@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 <i>Ra<sub>c</sub></i> and the critical wave number <i>a<sub>c</sub></i> are monotonically decreasing functions of the rate of melting of the solid. We conclude that the parameters <i>Ra<sub>c</sub></i> and <i>a<sub>c</sub></i> are independent functions of the Prandtl number in the range 1 ≤ <i>Pr</i> ≤ 10,000. We also show that as the <i>Pr</i> number is reduced, <i>Pr</i> < 1, the critical parameters are nonmonotonic functions of the rate of melting.},
DOI = {10.3970/cmes.2009.051.073}
}