The Optimum Dimensions of Circular Fins with Variable Thermal Parameters

Abstract

Optimum dimensions of circular fins of trapezoidal profile with variable thermal conductivity and heat transfer coefficients are obtained. Linear variation of the thermal conductivity is considered of the form k = k0(1 + εT/T0), and the heat transfer coefficient is assumed to vary according to a power law with distance from the bore, expressed as h = K[(r − r0)/(r0 − re)]m. The results for m = 0, 0.8, 2.0, and −0.4 ≤ ε ≤ 0.4, have been expressed by suitable nondimensional parameters which are presented graphically. It is shown that considering the thermal conductivity as constant, the optimum base thickness and volume of the fin are inversely proportional to the thermal conductivity of the material of the fin, while the optimum length and effectiveness are independent of the properties of the material used.

Natural convection heat transfer coefficients in phase change material (PCM) modules with external vertical fins

“…In a vertical module two different fins geometries can be considered: horizontal and vertical fins. There is much more literature for horizontal fins [10][11][12][13][14][15][16][17][18][19][20][21][22], but this geometry interferes with the natural convection in the PCM module. On the other hand there is no literature for vertical fins around circular vertical tubes, but this geometry would improve natural convection in the water side of the PCM module.…”

A model on the basis of analytics for computing maximum heat transfer in porous fins

“…In the optimization analysis, the fin volume was taken as fixed to determine dimensionless geometrical parameters of the fin with maximum heat transfer rate. The optimum dimensions of circular fins of trapezoidal profile with variable thermal conductivity and heat transfer coefficient had been calculated by Razelos and Imre [6]. They considered a linear variation of the thermal conductivity with the temperature and a power law variation of heat transfer coefficient with the distance from the base.…”

A note on a symmetry analysis and exact solutions of a nonlinear fin equation

“…One of the early studies of temperature dependent straight fins with internal heat generation was done in [2]. Razelos and Imre [3] analyzed the conductive heat transfer of a convecting fin from the base to its tip. Jany and Bejan [4] have investigated the optimum shape for straight fins with temperature dependent conductivity.…”