from that of Lobo et al [19] and Liu and Cheng [20]. The reason is that the numerical procedure adopted by them requires every time an input parameter for the evaluation of each and every pair of complex conjugate roots.…”

Section: Discussionmentioning

confidence: 96%

“…By using a novel technique [21], we now critically examine the roots of the transcendental equation in order to answer the questions raised previously regarding the existence of complex roots [18][19][20], and if they exist, their in uence on the existing solutions that consider only real roots. This technique is a combination of the bisection method which determines the real roots and Newton-Raphson method, utilizing the complex arithmetic, determines the complex roots.…”

Section: Discussionmentioning

confidence: 99%

“…However, Lobo et al [19] established the conditions for the existence of complex roots as indicated by Rossen and Hayakawa [18], and noticed that several of the early numerical computational works could be in error, particularly for those results reported for small values of the dimensionless time due to the occurrence of complex eigenvalues not accounted for in such earlier contributions. Liu and Cheng [20] developed an analytical approach that leads to, in the case of a moist sheet, the exact solutions for the linearized Luikov system of equations subjected to speciÿed initial and boundary conditions, and also established the existence of complex roots after an exhaustive search in the complex domain. However, they reported numerical di culties in evaluating the complex roots, restricting their computations to one single pair, whereas, for the ÿrst time the present authors have successfully evaluated a number of complex conjugate roots by using a novel technique [21], which is a combination of the bisection method and Newton-Raphson method.…”

Section: Introductionmentioning

confidence: 99%

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Temperature and moisture distributions in a moist spherical capillary-porous body?a new approach

Pandey

Mikhailov

1999

Int. J. Numer. Meth. Engng.

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SUMMARYA novel technique, which is a combination of the Laplace transform and matrix calculus, is employed to obtain the exact solutions of the linearized Luikov system of coupled heat and moisture transport equations in a spherical capillary porous body addressed to speciÿed initial and boundary conditions. It is shown that under certain restrictions, in the case of convective-type boundary conditions, the transcendental equation yields a countable number of complex conjugate roots. Here, a new computational scheme is employed, which evaluates real as well as a countable number of pairs of complex conjugate roots. A set of benchmark results is generated for the Luikov drying model, and in a way better than the alternative solutions proposed by Lobo et al. [19] for linear problems.

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“…This approach has been used by Thomas et al (1980) and Irudayaraj et al (1990). The numerical solution is, however, complicated (Liu and Cheng, 1991). Malan and Lewis (2003) and Lewis et al (1996) solved the highly non-linear equations describing drying systems using the finite element method.…”

Section: Introductionmentioning

confidence: 99%

Thermal modelling of the high temperature treatment of wood based on Luikov's approach

Younsi¹,

Kocaefe²,

Poncsák³

et al. 2006

Int. J. Energy Res.

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SUMMARYA 3D, unsteady-state mathematical model was used to simulate the behaviour of wood during high temperature treatment. The model is based on Luikov's approach and solves a set of coupled heat and mass transfer equations. Using the model, the temperature and moisture content profiles of wood were predicted as a function of time for different heating rates. Parallel to the modelling study, an experimental study was carried out using small birch samples. The samples were subjected to high temperature treatment in a thermogravimetric system under different operating conditions. The experimental results and the model predictions were found to be in good agreement. The results show that the distributions of temperature and moisture content are influenced appreciably by the heating rate and the initial moisture content.

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Solutions of Luikov equations of heat and mass transfer in capillary-porous bodies

Cited by 60 publications

References 6 publications

On comparing finite difference schemes applied to a nonlinear multi-region heat and mass transfer problem

On comparing finite difference schemes applied to a nonlinear multi-region heat and mass transfer problem

Temperature and moisture distributions in a moist spherical capillary-porous body?a new approach

Thermal modelling of the high temperature treatment of wood based on Luikov's approach

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