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Sunday, December 30, 2012

Golden Musings and Bottle Necks or How to Introduce Selvam's SOC Concepts to Climate Models

The Bottle Necks

Energy is fungible, the work done is not.

Energy is energy.  It can't be created nor destroyed, but you can convert it to your hearts content with some loss with each conversion.  You can convert wind power into mechanical power to pump water into a water tower then use that water and the head pressure (height) to drive a turbine to make electricity to power a fan to turn your wind mill.  That would be a complete waste of time, but energy is energy.  Each stage of the conversion processes requires work.  Since you lose energy due to inefficiency (entropy) doing the work, each stage has to be considered separately.  Since Work and Entropy are joined at the hip so to speak, the energy is fungible but the work done is not.

A radiant surface cannot emit energy any faster than energy can be transferred to the radiant surface.

This is one of my favorite reminders that is almost always missed.  It is a reminder that there is no such thing as a perfect black body.  When I mention conductive heat transfer most think I am daft, but there are only two direct means of heat transfer, conduction and radiation.  Latent and convective heat transfer has to be initiated by either conduction or radiation.  Since a large "black body" with enormous amount of energy stored has to rely on conduction and conduction initiated convection to transfer heat to the radiant surface, conduction is not a bit player.

So why do I tend to make such obvious comments?  Because they are the main two bottle necks.  Bottle necks are natural control limits.

When I wander off into Selvam's Golden Ratio land, it is because the Golden ratio actually makes sense.  Not the 1.618033 etc., but the 0.618033- and 0.381966- parts.  0.382 is very close to the maximum reliable efficiency of a single cycle heat engine.  A combined cycle heat engine can reliably produce 0.618 percent efficiency.  That is the 0.382 of the base cycle and 0.382% of the waste heat 0.618 percentage which happens to invert the work to waste ratio.

 Using the Golden Efficiency, the table above lists the stages required to achieve a desired efficiency if you use all of the waste heat for the next stage,above stage 1.  Below stage 1, the efficiency drops off rapidly.  Since efficiency cannot be greater than one (100%) and waste energy cannot be greater than the available energy,  only factors of the Golden Ratio would apply to efficiency.  The curves to the right are the theoretical control range for a "Golden Efficiency" world.  

Now think of the two bottle necks.  Going to the right, as efficiency increases more "work"is done per unit effort.  Going to the left,more energy has to be transferred in order to generate the "waste".  The time and effort to store that energy limits uptake and the properties of the energy storage media limits the rate or release of the energy.  There is only one point on the curve where the two are equal.  Depending on your perspective, that point would be maximum or minimum entropy or the point where the most rapid change in both work and entropy is possible.  That is a control point.

 The "waste" energy which is limited by the ability of the object to transfer energy, is the emissivity of the object.  The "work" done, which is limited by the ability of the object to store energy, is effectively the absorptivity of the object.  The two are related, but only equal at perfection, which glancing at the Golden Efficiency chart, doesn't exist as a stable point.  There is a stable "range", but not a stable point.  An excellent property for an effective control system by the way.

Now I am in the midst of my busy season, so I doubt I will spend much time on this for a while, but there may be some enterprising modelers, probably from India, that might like to play with Golden Efficiency Stages concept.  With a quick glance one should notice that 0.618 is close to the TOA emissivity and 0.9655 is close to the absorptivity of salt water.

Probably one of my crazier ideas, but hey, what's the internet for?

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