Wednesday 24 February 2010

Geeky Addendum

I don’t let the inner physics geek out very often in public but here goes:

If you’re feeling geeky the total area of metal exposed to the sun is a 1m2 (0.5*1 for the collector and the box itself), Solar radiation has a peak power of around 800wm-2 and the energy required to evaporate water is 2260kjkg-1. Some simple maths later shows that it will take four hours to evaporate a kilo of water if the whole process is 25% efficient, the limiting factor i think will be airflow around the fruit.

From an extensive literature review (hahaha) there will be two stages to the drying, the first evaporation limited and then a second stage where the limiting factor will be the transport of water from inside the fruit to the edges where it can be removed. (they’ll also be some boundary layer effects, but i unless anyone has a PhD in fluid dynamics i think we’ll just leave it with, this will slow the process down somewhat.

In terms of the evaporation and and humidity limitations, I have stolen the following graph from Wikipedia:



As you can see at 35°C water can hold 38g of water per m2 (also assuming density of air to be 1kgm-2 as I am very lazy and this isn’t the most rigorous of analysis). If you heat the air to 50°C the holding capacity rises to 95g. The total volume of the Mk I is 0.5m2 meaning to evaporate 1 kg of water will need the air to change around 10 times, but probably closer to 30 if you assume a 30% efficiency. If i had some form of flow meter i could work out how quickly the air is changing inside the box from the flow at the top, but i dont so we'll all have to wonder what could have been if i had brought one with me.

What this graph does show conveniently is that even if the air is saturated at 35°C, you can still use a dryer effectively if the temperature is increased by 15°C.

Also you can see that at the current difference between night and day temperatures (23°C night, 38°C day) the humidity would have to pass RH50% for dew to become a significant problem, as its around 10% at the moment fruit can be left overnight with minimal worry.


2 comments:

  1. I'm going to email this to Ben Goldacre.

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  2. Heard a great/terrible physics joke in race commentary the other day. American motorbike rider called Ben Spies (pronounced Spees) coming over the line to win a race. Over excitable commentator shouting at top of his voice:

    "Spies equals distance over time"

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