Two-dimensional fin performance: Bi (top surface) >= Bi (bottom surface)

The purpose of this work is to present an analysis of the performance and optimization of longitudinal rectangular fins, when the heat transfer coefficients at the top (h(+)) and bottom surface (h(-)), which are expressed in terms of their respective Biot numbers, may be unequal. It is shown that, with the introduction of an equivalent semi-thickness, w(eq), and Biot number based on the average heat transfer coefficient, (h) over bar = (h(+) + h(-))/2, the problem is reduced to the standard fin problem with equal heat transfer coefficients at the lateral surfaces, with insulated or non-insulated tip that was analyzed in [1]. (C) 2004 Elsevier Science Ltd

Analysis of multiplicity phenomena in longitudinal fins under multi-boiling conditions

A numerical bifurcation analysis is carried out in order to determine the solution structure of longitudinal fins subject to multi-boiling heat transfer mode. The thermal analysis can no longer be performed independently of the working fluid since the heat transfer coefficient is temperature dependent and includes the nucleate, the transition and the film boiling regimes 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 (Conduction-Convection Parameter) or operation parameter (base Temperature Difference). Specifically the effects of the base Temperature Difference, of the Conduction-Convection Parameter 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 mechanism such as the number of the possible steady states and the influence of a change in one or more operating variables to these states