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