Bifurcation Analysis for Horizontal Longitudinal Fins Under Multi-Boiling Conditions

A numerical bifurcation analysis is carried out in order to determine the solution structure of a fin subject to multi-boiling heat transfer mode. The thermal analysis can no longer performed independently of the working fluid since the heat transfer coefficient is temperature dependent and includes the nucleate, the transition and the film boiling regime where the boiling curve is obtained experimentally for a specific fluid. The heat transfer process is modeled using one-dimensional heat conduction with or without heat transfer from the fin tip. Furthermore, five fin profiles are considered: the constant thickness, the trapezoidal, the triangular, the convex parabolic and the parabolic. The multiplicity structure is obtained in order to determine the different types of bifurcation diagrams, which describe the dependence of a state variable of the system (for instance the fin temperature or the heat dissipation) on a design (CCP) or operation parameter (base TD). Specifically the effects of the base TD, of CCP and of the Biot number are analyzed and presented in several diagrams since it is important to know the behavioral features of the heat rejection mechamism such as the number of the possible steady states and the influence of a change in one or more operating variables to these states. Stability analysis is carried out using the “resonance integral” technique and the Sturm-liouville eigen system analysis.