Fin Analysis Under Transition Boiling Heat Transfer: Part II — Radial Fins

The thermal characteristics of six profiles of radial fins subject to transition boiling heat transfer are analyzed. The profiles considered are the rectangular the trapezoidal, the triangular, the convex parabolic, the parabolic and the hyperbolic. The model of the physical mechanism is based on one-dimensional heat conduction using certain simplifying assumptions while the heat transfer coefficient is modeled as a power-law function of the temperature difference between the fin and the saturated boiling liquid with a negative exponent. The problem is formulated by means of dimensionless variables and parameters such as the conduction-convection parameter, the radius ratio and the Biot number that characterize the problem. 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, radius ratio) or operation parameter (power-law exponent). Specifically the effects of the radius ratio, of the 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 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.