Archive for November, 2018

Ignorance: Eggs & Weather Forecasts

November 26, 2018

Every so I often I learn something so simple and shocking that I find myself asking:

How can I possibly not have known that already?“.

Eggs

Eggs

Eggs

While listening to Farming Today the other morning, learned that:

Large eggs come from old hens

In order to produce large eggs – the most popular size with consumers – farmers need to allow hens to reach three years old.

So during the first and second years of their lives they will first lay small eggs, then medium eggs, and finally large eggs.

On Farming Today a farmer was explaining that egg production naturally resulted a range of egg sizes, and it was a challenge to find a market for small eggs. Then came the second bomb’shell’.

The yolk is roughly same size in all eggs

What varies between small and large eggs is mainly the amount of egg white (albumen).

How could I have reached the age of 58 and not  known that? Or not have even been curious about it?

Since learning this I have become a fan of small eggs: more yolk, less calories, more taste!

But my deep ignorance extends beyond everyday life and into the professional realm. And even my status as ‘an expert’ cannot help me.

Weather Forecasts & Weather Stations

Professionally I have become interested in weather stations and their role in both Numerical Weather Prediction (NWP, or just weather forecasting) and in Climate Studies.

And as I went about my work I had imagined that data from weather stations were used as inputs to NWP algorithms that forecast the weather.

But in September I attended CIMO TECO-2018 (Technical Conference on Meteorological and Environmental Instruments and Methods of Observation) in Amsterdam.

And there I learned in passing from an actual expert, that I had completely misunderstood their role.

Weather station data is not considered in the best weather forecasts.

And, on a moment’s reflection, it was completely obvious why.

Weather forecasting work like this:

  • First one gathers as much data as possible about the state of the atmosphere ‘now’. The key inputs to this are atmospheric ‘soundings’:
    • Balloon-borne ‘sondes’ fly upwards through the atmosphere sending back data on temperature, humidity and wind (speed and direction) versus height.
    • Satellites using infrared and microwave sensors probe downwards to work out the temperature and humidity at all points in the atmosphere in a swathe below the satellite’s orbit.
  • The NWP algorithms accept this vast amount of data about the state of the atmosphere, and then use basic physics to predict how the state of the entire atmosphere will evolve over the coming hours and days

And then, after working out the state of the entire atmosphere, the expected weather at ground level is extracted.

Visualisation of the amount of moisture distributed across different heights in the atmosphere based on a single pass of a 'microwave sounding' satellite. Image credit: NASA/JPL-Caltech

Visualisation of the amount of moisture distributed across different heights in the atmosphere based on a single pass of a ‘microwave sounding’ satellite. The data gathered at ground level is just a tiny fraction of the data input to NWP models. Image credit: NASA/JPL-Caltech

Ground-based weather stations are still important:

  • They are used to check the outputs of the NWP algorithms.
  • But they are not used as inputs to the NWP algorithms.

So why did I not realise this ‘obvious’ fact earlier? I think it was because amongst the meteorologists and climate scientists with whom I spoke, it was so obvious as to not require any explanation.

Life goes on

So I have reached the age of 58 without knowing about hen’s eggs and the role of weather stations in weather forecasting?

I don’t know how it happened. But it did. And I suspect that many people have similar areas of ignorance, even regarding aspects of life with which we are totally familiar – such as eggs – or where one is nominally an expert.

And so life goes on. Anyway…

This pleasing Met Office video shows the importance of understanding the three-dimensional state of the atmosphere…

And here is a video of some hens

 

Mug Cooling: Salty fingers

November 23, 2018

You wait years for an article about heat transfer at beverage-air interfaces and then four come along at once!

When I began writing these articles (1, 2, 3) I was just curious about the effect of insulation and lids.

But as I wrote more I had two further insights.

  • Firstly the complexity of the processes at the interface was mind-boggling!
  • Secondly, I realised that cooling beverages are just one example of the general problem of energy and material transfer at interfaces.

This is one of the most important processes that occurs on Earth. For example, it is how the top layer of the oceans – where most of the energy arriving on Earth from the Sun is absorbed – exchanges energy with the deeper ocean and the atmosphere.

But in the oceans there is another factor: salinity.

Salinity 

Sea water typically contains 35 grams of salt per litre of water, and is about 2.4% denser than pure water.

So pure water – such as rain water falling onto the ocean surface – will tend to float above the brine.

This effect is exacerbated if the pure water is warm. For example, water at 60 °C is approximately 1.5% less dense than water at around 20 °C.

Video 

In the video at the top of the article I added warm pure water (with added red food colouring) to a glass of cold pure water (on the left) and a glass of cold salty water (on the right).

[For the purposes of this article I hope you will allow that glasses are a type of mug]

The degree to which the pure and salty water spontaneously separated surprised me.

But more fascinating was the mechanism of eventual mixing – a variant on ‘salt fingering‘.

Salt Fingers Picture

The formation of ‘salty fingers’ of liquid is ubiquitous in the oceans and arises from density changes caused by salt diffusion and heat transfer.

As the time-lapse section of the movie shows – eventually the structure is lost and we just see ‘mixed fluid’ – but the initial stages, filmed in real time, are eerily beautiful.

Now I can’t quite explain what is happening in this movie – so I am not going to try.

But the web has articles, home-made videos and fancy computer simulations.

 

Mug Cooling: Visualising complexity with peanut butter

November 20, 2018

I hope you’ve enjoyed the last couple of articles (1, 2)  about mug cooling. I have enjoyed writing them, but I am having trouble stopping.

My problem in trying to finish this investigation is the sheer complexity of the physics involved in the cooling of beverages.

Complexity? Yes, mind-boggling complexity. In the liquid, the air, and the profoundly mysterious ‘boundary layer’ between them.

First there is the liquid.

When one looks at a cup of tea or coffee, its opacity hides the complexity of the flow patterns in the liquid.

But with different fluids, such as the mixture of Marmite™, Peanut Butter, and hot water shown in the movie at the top, the turgid flows become visible.

[ASIDE: Some might ask: “Michael, what made you think of mixing Marmite™, Peanut Butter, and hot water?”.  Sadly, the answer is confidential, but I urge readers: please: do try this at home, but please don’t blame me!]

These flows are driven by the convective instability of the liquid.

  • The hot liquid near the surface cools as its fast-moving molecules either evaporate or lose energy by colliding with the slower-moving air molecules.
  • As the liquid cools, its density increases until it begins to sink beneath the liquid layer below.
  • This lower layer is now lifted to the surface, cools, and then sinks in turn.
  • And so a circulating flow pattern can be established and sustained by a liquid cooling at a surface.

In the case of the  Marmite™  and Peanut Butter concoction in the movie above, matters are further complicated by oil from the peanut butter which appears to have formed a stable surface layer below which the convective flow takes place.

This roiling turmoil can also be measured quantitatively.

I repeated the cooling measurements from the previous articles, but this time I placed all four thermocouples close to the surface.

Thermocouples near the surface

Four thermocouples measuring the temperature close to the surface of hot water in an insulated mug.

Looking in detail at the data from just two of the thermocouples one can see apparently random heating and cooling events.

These temperature fluctuations are caused by rising and falling convecting liquid .

Slide 11

Then there is the air.

Analogous processes also occur in the air above the liquid. 

These are harder to visualise, but I have created a simulation of the process in the amazing (and free!) Energy2D application – more details at the end of this article.

Large Gif
Animated GIF made from selected frames of an Energy2D simulation of the  air cooling of a liquid in insulated mugs with a lid (left) and without (right).

In the simulationthe flow patterns in the air quickly develop a breathtaking fractal complexity that is completely familiar.

The simulation is not entirely realistic. It is only in two-dimensions, does not include the effects of evaporation, does not include convection in the ‘liquid’ (so it is more like a solid), and yet some how, when the data is exported, it looks qualitatively similar to that which I observed experimentally in a real 3-D mug!

Slide 10

Graph of data exported from the Energy 2D simulation showing the cooling of an insulated beverage cup with and without a lid.

 

Underlying the ‘simple’ beverage cooling curves are processes in both the liquid and the air which are at the limit of what can be realistically modelled.

And as we approach the interface between the liquid and the air and look in ever more detail, matters only get more complex.

At this apparently ‘static’ interface there are multiple dynamic processes:

  • The liquid is evaporating, cooling and convecting away from the surface.
  • Air molecules and liquid molecules are interacting strongly.
    • The air is dissolving in the liquid
    • The liquid is evaporating and re-condensing both as droplets in the air (steam) and back into the liquid.
  • The air is warming and convecting away from the surface.

And yet all we just notice is that our coffee is getting cold!

Energy 2D

Energy2D is a wonderful FREE application that carries out complex two-dimensional calculations based on real physics.

I have found it difficult to get exact numerical matches between simulations and real world situations, but the physics which the software simulates is deeply insightful.

I strongly recommend that you waste several hours playing with its example demonstrations.

 

Mug Cooling: The Lid Effect

November 12, 2018
IMG_7906

Droplets collect near the rim of a mug filled with hot water.

During my mug cooling experiment last week, I was surprised to find that taking the lid off a vacuum insulated mug increased its initial cooling rate by a factor 7.5.

Removing the lid allowed air from the room to flow across the surface of the water, cooling it in two ways.

  • Firstly, the air would warm up when it contacted the hot water, and then carry heat away in a convective flow.
  • Secondly, some hot water would evaporate into the moving air and carry away so – called ‘latent heat’.

I wondered which of these two effects was more important?

I decided to work out the answer by calculating how much evaporation would be required to explain ALL the cooling. I could then check my calculation against the measured mass of water that was lost to evaporation.

Where to start?

I started with the cooling curve from the previous blog.

Slide5

Graph#1: Temperature (°C) versus time (minutes) for water cooling in an insulated mug with and without a lid. Without a lid, the water cools more than 7 times faster.

Because I knew the mass of water (g) and its heat capacity (joule per gram per °C), I could calculate the rate of heat loss in watts required to cool the water at the observed rate.

In Graph#2 below I have plotted this versus the difference in temperature between the water and the room temperature, which was around 20 °C.

Slide6

Graph#2: The rate of heat flow (in watts) calculated from the cooling curve versus the temperature difference (°C) from the ambient environment. The raw estimates are very noisy so the dotted lines are ‘best fit lines’ which approximately capture the trend of the data.

I was struck by two things: 

  • Firstly, without the lid, the rate of heat loss was initially 40 watts – which seemed very high.
  • Secondly:
    • When the lid was on, the rate of heat loss was almost a perfect straight line This is broadly what one expects in a wide range of heat flow problems – the rate of heat flow is proportional to the temperature difference. But…
    • When the lid was off, the heat flow varied non-linearly with temperature difference.

To find out the effect of the lid, I subtracted the two curves from each other to get the difference in heat flow versus the temperature of the water above ambient (Graph#3).

[Technical Note: Because the data in Graph#2 is very noisy and irregularly spaced, I used Excel™ to work out a ‘trend line’ that describes the underlying ‘trend’ of the data. I then subtracted the two trend lines from each other.]

Slide7

Graph#3: The dotted line shows the difference in power (watts) between the two curves in the previous graph. This should be a fair estimate for the heat loss across the liquid surface.

This curve now told me the extra rate of cooling caused by removing the lid.

If this was ALL due to evaporative cooling, then I could work out the expected loss of mass by dividing by the latent heat of vaporisation of water (approximately 2260 joules per gram) (Graph#4).

Slide8c

Graph#4. The calculated rate of evaporation (in milligrams per second) that would be required to explain the increased cooling rate caused by removing the lid.

Graph#4 told me the rate at which water would need to evaporate to explain ALL the cooling caused by removing the lid.

Combining that result with the data in Graph#1, I worked out the cumulative amount of water that would need to evaporate to explain ALL the observed extra cooling (Graph#5)

Slide9

Graph#5: The red dashed line shows the cumulative mass loss (g) required to explain all the extra cooling caused by removing the lid. The green dashed lines show the amount of water that actually evaporated in each of the two ‘lid off’ experiments. The green data shows additional measurements of mass loss versus time from a third experiment.

In Lid-Off Experiments#1 and #2, I had weighed the water before and after the cooling experiment and so I knew that in each experiment with the lid off I had lost respectively 25 g and 31 g of water –  just under 10% of the water.

But Graph #5 really needed some data on the rate of mass loss, so I did an additional experiment where I didn’t measure the temperature, but instead just weighed the mug every few minutes. This is the data plotted on Graph#5 as discrete points.

Conclusions#1

In Graph#5, it’s clear that the measured rate of evaporation can’t explain all the increased cooling rate loss, but it can explain ‘about a third of it‘.

So evaporation is responsible for about a third of the extra cooling, with two thirds being driven by heat transfer to the flowing air above the cup.

It is also interesting that even though the cooling curves in Graph#1 are very similar, the amount of evaporation in Graph#5 is quite variable.

The video below is backlit to show the ‘steam’ rising above the mug, and it is clear that the particular patterns of air flow are very variable.

The actual amount of evaporation depends on the rate of air flow across the water surface, and that is driven both by

  1. natural convection – driven by the hot low-density air rising, but also by…
  2. forced convection – draughts flowing above the cup.

I don’t know, but I suspect it is this variability in air flow that caused the variability in the amount of evaporation.

Conclusions#2

I have wasted spent a several hours on these calculations. And I don’t really know why.

Partly, I was just curious about the answer.

Partly, I wanted to share my view that it is simply amazing how much subtle physics is taking place around us all the time.

And partly, I am still trying to catch my breath after deciding to go ‘part-time’ from next year. Writing blog articles such as this is part of just keeping on keeping on until something about the future becomes clearer.

P.S. Expensive Mugs

Finally, on the off-chance that (a) anybody is still reading and (b) they actually care passionately about the temperature of their beverages, and (c) they are prepared to spend £80 on a mug, then the Ember temperature-controlled Ceramic mug may be just thing for you. Enjoy 🙂

 

Mug Cooling: Initial Results

November 7, 2018

One of life’s greatest pleasures is a nice cup of tea or coffee.

  • But what temperature makes the drink ‘nice’?
  • And how long after making the beverage should we wait to drink it?
  • And what type of mug is optimal?

To answer these questions I devised a research proposal involving temperature measurements made inside mugs during the cooling process.

I am pleased to tell you that my proposal was fully-funded in its initial stage by the HBRC*, having scored highly on its societal impact.

Experimental Method

The basic experiment consisted of pouring approximately 300 ml of water (pre-stabilised at 90 °C) into a mug sitting on a weighing scale. The weighing allowed low uncertainty assessment of the amount of water added.

The temperature of the water was measured every 10 seconds using four thermocouples held in place by a wooden splint. The readings were generally very similar and so in the graphs below I have just plotted the average of the four readings.

Experiments were conducted for a fancy vacuum-insulated mug (with and without its lid) and a conventional thick-walled ceramic mug. The results for the vacuum-insulated mug without its lid were so surprising that I repeated them.

This slideshow requires JavaScript.

Results

The average temperature of the water in the mugs is shown in the two graphs below.

The first graph shows all the data – more than 8 hours for the vacuum insulated mug – , and the second graph shows the initial behaviour.

Also shown are horizontal lines at various temperatures that I determined (in a separate series of experiments) to be the optimal drinking range.

Slide1

The average temperature of the water in the mugs versus time.

Slide2

The first 120 minutes of the cooling curves. The water was poured in at 4 minutes.

Discussion

The most striking feature of the cooling curves is the massive difference between the results for the vacuum insulated mug with, and without, its lid.

As I mentioned at the start, the result was so striking that I repeated the measurements (marked as #1 and #2) on the graphs.

The table below shows how many minutes it took for the water to cool to the three states highlighted on the graphs above:

  • Too hot to drink, but just sippable
  • Mmmm. A nice hot cuppa.
  • I’ll finish this quickly otherwise it’ll be too cold.

Minutes to reach status

  Vacuum-Insulated Mug

Ceramic Mug

 No Lid

 With Lid

Just Sippable

2

10

66

Upper Drinkable Limit 12 24

151

Lower Drinkable Limit

28

53

296

Conclusion

The insulating prowess of the vacuum insulated mug (with lid) is outstanding.

But the purpose of a mug is not simply to prevent cooling. It is to enable drinking! 

So to me this data raises a profound question about the raison d’être for vacuum insulated mugs.

  • Who  makes a cup of coffee and then thinks “Mmm, that’ll be just right to drink in two and a half hours time!”

Admittedly,  the coffee will then stay in the drinkable range for an impressive two hours. But still.

In contrast, the ceramic mug cools the hot liquid initially and allows it to reach the optimal drinking temperature after just a few minutes.

Further work

The review committee rated this research very highly and suggested two further research proposals.

  • The first concerned the explanation for the very large effect of removing the lid from the vacuum insulated mug. That research has already been carried out and will be the result of a further report in this journal.
  • The second concerned the effect of milk addition which could significantly affect the time to reach the optimal drinking temperature. That research proposal is currently being considered by HBRC.

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*HBRC = Hot Beverage Research Council


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