On the Complex Eigen-Values of Luikov System of Equations

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

“…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.…”

“…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.…”

“…Rossen and Hayakawa [18] obtained the solutions and on examination of the functional behaviour of transcendental equations, they investigated that under certain conditions imposed on the transport parameters involved in the case of boundary conditions of the third kind, a countable number of complex conjugate roots can occur. 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.…”

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

“…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.…”

Improved lumped-differential formulations and hybrid solution methods for drying in porous media

“…For the mathematical modeling of such phenomena, Luikov [11,12] has proposed his widely known formulation, based on a system of coupled partial differential equations, which takes into account the effects of the temperature gradient on the moisture migration. A few approaches of analytical nature have been used for the solution of Luikov's equations in one-dimensional and multi-dimensional problems [13][14][15][16][17][18]. Nevertheless, several multidimensional heat transfer problems might involve small gradients along a specific spatial direction or even inside the whole body.…”