@Article{cmes.2009.051.073,
AUTHOR = {Rubén Avila, Eduardo Ramos, S. N. Atluri},
TITLE = {The Chebyshev Tau Spectral Method for the Solution of the Linear Stability Equations for Rayleigh-Bénard Convection with Melting},
JOURNAL = {Computer Modeling in Engineering \& Sciences},
VOLUME = {51},
YEAR = {2009},
NUMBER = {1},
PAGES = {73--92},
URL = {http://www.techscience.com/CMES/v51n1/25404},
ISSN = {1526-1506},
ABSTRACT = {A Chebyshev Tau numerical algorithm is presented to solve the perturbation equations that result from the linear stability analysis of the convective motion of a fluid layer that appears when an unconfined solid melts in the presence of gravity. The system of equations that describe the phenomenon constitute an eigenvalue problem whose accurate solution requires a robust method. We solve the equations with our method and briefly describe examples of the results. In the limit where the liquid-solid interface recedes at zero velocity the Rayleigh-Bénard solution is recovered. We show that the critical Rayleigh number *Ra*_{c} and the critical wave number *a*_{c} are monotonically decreasing functions of the rate of melting of the solid. We conclude that the parameters *Ra*_{c} and *a*_{c} are independent functions of the Prandtl number in the range 1 ≤ *Pr* ≤ 10,000. We also show that as the *Pr* number is reduced, *Pr* < 1, the critical parameters are nonmonotonic functions of the rate of melting.},
DOI = {10.3970/cmes.2009.051.073}
}