Heatsink surface temperature

This question is related to who knows how to design a thermal management. I started learn to do this, at hobbyst level.

So, this is the assumption of the situation: When someone design the thermal handling of an electronic component (let's say an average IC), briefly its starts from the max junction temperature and goes up to the ambient removing the kept heat from the initial temperature, due to the thermal resistance. Eventually, in order to achieve compatibility with a given ambient temperature, with an equation can devise the thermal resistance of the heatsink.

For example, Tj=130°C, Ta=30°C, P = 2.3W and the various thermal resistances from junction to ambien WITHOUT the heatsink one are in total 17°C/W. At 30°C of Ta, I need an heatsink of ((Tj-Ta)/P)-17°C/W = 26.5°C/W.

Now, I need few clarifications (assuming what I said unitl now is roughly correct...).

Clarification 1: this design will not allow the system to be used in ambient which is higher than 30°C (using only convection). Correct?

Clarification 2: the temperature of the surface of heatsink should be higher than 30°C? Measurements were indicating an heatsink temperature higher than 45°C at Ta = 20°C, so I'm supposing the answer is yes. But how to calculate them a priori, to make the proper controls?

Clarification 1

The re-arranged equation to determine the required thermal impedance of a heat sink is

$R_{\Theta s-a} = \frac{T_j -T_a}{P_d} - R_{\Theta j-c} - R_{\Theta c-s}$

So assuming you have used the correct values then yes, this essentially sets the maximum Heatsink ambient the system can work at.

Clarification 2

And this is a real problem. One solution is a valid Finite Element Analysis of the thermal capability to determine how efficient a certain fin topology is at removal of heat to the surrounding air

another solution is to pre-empt the optimum fin consideration: If the fins are too close the heat transfer coefficient decreases, if the fins are too far apart the heat transfer coefficient equally decreases due to a deduction in surface area...

There are some equations that help determine the optimum fin configuration.

Then there is empirically. The usual rule of thumb when passively cooling electronics is the heatsink will be at a temp range of 35-45C (w.r.t. a 25C room ambient) if the heatsink is exposed to the room. If the heatsink is enclosed or downstream of another thermal producing device then a local ambient of 50-60 is a reasonable 1st pass starting point

• Designing thermal management for LEDs, I have single LED from junction to heatsink of 17°C/W. If a LED consumes 2.3W, ambient maximum of 40°C and declaring maximum junction temperature of 130°C, you calculus lead to a 26°C/W (more or less... I didn't use the calc). If I have the same interface per LED of 17°C/W, but using 4LEDs and a bigger hatsink, shouldn't be (26/4)°C/W? Because now I am using an heatsink of 5.1°C/W at 20°C of ambient, but a drop of water boils when touch the heatsink. Seems too hot... – thexeno Jan 5 '16 at 15:14