Simulations: Levels of Consciousness

In a recent post I showed these results of simulations for our heat pump system:

I focused on the technical details – this post will be more philosophical.

What is a ‘simulation’ – opposed to simplified calculations of monthly or yearly average temperatures or energies? The latter are provided by tools used by governmental agencies or standardization bodies – allowing for a comparison of different systems.

In a true simulation the time intervals so small that you catch all ‘relevant’ changes of a system. If a heating system is turned on for one hour, then turned off again, he time slot needs to be smaller than one hour. I argued before that calculating meaningful monthly numbers requires to incorporate data that had been obtained before by measurements – or by true simulations.

For our system, the heat flow between ground and the water/ice tank is important. In our simplified sizing tool – which is not a simulation – I use average numbers. I validated them by comparing with measurements: The contribution of ground can be determined indirectly; by tallying all the other energies involved. In the detailed simulation I calculate the temperature in ground as a function of time and of distance from the tank, by solving the Heat Equation numerically. Energy flow is then proportional to the temperature gradient at the walls of the tank. You need to make assumptions about the thermal properties of ground, and a simplified geometry of the tank is considered.

Engineering / applied physics in my opinion is about applying a good-enough-approach in order to solve one specific problem. It’s about knowing your numbers and their limits. It is tempting to get carried away by nerdy physics details, and focus on simulating what you know exactly – forgetting that there are huge error bars because of unknowns.

This is the hierarchy I keep in mind:

On the lowest level is the simulation physics, that is: about modelling how ‘nature’ and system’s components react – to changes in the previous time slot. Temperatures change because energies flows, and energy flows because of temperature differences. The heat pump’s output power depends on heating water temperature and brine temperature. Energy of the building is ‘lost’ to the environment via heat conduction; heat exchangers immersed in tanks deposit energy there or retrieve it. I found that getting the serial connection of heat exchangers right in the model was crucial, and it required a self-consistent calculation for three temperatures at the same point of time, rather than trying to ‘follow round the brine’. I used the information on average brine temperatures obtained by these method to run a simplified version of the simulation using daily averages only – for estimating the maximum volume of ice for two decades.

So this means you need to model your exact hydraulic setup, or at least you need to know which features of your setup are critical and worthy to model in detail. But the same also holds for the second level, the simulation of control logic. I try to mirror production control logic as far as possible: This code determines how pumps and valves will react, depending on the system’s prior status before. Both in real life and in the simulation threshold values and ‘hystereses’ are critical: You start to heat if some temperature falls below X, but you only stop heating if it has risen above X plus some Delta. Typical brine-water heat pumps always provide approximately the same output power, so you control operations time and buffer heating energy. If Delta for heating the hot water buffer tank is too large, the heat pump’s performance will suffer. The Coefficient of Performance of the heat pump decreases with increasing heating water temperature. Changing an innocuous parameter will change results a lot, and the ‘control model’ should be given the same vigilance as the ‘physics model’.

Control units can be tweaked at different levels: ‘Experts’ can change the logic, but end users can change non-critical parameters, such as set point temperatures.We don’t restrict expert access in systems we provide the control unit for. But it make sense to require extra input for the expert level though – to prevent accidental changes.

And here we enter level 3 – users’ behavior. We humans are bad at trying to outsmart the controller.

[Life-form in my home] always sets the controller to ‘Sun’. [little sun icon indicating manually set parameters]. Can’t you program something so that nothing actually changes when you pick ‘Sun’?

With heat pumps utilizing ground or water sources – ‘built’ storage repositories with limited capacity – unexpected and irregular system changes are critical: You have to size your source in advance. You cannot simply order one more lorry load of wood pellets or oil if you ‘run out of fuel’. If the source of ambient energy is depleted, the heat pump finally will refuse to work below a certain source temperature. The heat pump’s rated power has match the heating demands and the size of the source exactly. It also must not be oversized in order to avoid turning on and off the compressor too often.

Thus you need good estimates for peak heat load and yearly energy needs, and models should include extreme weather (‘physics’) but also erratic users’ behaviour. The more modern the building, the more important spikes in hot tap water usage get in relation to space heating. A vendor of wood pellet stoves told me that delivering peak energy for hot water – used in private bathrooms that match spas – is a greater challenge today than delivering space heating energy. Energy certificates of modern buildings take into account huge estimated solar and internal energy gains – calculated according to standards. But the true heating power needed on a certain day will depend on the strategy or automation home owners use when managing their shades.

Typical gas boilers are oversized (in terms of kW rated power) by a factor of 2 or more in Germany, but with heat pumps you need to be more careful. However, this also means that heat pump systems cannot and should not be planned for rare peak demands, such as: 10 overnight guests want to shower in the morning one after the other, on an extremely cold day, or for heating up the building quickly after temperature had been decreased during a leave of absence.

The nerdy answer is that a smart home would know when your vacation ends and start heating up well in advance. Not sure what to do about the showering guests as in this case ‘missing’ power cannot be compensated by more time. Perhaps a gamified approach will work: An app will do something funny / provide incentives and notifications so that people wait for the water to heat up again. But what about planning for renting a part of the house out someday? Maybe a very good AI will predict what your grandchildren are likely to do, based on automated genetics monitoring.

The challenge of simulating human behaviour is ultimately governed by constraints on resources – such as the size of the heat source: Future heating demands and energy usage is unknown but the heat source has to be sized today. If the system is ‘open’ and connected to a ‘grid’ in a convenient way problems seem to go away: You order whatever you need, including energy, any time. The opposite is planning for true self-sufficiency: I once developed a simulation for an off-grid system using photovoltaic generators and wind power – for a mountain shelter. They had to meet tough regulations and hygienic standards like any other restaurant, e.g.: to use ‘industry-grade’ dishwashers needing 10kW of power. In order to provide that by solar power (plus battery) you needed to make an estimate on the number of guests likely to visit … and thus on how many people would go hiking on a specific day … and thus maybe on the weather forecast. I tried to factor in the ‘visiting probability’ based on the current weather.

I think many of these problem can be ‘resolved’ by recognizing that they are first world problems. It takes tremendous efforts – in terms of energy use or systems’ complexity – to obtain 100% availability and to cover all exceptional use cases. You would need the design heat load only for a few days every decade. On most winter days a properly sized heat pump is operating for only 12 hours. The simple, low tech solution would be to accept the very very rare intermittent 18,5°C room temperature mitigated by proper clothing. Accepting a 20-minute delay of your shower solves the hot water issue. An economical analysis can reveal the (most likely very small) trade-off of providing exceptional peak energy by a ‘backup’ electrical heating element – or by using that wood stove that you installed ‘as a backup’ but mostly for ornamental reasons because it is dreadful to fetch the wood logs when it is really cold.

But our ‘modern’ expectations and convenience needs are also reflected in regulations. Contractors are afraid of being sued by malicious clients who (quote) sit next their heat pump and count its operating cycles – to compare the numbers with the ones to be ‘guaranteed. In a weather-challenged region at more than 2.000 meters altitude people need to steam clean dishes and use stainless steel instead of wood – where wooden plates have been used for centuries. I believe that regulators are as prone as anybody else to fall into the nerdy trap described above: You monitor, measure, calculate, and regulate the things in detail that you can measure and because you can measure them – not because these things were top priorities or had the most profound impact.

Still harvesting energy from air - during a record-breaking cold January 2017

Heat Transport: What I Wrote So Far.

Don’t worry, The Subversive Elkement will publish the usual silly summer posting soon! Now am just tying up loose ends.

In the next months I will keep writing about heat transport: Detailed simulations versus maverick’s rules of thumb, numerical solutions versus insights from the few things you can solve analytically, and applications to our heat pump system.

So I checked what I have already written – and I discovered a series which does not show up as such in various lists, tags, categories:

[2014-12-14] Cistern-Based Heat Pump – Research Done in 1993 in Iowa. Pioneering work, but the authors dismissed a solar collector for economic reasons. They used a steady-state estimate of the heat flow from ground to the tank, and did not test the setup in winter.

Cistern-Based Water-Source Heat Pump System Design, 1993[2015-01-28] More Ice? Exploring Spacetime of Climate and Weather. A simplified simulation based on historical weather data – only using daily averages. Focus: Estimate of the maximum volume of ice per season, demonstration of yearly variations. As explained later (2017) in more detail I had to use information from detailed simulations though – to calculate the energy harvested by the collector correctly in such a simple model.

Simple simulations of volume of ice[2015-04-01] Ice Storage Challenge: High Score! Our heat pump created an ice cube of about 15m3 because we had turned the collector off. About 10m3 of water remained unfrozen, most likely when / because the ice cube touched ground. Some qualitative discussions of heat transport phenomena involved and of relevant thermal parameters.

Ice formation during the 'ice storage challenge'[2016-01-07] How Does It Work? (The Heat Pump System, That Is) Our system, in a slide-show of operating statuses throughput a typical year. For each period typical temperatures are given and the ‘typical’ direction of heat flow.

System in September - typical operations conditions[2016-01-22] Temperature Waves and Geothermal Energy. ‘Geothermal’ energy used by heat pumps is mainly stored solar energy. A simple model: The temperature at the surface of the earth varies sinusoidally throughout the year – this the boundary condition for the heat equation. This differential equation links the temporal change of temperature to its spatial variation. I solve the equation, show some figures, and check how results compare to the thermal diffusivity of ground obtained from measurements.

Measured 'wave' and propagation time[2016-03-01] Rowboats, Laser Pulses, and Heat Energy (Boring Title: Dimensional Analysis). Re-visiting heat transport and heat diffusion length, this time only analyzing dimensional relationships. By looking at the heat equation (without the need to solve it) a characteristic length can be calculated: ‘How far does heat get in a certain time?’

Temperature waves in ground - attenuation length of about 10 meters[2017-02-05] Earth, Air, Water, and Ice. Data analysis of the heating season 2014/15 (when we turned off the solar/air collector to simulate a harsher winter) – and an attempt to show energy storages, heat exchangers, and heat flows in one schematic. From the net energy ‘in the tank’ the contribution of ground can be calculated.

Energy storage, heat exchangers, heat flow[2017-02-22] Ice Storage Hierarchy of Needs. Continued from the previous post – bird’s eye view: How much energy comes from which sources, and which input parameters are critical? I try to answer when and if simple energy accounting makes sense in comparison to detailed simulations.

Hierarchy of needs - ambient energy in ice months[2017-05-02] Simulating Peak Ice. I compare measurements of the level in the tank with simulations of the evolution of the volume of ice. Simulations (1-minute intervals) comprise a model of the control logic, the varying performance factor of the heat pump, heat transport in ground, energy balances for the hot and cold tanks, and the heat exchangers connected in series.

Simulations of brine and tank temperature and volume of ice, based on system state in 1-minute intervals.(Adding the following after having published this post. However, there is no guarantee I will update this post forever ;-))

[2017-08-17] Simulations: Levels of Consciousness. Bird’s Eye View: How does simulating heat transport fit into my big picture of simulating the heat pump system or buildings or heating systems in general? I consider it part of the ‘physics’ layer of a hierarchy of levels.

Simulation - levels of consciousnessPlanned episodes? Later this year (2017) or next year I might write about the error made when considering simplified geometry – like modeling a linear 1D flow when the actualy symmetry is e.g. spherical.

Simulating Peak Ice

This year ice in the tank was finally melted between March 5 to March 10 – as ‘visual inspection’ showed. Level sensor Mr. Bubble was confused during the melting phase; thus it was an interesting exercise to compare simulations to measurements.

Simulations use the measured ambient temperature and solar radiation as an input, data points are taken every minute. Air temperature determines the heating energy needed by the house: Simulated heat load is increasing linearly until a maximum ‘cut off’ temperature.

The control logic of the real controller (UVR1611 / UVR16x2) is mirrored in the simulation: The controller’s heating curve determines the set temperature for the heating water, and it switches the virtual 3-way valves: Diverting heating water either to the hygienic storage or the buffer tank for space heating, and including the collector in the brine circuit if air temperature is high enough compared to brine temperature. In the brine circuit, three heat exchangers are connected in series: Three temperatures at different points are determined self-consistently from three equations that use underground tank temperature, air temperature, and the heat pump evaporator’s power as input parameters.

The hydraulic schematic for reference, as displayed in the controller’s visualization (See this article for details on operations.)

The Coefficient of Performance of the heat pump, its heating power, and its electrical input power are determined by heating water temperature and brine temperature – from polynomial fit curves to vendors’ data sheet.

So for every minute, the temperatures of tanks – hot and cold – and the volume of ice can be calculated from energy balances. The heating circuits and tap water consume energy, the heat pump delivers energy. The heat exchanger in the tank releases energy or harvests energy, and the collector exchanges energy with the environment. The heat flow between tank and ground is calculated by numerically solving the Heat Equation, using the nearly constant temperature in about 10 meters depth as a boundary condition.

For validating the simulation and for fine-tuning input parameters – like the thermal properties of ground or the building – I cross-check calculated versus measured daily / monthly energies and average temperatures.

Measurements for this winter show the artificial oscillations during the melting phase because Mr. Bubble faces the cliff of ice:

Simulations show growing of ice and the evolution of the tank temperature in agreement with measurements. The melting of ice is in line with observations. The ‘plateau’ shows the oscillations that Mr. Bubble notices, but the true amplitude is smaller:

2016-09 - 2017-03: Temperatures and ice formation - simulations.

Simulated peak ice is about 0,7m3 greater than the measured value. This can be explained by my neglecting temperature gradients within water or ice in the tank:

When there is only a bit of ice yet (small peak in December), tank temperature is underestimated: In reality, the density anomaly of water causes a zone of 4°C at the bottom, below the ice.

When the ice block is more massive (end of January), I overestimate brine temperature as ice has less than 0°C, at least intermittently when the heat pump is turned on. Thus the temperature difference between ambient air and brine is underestimated, and so is the simulated energy harvested from the collector – and more energy needs to be provided by freezing water.

However, a difference in volume of less than 10% is uncritical for system’s sizing, especially if you err on the size of caution. Temperature gradients in ice and convection in water should be less critical if heat exchanger tubes traverse the volume of tank evenly – our prime design principle.

I have got questions about the efficiency of immersed heat exchangers in the tank – will heat transfer deteriorate if the layer of ice becomes too thick? No, according also to this very detailed research report on simulations of ‘ice storage heat pump systems’ (p.5). We grow so-called ‘ice on coil’ which is compared to flat-plate heat exchangers:

… for the coil, the total heat transfer (UA), accounting for the growing ice surface, shows only a small decrease with growing ice thickness. The heat transfer resistance of the growing ice layer is partially compensated by the increased heat transfer area around the coil. In the case of the flat plate, on the contrary, also the UA-value decreases rapidly with growing ice thickness.

__________________________________

For system’s configuration data see the last chapter of this documentation.

Mr. Bubble Was Confused. A Cliffhanger.

This year we experienced a record-breaking January in Austria – the coldest since 30 years. Our heat pump system produced 14m3 of ice in the underground tank.

The volume of ice is measured by Mr. Bubble, the winner of The Ultimate Level Sensor Casting Show run by the Chief Engineer last year:

The classic, analog level sensor was very robust and simple, but required continuous human intervention:

Level sensor: The old way

So a multitude of prototypes had been evaluated …

Level sensors: The precursors

The challenge was to measure small changes in level as 1 mm corresponds to about 0,15 m3 of ice.

Mr. Bubble uses a flow of bubbling air in a tube; the measured pressure increases linearly with the distance of the liquid level from the nozzle:

blubber-messrohr-3

Mr. Bubble is fine and sane, as long as ice is growing monotonously: Ice grows from the heat exchanger tubes into the water, and the heat exchanger does not float due to buoyancy, as it is attached to the supporting construction. The design makes sure that not-yet-frozen water can always ‘escape’ to higher levels to make room for growing ice. Finally Mr. Bubble lives inside a hollow cylinder of water inside a block of ice. As long as all the ice is covered by water, Mr. Bubble’s calculation is correct.

But when ambient temperature rises and the collector harvests more energy then needed by the heat pump, melting starts at the heat exchanger tubes. The density of ice is smaller than that of water, so the water level in Mr. Bubble’s hollow cylinder is below the surface level of ice:

Mr. Bubble is utterly confused and literally driven over the edge – having to deal with this cliff of ice:

When ice is melted, the surface level inside the hollow cylinder drops quickly as the diameter of the cylinder is much smaller than the width of the tank. So the alleged volume of ice perceived by Mr. Bubble seems to drop extremely fast and out of proportion: 1m3 of ice is equivalent to 93kWh of energy – the energy our heat pump would need on an extremely cold day. On an ice melting day, the heat pump needs much less, so a drop of more than 1m3 per day is an artefact.

As long as there are ice castles on the surface, Mr. Bubble keeps underestimating the volume of ice. When it gets colder, ice grows again, and its growth is then overestimated via the same effect. Mr. Bubble amplifies the oscillations in growing and shrinking of ice.

In the final stages of melting a slab-with-a-hole-like structure ‘mounted’ above the water surface remains. The actual level of water is lower than it was before the ice period. This is reflected in the raw data – the distance measured. The volume of ice output is calibrated not to show negative values, but the underlying measurement data do:

Only when finally all ice has been melted – slowly and via thermal contact with air – then the water level is back to normal.

In the final stages of melting parts of the suspended slab of ice may break off and then floating small icebergs can confuse Mr. Bubble, too:

So how can we picture the true evolution of ice during melting? I am simulating the volume of ice, based on our measurements of air temperature. To be detailed in a future post – this is my cliffhanger!

>> Next episode.

Where to Find What?

I have confessed on this blog that I have Mr. Monk DVDs for a reason. We like to categorize, tag, painstakingly re-organize, and re-use. This is reflected in our Innovations in Agriculture …

The Seedbank: Left-over squared timber met the chopsaw.

The Nursery: Rebirth of copper tubes and newspapers.

… as well as in my periodical Raking The Virtual Zen Garden: Updating collections of web resources, especially those related to the heat pump system.

Here is a list of lists, sorted by increasing order of compactification:

But thanks to algorithms, we get helpful advice on presentation from social media platforms: Facebook, for example, encouraged me to tag products in the following photo, so here we go:

“Hand-crafted, artisanal, mobile nursery from recycled metal and wood, for holding biodegradable nursery pots.” Produced without crowd-funding and not submitted to contests concerned with The Intersection of Science, Art, and Innovation.

Ice Storage Hierarchy of Needs

Data Kraken – the tentacled tangled pieces of software for data analysis – has a secret theoretical sibling, an older one: Before we built our heat source from a cellar, I developed numerical simulations of the future heat pump system. Today this simulation tool comprises e.g. a model of our control system, real-live weather data, energy balances of all storage tanks, and a solution to the heat equation for the ground surrounding the water/ice tank.

I can model the change of the tank temperature and  ‘peak ice’ in a heating season. But the point of these simulations is rather to find out to which parameters the system’s performance reacts particularly sensitive: In a worst case scenario will the storage tank be large enough?

A seemingly fascinating aspect was how peak ice ‘reacts’ to input parameters: It is quite sensitive to the properties of ground and the solar/air collector. If you made either the ground or the collector just ‘a bit worse’, ice seems to grow out of proportion. Taking a step back I realized that I could have come to that conclusion using simple energy accounting instead of differential equations – once I had long-term data for the average energy harvesting power of the collector and ground. Caveat: The simple calculation only works if these estimates are reliable for a chosen system – and this depends e.g. on hydraulic design, control logic, the shape of the tank, and the heat transfer properties of ground and collector.

For the operations of the combined tank+collector source the critical months are the ice months Dec/Jan/Feb when air temperature does not allow harvesting all energy from air. Before and after that period, the solar/air collector is nearly the only source anyway. As I emphasized on this blog again and again, even during the ice months, the collector is still the main source and delivers most of the ambient energy the heat pump needs (if properly sized) in a typical winter. The rest has to come from energy stored in the ground surrounding the tank or from freezing water.

I am finally succumbing to trends of edutainment and storytelling in science communications – here is an infographic:

Ambient energy needed in Dec/Jan/Fec - approximate contributions of collector, ground, ice

(Add analogies to psychology here.)

Using some typical numbers, I am illustrating 4 scenarios in the figure below, for a  system with these parameters:

  • A cuboid tank of about 23 m3
  • Required ambient energy for the three ice months is ~7000kWh
    (about 9330kWh of heating energy at a performance factor of 4)
  • ‘Standard’ scenario: The collector delivers 75% of the ambient energy, ground delivers about 18%.
  • Worse’ scenarios: Either collector or/and ground energy is reduced by 25% compared to the standard.

Contributions of the three sources add up to the total ambient energy needed – this is yet another way of combining different energies in one balance.

Contributions to ambient energy in ice months - scenarios.

Ambient energy needed by the heat pump in  Dec+Jan+Feb,  as delivered by the three different sources. Latent ‘ice’ energy is also translated to the percentage of water in the tank that would be frozen.

Neither collector nor ground energy change much in relation to the base line. But latent energy has to fill in the gap: As the total collector energy is much higher than the total latent energy content of the tank, an increase in the gap is large in relation to the base ice energy.

If collector and ground would both ‘underdeliver’ by 25% the tank in this scenario would be frozen completely instead of only 23%.

The ice energy is just the peak of the total ambient energy iceberg.

You could call this system an air-geothermal-ice heat pump then!

____________________________

Continued: Here are some details on simulations.

Earth, Air, Water, and Ice.

In my attempts at Ice Storage Heat Source popularization I have been facing one big challenge: How can you – succinctly, using pictures – answer questions like:

How much energy does the collector harvest?

or

What’s the contribution of ground?

or

Why do you need a collector if the monthly performance factor just drops a bit when you turned it off during the Ice Storage Challenge?

The short answer is that the collector (if properly sized in relation to tank and heat pump) provides for about 75% of the ambient energy needed by the heat pump in an average year. Before the ‘Challenge’ in 2015 performance did not drop because the energy in the tank had been filled up to the brim by the collector before. So the collector is not a nice add-on but an essential part of the heat source. The tank is needed to buffer energy for colder periods; otherwise the system would operate like an air heat pump without any storage.

I am calling Data Kraken for help to give me more diagrams.

There are two kinds of energy balances:

1) From the volume of ice and tank temperature the energy still stored in the tank can be calculated. Our tank ‘contains’ about 2.300 kWh of energy when ‘full’. Stored energy changes …

  • … because energy is extracted from the tank or released to it via the heat exchanger pipes traversing it.
  • … and because heat is exchanged with the surrounding ground through the walls and the floor of the tank.

Thus the contribution of ground can be determined by:

Change of stored energy(Ice, Water) =
Energy over ribbed pipe heat exchanger + Energy exchanged with ground

2) On the other hand, three heat exchangers are serially connected in the brine circuit: The heat pump’s evaporator, the solar air collector, and the heat exchanger in the tank. .

Both of these energy balances are shown in this diagram (The direction of arrows indicates energy > 0):

Energy sources, transfer, storage - sign conventions

The heat pump is using a combined heat source, made up of tank and collector, so …

Ambient Energy for Heat Pump = -(Collector Energy) + Tank Energy

The following diagrams show data for the season containing the Ice Storage Challenge:

Season 2014 - 2015: Monthly Energy Balances: Energy Sources, Transfer, Storage

From September to January more and more ambient energy is needed – but also the contribution of the collector increases! The longer the collector is on in parallel with the heat pump, the more energy can be harvested from air (as the temperature difference between air and brine is increased).

As long as there is no ice the temperature of the tank and the brine inlet temperature follow air temperature approximately. But if air temperature drops quickly (e.g. at the end of November 2014), the tank is still rather warm in relation to air and the collector cannot harvest much. Then the energy stored in the tank drops and energy starts to flow from ground to the tank.

2014-09-01 - 2015-05-15: Temperatures and ice formation

2014-09-01 - 2015-05-15: Daily Energy Balances: Energy Sources, Transfer, Storage

On Jan 10 an anomalous peak in collector energy is visible: Warm winter storm Felix gave us a record harvest exceeding the energy needed by the heat pump! In addition to high ambient temperatures and convection (wind) the tank temperature remained low while energy was used for melting ice.

On February 1, we turned off the collector – and now the stored energy started to decline. Since the collector energy in February is zero, the energy transferred via the heat exchanger is equal to the ambient energy used by the heat pump. Ground provided for about 1/3 of the ambient energy. Near the end of the Ice Storage Challenge (mid of March) the contribution of ground was increasing while the contribution of latent energy became smaller and smaller: Ice hardly grew anymore, allegedly after the ice cube has ‘touched ground’.

Mid of March the collector was turned on again: Again (as during the Felix episode) harvest is high because the tank remains at 0°C. The energy stored in the tank is replenished quickly. Heat transfer with ground is rather small, and thus the heat exchanger energy is about equal to the change in energy stored.

At the beginning of May, we switched to summer mode: The collector is turned off (by the control system) to keep tank temperature at 8°C as long as possible. This temperature is a trade-off between optimizing heat pump performance and keeping some energy for passive cooling. The energy available for cooling is reduced by the slow flow of heat from ground to the tank.