Improving the temperature stability of a temperature controlled water bath

[jonlg_uk]

Hello, I have a temperature controlled water bath that is capable of controlling the temperature of the water to 0.2 degrees C. However this isn't good enough for my application and I require a greater level of stability. I want to place a metal box filled with oil inside the temperature controlled water bath in order to dampen down the temperature fluctuations that occur in the water.

Will this work? My intuition tells me that in order for this to work the specific heat capacity of the oil inside the metal box needs to be greater than the specific heat capacity of the water to have any effect.

Another factor I have consider is the viscosity of the oil. Because the oil is more thick than the water I may get areas inside that are hotter than others and because the oil does not circulate as readily as water I may get hot areas. For example the oil near the inside walls of the metal box will be hotter than the oil at the surface of oil as I do not intend to fully submerse the metal box in the water because I am worried that water will leak through the list of the metal box. I need a uniform temperature throughout the oil.

 

[Andy Resnick]

How large a volume do you require to have the temperature controlled to better than 0.2 K? How well do you have to control the temperature? What is the target temperature (i.e, 0 C? 40 C? 700C?)?

When we needed to hold temperature variations to less than 0.05K, we used Peltier devices, but the active volume was only about 1 cm x 1 cm x 10 cm.

 

[jonlg_uk]

The dimensions of the temperature bath is 274 x 330 x 559 (H x W x L). The volume of the metal box filled with inside the bath is 150 x 300 x 240.

The best performance I can get from the temperature controlled bath is 0.2 degrees C/hour when it is set to 35 degrees C.

I want to use the oil to dampen down this and see if I can reduce it to maybe 0.1 degrees per hour when it is set to 35 degrees C.

I am sure you can calculate the thermal fluctuations of the oil as a result of the water temperature varying. I just don't know about thermodynamics, thermal mass, diffusivity and heat capacity can solve this...N.B I am using silicone oil with a viscosity of 50 Centistokes.

 

[jonlg_uk]

Can anyone offer some help for my problem?

I thank you in advance :)

 

[jonlg_uk]

In the interest of offering something back to the website I will paste my notes I made on this subject:



I have investigated the effect of using a bain-marie method for improving temperature stability. The idea is to place a metal container of oil inside the temperature controlled water bath. I have been trying to figure out why this will work last night.

If we examine the equation for thermal diffusivity:

where:
k : thermal conductivity (SI units: W/(m·K))
p : density (kg/m³)
cp : specific heat capacity (J/(kg·K))


The definitions for the terms are:

Specific heat capacity, is the measurable physical quantity that characterizes the amount of heat required to change a substance's temperature by a given amount

Thermal conductivity is the property of a material's ability to conduct heat. Heat transfer across materials of high thermal conductivity will occur at a faster rate than across materials of low thermal conductivity.

The denominator of the thermal diffusivity expression above, p*cp , can be identified as the volumetric heat capacity with the SI unit of J/(m³·K). Also know as volume-specific heat capacity that describes the ability of a given volume of a substance to store internal energy while undergoing a given temperature change. It is very similar to the specific heat capacity. However specific heat capacity is based on the mass of the material, while volumetric heat capacity is based on a given volume. Multiplying the specific heat capacity(cp) by the material density (p) will give us volumetric heat capacity.

Substances with high thermal diffusivity rapidly adjust their temperature to that of their surroundings because they conduct heat quickly in comparison to their volumetric heat capacity or 'thermal bulk' and they generally do not require much energy from their surroundings to reach thermal equilibrium.

The thermal diffusivity of the materials that we are concerned with have been calculated in the following table:

By observing the calculated values for diffusivity in the table it is possible to conclude what will happen with a Bain-marie setup using silicon oil and water with a stainless steel container/pot.

As we can see water has a volumetric heat capacity three times greater than silicone oil. This means it has a greater the ability for a given volume to store internal energy while undergoing a given temperature change. Basically it means that water will take longer to reach equilibrium and has greater thermal inertia.
This is a good, because the main volume of the liquid will be water that will be less subject to temperature fluctuation.

Water also has a thermal conductivity 6 times greater than silicone oil. This means that any heat transferred from ambient or the heater coil will transfer at a faster rate across water than it would silicone oil.
This is again good, because it means that water will have more temperature uniformity and there will be less chances of having any localized hot spots.

Stainless steel has a thermal conductivity 26.666 times greater than water and 160 times greater than silicone oil. This means that the stainless steel container/pot will quickly reach temperature uniformity throughout, so it will heat the silicon oil inside of it equally.

Silicone oils volumetric heat capacity is 3 times less than water In heat transfer, meaning that it will take a shorter time to reach equilibrium. However its thermal silicone oil is 6 times less than water. Meaning silicone oils thermal diffusivity is half as much of water. This basically means that it will be slower and therefore take longer to adjust its temperature to its surroundings. This provides the is the dampening effect we are looking for.

So if we are seeing 0.1 degrees C increase in water temperature over a 5 min period, ignoring the stainless steel container/pot we can say that the temperature increase over that 5 min period in the oil will be 0.05 degrees C (0.1 *0.5).


*******UPDATE***********

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These calculations assume there is a equal volume of oil and water

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