Temperature distribution on a convection cooled PCBs.

The algorithm is based on modified Bessel functions and is ideal for a front end purposes.

The inlet air temperature is 0 C.

Move a heat source with the mouse and notice how fast the temperatures are updated.

Related links
Thermal design for electronics
Thermal online tools
Unit conversion
Comments

General

The theory is explained in the article: A Bessel Function Solution . The kernel is a 2-D Bessel function solution to the Fourier equation. It executes fast and is therefore ideal for overview and optimizations purposes.

There are nevertheless some drawbacks. The solution is based on a uniform heat transfer coefficient assumption and also does not account for the fact that actual components propound from the surface.

The first of these disadvantages can be fairly well compensated by a set of invisible heat sources. This technique is implemented in the calculator.

The second drawback can be compensated for if the component-to-air heat is small. Although theoretically possible, this has not been done here because it would require a much more complex component specification than feasible for a simple applet.

To experience how this procedure can serve as a great help for real world problems download the demo version of Btemp, (zip file). Install and select "Estimate" - "Real time estimate".

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Inputs

Source
A heat source is a rectangular area with a uniform heat flux. The coordinate system has its origin in the lower left corner and the base point for the sources is their lower left corners. There is also a fix 1 mm layout grid.

Any source can be moved with the mouse when the program is in 2-D mode. On clicked, a heat source becomes the active heat source and this is marked by a thicker frame.

X-pos
Is the X-coordinate position.

Y-pos
Is the Y-coordinate position.

Width.
Is the width of the heat source.

Height>br> Is the height of the heat source.

Heat diss
Is the heat dissipation of the heat source. The grayed area to the left shows the total heat dissipation on the PCB.

Set source data
Validates the properties in the input area. If the program is in result mode it also recalculates.

Add source
Adds a heat source.

Delete source
Deletes a heat source.

Calculate
Recalculates the temperature field.

Save/read data
Implements a cut and paste procedure for the layout. See below.

Width
Is the width of the PCB.

Height
Is the height of the PCB.

Thickness
Is the thickness of the PCB.

Conductivity
Is the thermal conductivity of the PCB. It can be calculated on the page
Thermal conductivity for PCBs.
For other materials see:
Tools from Maya

Coeff
Is the heat transfer coefficient based on the inlet temperature difference if the PCB had been isothermal. It can be calculated on the page Heat transfer coefficient for parallel plates.

Air temp inc
Is the air temperature rise at the outlet from the flow channel. It is automatically limited upwards to 80% of the virtual inlet temperature difference had the PCB been isothermal.

Set board data
Validates the inputs. If the program is in result mode it also recalculates.

Edit mode
Transfers to edit mode and shows the measures of the PCB.

3-D mode
Shows the PCB in 3-D graphics.

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Output

Cooling efficiency
Is a measure on how well the surface is used for convection. See the article: The Cooling Efficiency Concept.


Editing

Safety concerns makes it impossible to read and write files in applets. A work around is to use copy and paste.
Press the "Save/read data" button. Use copy, paste and press the "Read data" button to enter the layouts below.

This XML code holds a PCB with a single component.

<Comment> Single component. </Comment>
<PCB>
<Width> 0.2 </Width>
<Height> 0.2 </Height>
<Thickness> 0.0016 </Thickness>
<Conductivity> 15.0 </Conductivity>
<heat transfer coefficient> 3.5 </heat transfer coefficient>
<Air temperature increase> 6.0 </Air temperature increase>
</PCB>
<Source>
<X-width> 0.02 </X-width>
<Y-width> 0.02 </Y-width>
<X-pos> 0.090 </X-pos>
<Y-pos> 0.090 </Y-pos>
<heat dissiaption> 2.0 </heat dissiaption>
</Source>


This XML code holds a PCB with a processor surrounded by memories.

<Comment>
A quick check on the cooling efficiency that can be achieved for a processor surrounded by memories </Comment> <PCB>
<Width> 0.178 </Width>
<Height> 0.222 </Height>
<Thickness> 0.0020 </Thickness>
<Conductivity> 24.0 </Conductivity>
<heat transfer coefficient> 15.0 </heat transfer coefficient>
<Air temperature increase> 3.0 </Air temperature increase>
</PCB>
<Source>
<X-width> 0.035 </X-width>
<Y-width> 0.035 </Y-width>
<X-pos> 0.137 </X-pos>
<Y-pos> 0.077 </Y-pos>
<heat dissiaption> 4.0 </heat dissiaption>
</Source>
<Source>
<X-width> 0.028 </X-width>
<Y-width> 0.011 </Y-width>
<X-pos> 0.137 </X-pos>
<Y-pos> 0.121 </Y-pos>
<heat dissiaption> 0.5 </heat dissiaption>
</Source>
<Source>
<X-width> 0.028 </X-width>
<Y-width> 0.011 </Y-width>
<X-pos> 0.1 </X-pos>
<Y-pos> 0.104 </Y-pos>
<heat dissiaption> 0.5 </heat dissiaption>
</Source>
<Source>
<X-width> 0.028 </X-width>
<Y-width> 0.011 </Y-width>
<X-pos> 0.1 </X-pos>
<Y-pos> 0.121 </Y-pos>
<heat dissiaption>0.5 </heat dissiaption>
</Source>
<Source>
<X-width> 0.028 </X-width>
<Y-width> 0.011 </Y-width>
<X-pos> 0.067 </X-pos>
<Y-pos> 0.121 </Y-pos>
<heat dissiaption> 0.5 </heat dissiaption>
</Source>
<Source>
<X-width> 0.028 </X-width>
<Y-width> 0.011 </Y-width>
<X-pos> 0.137 </X-pos>
<Y-pos> 0.137 </Y-pos>
<heat dissiaption> 0.5 </heat dissiaption>
</Source>
<Source>
<X-width> 0.028 </X-width>
<Y-width> 0.011 </Y-width>
<X-pos> 0.067 </X-pos>
<Y-pos> 0.104 </Y-pos>
<heat dissiaption> 0.5 </heat dissiaption>
</Source>
<Source>
<X-width> 0.028 </X-width>
<Y-width> 0.011 </Y-width>
<X-pos> 0.067 </X-pos>
<Y-pos> 0.089 </Y-pos>
<heat dissiaption> 0.5 </heat dissiaption>
</Source>
<Source>
<X-width> 0.028 </X-width>
<Y-width> 0.011 </Y-width>
<X-pos> 0.1 </X-pos>
<Y-pos> 0.089 </Y-pos>
<heat dissiaption> 0.5 </heat dissiaption>
</Source>
<Source>
<X-width> 0.028 </X-width>
<Y-width> 0.011 </Y-width>
<X-pos> 0.067 </X-pos>
<Y-pos> 0.074 </Y-pos>
<heat dissiaption> 0.5 </heat dissiaption>
</Source>
<Source>
<X-width> 0.028 </X-width>
<Y-width> 0.011 </Y-width>
<X-pos> 0.1 </X-pos>
<Y-pos> 0.074 </Y-pos>
<heat dissiaption> 0.5 </heat dissiaption>
</Source>
<Source>
<X-width> 0.028 </X-width>
<Y-width> 0.011 </Y-width>
<X-pos> 0.067 </X-pos>
<Y-pos> 0.059 </Y-pos>
<heat dissiaption> 0.5 </heat dissiaption>
</Source>
<Source>
<X-width> 0.028 </X-width>
<Y-width> 0.011 </Y-width>
<X-pos> 0.1 </X-pos>
<Y-pos> 0.059 </Y-pos>
<heat dissiaption> 0.5 </heat dissiaption>
</Source>
<Source>
<X-width> 0.028 </X-width>
<Y-width> 0.011 </Y-width>
<X-pos> 0.067 </X-pos>
<Y-pos> 0.044 </Y-pos>
<heat dissiaption> 0.5 </heat dissiaption>
</Source>
<Source>
<X-width> 0.028 </X-width>
<Y-width> 0.011 </Y-width>
<X-pos> 0.137 </X-pos>
<Y-pos> 0.059 </Y-pos>
<heat dissiaption> 0.5 </heat dissiaption>
</Source>
<Source>
<X-width> 0.028 </X-width>
<Y-width> 0.011 </Y-width>
<X-pos> 0.1 </X-pos>
<Y-pos> 0.044 </Y-pos>
<heat dissiaption>0.5 </heat dissiaption> </Source>
<Source>
<X-width> 0.028 </X-width>
<Y-width> 0.011 </Y-width>
<X-pos> 0.137 </X-pos>
<Y-pos> 0.044 </Y-pos>
<heat dissiaption> 0.5 </heat dissiaption>
</Source>
<Source>
<X-width> 0.028 </X-width>
<Y-width> 0.011 </Y-width>
<X-pos> 0.1 </X-pos>
<Y-pos> 0.137 </Y-pos>
<heat dissiaption> 0.5 </heat dissiaption>
</Source>
<Source>
<X-width> 0.028 </X-width>
<Y-width> 0.011 </Y-width>
<X-pos> 0.067 </X-pos>
<Y-pos> 0.137 </Y-pos>
<heat dissiaption> 0.5 </heat dissiaption>
</Source>


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