Optimum Geometry of Plate Fins

Abstract

A method and practical results are presented for finding the geometries of fixed volume plate fins for maximizing dissipated heat flux. The heat transfer theory used in optimization is based on approximate analytical solutions of conjugated heat transfer, which couple conduction in the fin and convection from the fluid. Nondimensional variables have been found that contain thermal and geometrical properties of the fins and the flow, and these variables have a fixed value at the optimum point. The values are given for rectangular, convex parabolic, triangular, and concave parabolic fin shapes for natural and forced convection including laminar and turbulent boundary layers. An essential conclusion is that it is not necessary to evaluate the convection heat transfer coefficients because convection is already included in these variables when the flow type is specified. Easy-to-use design rules are presented for finding the geometries of fixed volume fins that give the maximum heat transfer. A comparison between the heat transfer capacities of different fins is also discussed.

Optimal Shapes of Straight Fins and Finned Heat Sinks

“…2, because when the fin thickness at the tip t t is allowed to vary freely between 0 and t b , optimal trapezoidal fins assume a triangular shape (t t ¼ 0) regardless of whether the fin length L or thickness t b is fixed. This is consistent with a previous finding that triangular fins are better than parabolic fins, which again are better than rectangular fins [5]. In other words, making the fin surface more concave is the best compromise between mass and thermal resistance for single straight fins.…”

“…[5] was presented using nondimensional variables, which might be difficult to use. We present these results in a simplified form in Tables 3 and 4.…”

“…1 Schematics of a single fin (a) and a plate fin heat sink (b) 3.1 Optimal Fin Geometry. Studies of fin optimization usually focus on minimizing thermal resistance with a fixed volume [3,5,[19][20][21], which gives the maximum heat transfer rate when the base temperature is fixed. Equivalent results are obtained also when volume is minimized and thermal resistance is fixed.…”

“…1(a), when the mean heat transfer coefficient of the flow over an isothermal surface is used [4]. Consequently, simple analytical expressions have been found for optimal fin geometries [5].…”

Optimization of geometric design parameters for a parallel plate fins heatsink of broadcast vehicle system

“…2 showed a method that finds the optimal geometric parameters of fins to maximize the total heat transfer cooled by natural or forced convection. 3 presented a method and practical results for finding the geometries of fixed volume plate-fins heatsink for maximizing dissipated heat flux. Beriache et al 4,5 developed a simple model for expecting thermal and hydraulic performances of a parallel fin heat sink with impinging airflow.…”