## Abstract

The effects of varying fuel layer depth on the thermal stability of a two fluid system, with thermal radiative heating from above, has been considered. The effects of thermal radiation are assumed to be significant in the fuel layer only. The divergence of the radiative heat flux term, appearing in the fuel layer energy equation, is approximated using the Milne-Eddington approximation. Appropriate boundary conditions are presented. The normal mode disturbance formulation, a system of ordinary differential equations and boundary conditions, is derived. Using a modified Chebyshev Tau method, the system is transformed into an unsymmetric, generalized, algebraic eigenvalue problem. The QZ algorithm is used to find system eigenvalues. The system was found to exhibit several bifurcations in the maximum eigenvalue associated with the critical value of Marangoni number. For small wave numbers, the critical value of the Marangoni number decreases significantly as the depth ratio approaches one. For larger wave numbers, the critical Marangoni numbers were on the same order of magnitude for all depth ratios.

Original language | English |
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Pages (from-to) | 153-171 |

Number of pages | 19 |

Journal | Proceedings of the Heat Transfer and Fluid Mechanics Institute |

State | Published - 1993 |

Event | Proceedings of the 33rd Heat Transfer and Fluid Mechanics Institute - Sacramento, CA, USA Duration: Jun 3 1993 → Jun 4 1993 |

## ASJC Scopus subject areas

- Fluid Flow and Transfer Processes