Fin (extended surface)
Cooling fins (English cooling fins ) are used to increase the surface area of a body to enhance heat transfer to the environment, and hence the cooling. Ribbed surfaces can thereby be part of the heat generating machine itself, such as on an engine block, or as a separate component of it are executed. Such heat sinks may in turn be connected via an additional medium with her, as practiced for example in the cooling water are in direct mechanical contact with the heat source or. Heatsink provide passive or as part of an active cooling system for compliance with a permissible operating temperature of machinery, electrical and electronic systems.
Invented and first used was the fin by the Austrian engineer Franz Pichler, of a thriving company founded to produce electrical machinery and equipment in 1892.
Operation
The heat flow from a surface to the surrounding cooling medium depends on the temperature difference, from the contact surface and the heat transfer coefficient in accordance with the following relationship from
With
By increasing the contact area A that is the amount of heat dissipated can be increased. However, the heat flow will not increase proportional to the increase in area, but depends on the fin efficiency ( see below).
The ribs mean a - usually unwanted - increase the weight and external dimensions. However, you can use the targeted addition to cooling the mechanical strength of a component to increase or decrease the sound radiation of a machine ( by suppressing surface oscillations).
Heat flow through a fin
At the steady-state heat conduction along a rod or a rib is an equilibrium between the flow of heat that occurs in the rod and the heat flow is discharged through the surface to the environment. In the following we consider the simplest case, mathematically: a rod or a rib having a rectangular cross -section, a constant ambient temperature, and a constant heat transfer coefficient. Looking at the bar element dx yields the following equilibrium condition.
Entrants heat flow:
Escaping the heat flow:
The heat transfer at the surface to the surroundings is:
Mean here:
From the heat balance gives:
This leads to the differential equation for the fin temperature:
Here mean:
The solution of the differential equation leads to the following results ( the heat flow at the rib end is neglected).
Temperature profile along the rib:
Temperature at the rib end:
Heat flow through the base of the rib:
Here mean:
The cooling effect of a rib decreases with increasing temperature drop from the rib base to fin tip. Main reason for this drop in temperature is according to the above equations, the dimensionless parameter ( m · L).
Example
In the adjacent picture is shown the ( normalized to 1 ) ribs over temperature? T on a rib of length L for different values of the parameter (m · L). The parameters (m · L ) were calculated for a 0.5 mm thick and 30 mm high rectangular rib of four different materials in an air stream in a heat transfer coefficient of 15 W/m2/K. With the copper and aluminum fins (m · L = 0.37 and 0.52 ), the fall in temperature to fin tip less than 10%. These ribs have a nearly ideal cooling effect. However, in the plastic rib (m · L = 14) falls after a quarter of the length (L / 4), the ribs over temperature to less than 5 % of the initial value. This rib is practically ineffective for the cooling.
Fin efficiency
The fin efficiency is defined as the ratio of the heat flow, the fin actually delivers to the ideal heat flow, the would make the rib if they possess the initial temperature T1 over their entire length (with an infinitely high thermal conductivity).
With
For a rectangular rib, a constant heat transfer coefficient and a constant ambient temperature was derived above:
Thus, the fin efficiency is calculated as:
With
Example: Effect of fin thickness on the efficiency
The images below show the calculated temperature distribution at two aluminum heatsinks. By increasing the fin thickness of 0.2 mm (left) to 2.0 mm ( right), the temperature drop was significantly reduced to fin tip and increases the fin efficiency.
Cooling fins at a high efficiency
Fin density
A higher fin density leads to an increase of the heat release surface, and thus a higher efficiency of the cooling. On the other hand has a higher fin density fin closer channels with an increasing flow resistance to the sequence. This leads to a so-called by-pass effect: the flowing air is ' replaced ' of the ribs and channels flows increasingly unused past the ribs. This is due to the wall friction with the formation of a flow boundary layer. The thickness of the boundary layer is a function of the Reynolds number, the boundary layer equations, see. A numerical simulation of this by- pass metabolism show the two images below.
Flow of air through a heat sink with too little rib spacing