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I have some results to share on the concept of low temperature cooking using long term stored heat. My idea was to combine interseasonal heat storage with low temperature cooking and build a cooker that was large enough and stored enough solar heat long enough, to cook for a whole town over winter. On Mars, the cooker woukd need to store heat over twice as long a period, but would also benefit from the fact that regolith is an excellent thermal insulator at Mars ambient pressure. This cooker is essentially a tank of hot water, surrounded by thermal insulation, with a tunnel at its base, which would serve as an oven.
All food can be safely cooked at temperatures greater than 68°C, which kills undesirable bacteria. Meat can be tenderised at temperatures between 55 and 65°C. So a temperature of 68°C will tenderise meat and kill bacteria. But for poultry a slightly higher temperature of 74°C is recommended. However, many vegetables require a cooking temperature of 80 - 90°C to properly soften. So I am going to assume a minimum cooking temperature of 90°C.
https://en.m.wikipedia.org/wiki/Low-temperature_cooking
https://en.m.wikipedia.org/wiki/Sous_vide
https://coldgbcprodstd.blob.core.window … _guide.pdf
Base case. The water tank is a right circular cylinder, 4m in diameter and 4m high. At its base, it sits upon a plinth some 0.5m thick made from aerated concrete blocks, with thermal conductivity k = 0.15W/m.K. The sides and top are insulated by 1m of loose, dry sand with k = 0.3W/m.K.
I had tinkered with the idea of modelling the scenario using a finite element spreadsheet. But I realised after a few screening calcs that a straightforward application of fourier's law would be only slightly pessimistic, overestimating thermal leakage by a few percent. My assumption is that the tank has a starting temperature of 100°C and the outside temperature is a constant 10°C. Applying fouriers law, I calculated the time taken to drop tank temperature to 90°C in 1°C increments, adjusting the thermal gradient each time.
Results: For the base case, the tank would drop in temperature from 100°C to 90°C in 12.6 days. The heat flux to the environment is 2.036kW at 100°C and 1.81kW at 90°C. Although the base case does not fulfil the design goal of storing summer heat for winter cooking, it could still be useful as a town cooker by absorbing intermittent electricity from a wind turbine. A 12.6 day cooldown period is enough to cover most lulls in wind power.
How do we increase the cooldown time further? By doubling the diameter of the tank, cooldown rate halves, because surface area per unit volume halves. By doubling the thickness of insulation and depth of the plinth, the rate of cooling halves again. By using a more efficient insulating material, cooldown can be extended further. The consecutive effect of each variable on increasing cooldown time (from 100 to 90°C):
Case 1: (base) - 12.6 days.
Case 2: Doubling tank diameter - 25.2 days.
Case 3: Doubling insulation thickness (2m) and plinth thickness (1m) - 50.4 days
Case 4: Swapping sand insulation (k = 0.3) to straw (k = 0.075) and increasing plinth thickness to 2m - 185 days (6 months).
Case 5: A 4m tank diameter, with 2m straw insulation and a 2m plinth - 85.3 days.
Case 4 meets the design requirement, as it would allow a community to cook year round on stored solar heat alone. However, unless the town happens to be large it may not be a desirable option, because the physical size of the tank (8m wide x 8m tall) and its insulation would constitute a significant capital cost.
Case 5 is for a tank with half these dimensions, but with better and thicker insulation. In locations where winter wind power resources are even moderately good, the base case (Case 1) or Case 5 is likely the best option, with the hot water tank provided with top up heat by a wind powered immersion heater. This can be activated intermittently when the wind provides more power than is needed for other applications. A time averaged power of 1.8kWe would be needed to keep the tank above 90°C for Case 1 and 0.27kWe (Case 5).
Last edited by Calliban (2024-04-25 17:22:10)
"Plan and prepare for every possibility, and you will never act. It is nobler to have courage as we stumble into half the things we fear than to analyse every possible obstacle and begin nothing. Great things are achieved by embracing great dangers."
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That puts the operating temperature in the range of an average high cooking temperature of a Crockpot is between 165 to 175 degrees Fahrenheit and possibly a bit higher over boiling.
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165F is low heat in a slow cooker (74°C). It turns out that vegetables will cook at that temperature. It just takes twice as long as it would at 100°C.
https://storables.com/articles/how-long … ow-cooker/
So my estimates may have been conservative. I will recalculate tomorrow. I would estimate that even the base I considered above, would take over 1 month to drop from 100°C to 74°C. Case 5 should provide year round cooking if we can allow temperature to drop that low.
Last edited by Calliban (2024-04-25 17:49:49)
"Plan and prepare for every possibility, and you will never act. It is nobler to have courage as we stumble into half the things we fear than to analyse every possible obstacle and begin nothing. Great things are achieved by embracing great dangers."
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District heating has long been popular in Nordic countries. In Denmark, some two-thirds of households are connected to a district heating network. Early systems distributed heat through steam with heat supplied by combined heat and power plants. The use of solar, geothermal and pumped heat, have prompted interest in distributing heat at lower temperatures. The logical end point of this is cold district heating.
https://en.m.wikipedia.org/wiki/Cold_district_heating
In this scenario, heat is distributed at 10-25°C and heat pumps use the cold water as a heat source, producing warm water at temperatures 30-60°C for heating. This is much more efficient than using cold air as a heat source, because water is denser, does not require high pumping power blowing it over a heat exchanger and is likely to be warmer than outside air if it is drawn from the sea and passed through the ground layer. A temperature of 10-25°C requires a smaller dT to provide warm water at 30°C, than air at say 5°C. So heat pumps supplied in this way will be more efficient.
Cold district heating is in some ways easier than hot water distribution, because the distribution pipework need not be heavily insulated. The soil above a buried pipe may provide sufficient insulation. But it has the disadvantage of requiring the use of heat pumps at the consumer end. In densely populated cities, we could compromise and install heat pumps that provide warm water to entire streets, using a cold water main as the heat source. In this scenario, cold water mains probably containing sea water, will pass beneath main streets. Heat pumps would serve branching roads, which would carry heat pipes at 30-40°C. The cold water mains would carry sea water, sourced at a temperature of about 10°C. We could boost this temperature up to say 20°C, by passing the pipe through soil that has been used to store summer heat. The heat collecting surfaces would be roads, carparks, building roofspace and decicated flat plate concrete solar collectors, which would reach temperatures up to 30°C in the summer sun.
It is noteworthy that district heating could provide heating for cooking applications as well. In this case, we want a minimum temperature of 74°C to slow cook food. A district cook house could take heat from a heat main at 30°C and use a heat pump to raise temperature to 74°C. Carnot COP would 6.89. I think a real system should be able to give us at least half of that COP.
"Plan and prepare for every possibility, and you will never act. It is nobler to have courage as we stumble into half the things we fear than to analyse every possible obstacle and begin nothing. Great things are achieved by embracing great dangers."
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One thing I neglected to include in the opening post of this thread, was the amount of heat consumed by food as it cooks. Ignoring the effects of evaporation, the specific heat of food varies significantly, but 3.7KJ/kg.K appears to be a good average. Let's say we cook 1 tonne of food per day - enough for 1000 people. The amount of heat the food will absorb just by heating from 10 to 90°C would be:
Q = 1000 x 3700 x 80 = 296MJ (82kWh).
That is almost twice as much heat as the store loses to conduction in the base case. This suggests to me that there is limited point in making the thermal store much larger than 4m in diameter or using much better insulation. The cooker is already almost as efficient as it can possibly be.
"Plan and prepare for every possibility, and you will never act. It is nobler to have courage as we stumble into half the things we fear than to analyse every possible obstacle and begin nothing. Great things are achieved by embracing great dangers."
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