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The power budget calculator estimates the maximum (or idealized) heat dissipation on a passive device. The calculation is based on the assumption that all surfaces dissipate heat at a uniform temperature.
The heat dissipation in a real device can be considerably lower. The idealized value can be adjusted by a factor (0 – 1).
Example: Determine the power budget for the new iPhone 6+. The product dimensions are, length 77.8 mm, width 7.1 mm, and height 158.1 mm. Assuming an ambient temperature of 25 °C and maximum touch temperature of 40 °C (metal/glass surface). The calculator estimates an ideal budget of 4.3 W. Considering the iPhone 6+ is a well designed product (thermally), a factor of 75% efficiency is applied to give a total power budget of 3.2 W.
These estimations help thermal designers to quickly determine if a product can be passively cooled.
The calculator determines the maximum heat removed by convection and radiation. The device is assumed to be floating in air.
Heat dissipation by radiation:![\[ q = \epsilon\ \sigma\ A(T_{Surface}^4-T_{Amb}^4) \]](http://www.fluxthermaldesign.com/wp-content/ql-cache/quicklatex.com-3fbfba26cb521e70d7d750fc9f0cc670_l3.png "Rendered by QuickLaTeX.com")
Heat dissipation by convection:
![\[ q=h\ A(T_{Surface}-T_{Amb}) \]](http://www.fluxthermaldesign.com/wp-content/ql-cache/quicklatex.com-951997992f12a954d0df56c0120f5a4a_l3.png "Rendered by QuickLaTeX.com")
where:
![\[ h=\frac{Nu\ k}{L} \]](http://www.fluxthermaldesign.com/wp-content/ql-cache/quicklatex.com-17ad1aa40b7b2183c190ef9b95cd5491_l3.png "Rendered by QuickLaTeX.com")
The Nusselt number is then calculated using empirical correlations.
Top surface:![\[ Nu=0.54\ Ra_L^{1/4}\quad 10^4<Ra_L<10^7\\ \]](http://www.fluxthermaldesign.com/wp-content/ql-cache/quicklatex.com-cc2ff397df24e9caaf9aabc3aeff0113_l3.png "Rendered by QuickLaTeX.com")
![\[ Nu=0.15\ Ra_L^{1/3}\quad 10^7<Ra_L<10^{11}\\ \]](http://www.fluxthermaldesign.com/wp-content/ql-cache/quicklatex.com-bb55b1eac6a42a383242628839e7d852_l3.png "Rendered by QuickLaTeX.com")
Bottom surface:
![\[ Nu=0.27\ Ra_L^{1/4}\quad 10^5<Ra_L<10^{10} \]](http://www.fluxthermaldesign.com/wp-content/ql-cache/quicklatex.com-61ad468db22b45bcf9346c88765a52bb_l3.png "Rendered by QuickLaTeX.com")
Sides, front and back:
![\[ Nu=0.68+\frac{0.67\ Ra_L^{1/4}}{[1+(0.492/Pr)^{9/16}]^{4/9}}\quad Ra_L<10^9 \]](http://www.fluxthermaldesign.com/wp-content/ql-cache/quicklatex.com-c6d5a3d3a3e5630a8c3c89241ed08c4b_l3.png "Rendered by QuickLaTeX.com")
(3 votes, average: 4.67 out of 5)
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I have similar calculator built in Excel based on the same equations you presented. A couple of suggestions:
1. different surface material has different emissivity. You can add more details here.
2. Show how you calculate characteristic length. This relates to the orientation of the box;
3. Show how you get the air properties based on which temperature.
Hi Yin
1 The calculator assumes all surfaces have the same emissivity. Not true for all cases.
2 Right now the calculator assumes the devices is floating in free air on vertical orientation (the height should be aligned with the gravity vector). Again not true for all cases.
3 Air properties are calculated from the given ambient temperature.
More details can be easily added but the main idea of the calculator is to get a quick estimation of the power dissipation assuming a Cu-block case (all surfaces dissipating heat at a uniform temperature).
Thanks for your valuable comment!
This article is about the thermal design envelope of microprocessors. For the general concept, see power rating .