Entropy Production and Efficiency in Longitudinal Convecting–Radiating Fins

Abstract

The properties of the entropy production in convecting–radiating fins were analyzed. By taking advantage of the explicit expression for the distribution of heat along the fin, we investigated the possibility of assessing the efficiency of these devices through the amount of entropy produced in the heat transfer process. The analysis was performed both for purely convecting fins and for convecting–radiating fins. A comparison with standard definitions of efficiency is given.

On the Optimal Shape and Efficiency Improvement of Fin Heat Sinks

“…where m = √ α. If the fin profile changes, the steady-state temperature distribution will not be ( 16), but will change accordingly to Equation (5). Vice versa, if we change the temperature profile, the fin profile will change according to Equation (5).…”

“…If the fin profile changes, the steady-state temperature distribution will not be ( 16), but will change accordingly to Equation (5). Vice versa, if we change the temperature profile, the fin profile will change according to Equation (5). As explained in the lines above, we would like to expand the area under the graph of θ(z), stretching up the temperature distribution.…”

“…In this paper, we consider a fin dissipating heat both by convection and radiation mechanisms. The model, described for example by Kraus et al [1] and Nguyen and Aziz [3], has been extensively investigated by Bochicchio et al [4] and Giorgi and Zullo [5]. In [6] the authors of this paper introduced a novel indicator for the effectiveness of longitudinal, convecting-radiating fins to dissipate heat: this new indicator measures the dissipation, through entropy rates, of the steady state of the fin with respect to the same dissipation of an ideal fin with the highest dissipation possible.…”

Entropy Rates and Efficiency of Convecting-Radiating Fins

“…We observe that Gardner's result is independent of the temperature gradient between the base and the fluid adjacent to the fin: this fact is a consequence of the linearity of the equations for the temperature when the only mechanism of dissipation is the convection. In our opinion, the independence of the efficiency from the temperature of the base of the fin and from the temperature of the fluid is a weak point of the classical formulation of the efficiency, and this idealization is expected to give accurate results only for small values of the difference between the base temperature and the fluid temperature: as the gradient increases, both the values of actual and ideal heat transferred to the environment increase, but their ratio may not result in a constant [5].…”