Lumped capacitance model if you insure the interior is well mixed?

In summary, the conversation discusses the speaker's experimental heat loss calculations on a sealed cube filled with hot water and placed in a larger tank of cooler fluid. The speaker is struggling to determine the applicability of the lumped capacitance model and the appropriate heat transfer coefficient to use. They also mention using a stirrer to maintain a uniform temperature within the cube and adjusting for heat flux from the stirrer. They ask for tips or guidance on calculating the Biot number in this setup.
  • #1
smithy360
8
0
Hi everybody. I have been doing some experimental heat loss calculations on a sealed cube of fluid, filling the volume of the cube with hot water then sitting it in a larger tank of fluid at a fixed cooler temperature and monitoring the drop of temperature inside the box. I have also positioned a stirrer inside the cube to maintain a uniform temperature within.

I am struggling to verify if the lumped capacitance model is applicable in terms of Biot number, I don't know what would be best to take as the value for the heat transfer coefficient in this situation. Will Newton's law of cooling be okay to apply given I am insuring that the temperature within the cube stays uniform at all times? The values I get from the calculations certainly seem in line with what I would expect, I just want to be able to justify it. (I should also say I am adjusting for the slight heat flux put into the system from the stirrer).

Any tips would be helpful, or even some guidance on how to calculate the Biot number in this setup would be great.

Kind regards.
 
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  • #2
Does anybody have any suggestions on how to calculate the Biot number in this setup as a starting point?

Many thanks again.
 

What is a lumped capacitance model?

A lumped capacitance model is a simplified approach for analyzing heat transfer in a system, assuming that the entire system can be treated as a single uniform temperature. It is commonly used in situations where the temperature gradient within the system is small and the thermal properties are constant.

How does the lumped capacitance model work?

The lumped capacitance model uses the concept of thermal capacitance, which is the ability of a material to store heat. It assumes that the entire system can be treated as a single thermal capacitance, and the rate of heat transfer is proportional to the temperature difference between the system and its surroundings.

Why is it important to insure the interior is well mixed in a lumped capacitance model?

In order for the lumped capacitance model to accurately predict the temperature of the system, it is important to ensure that the interior of the system is well mixed. This means that the temperature within the system is uniform and there are no significant temperature gradients. If the interior is not well mixed, the model may not accurately predict the temperature and heat transfer within the system.

What are some examples of systems where the lumped capacitance model is commonly used?

The lumped capacitance model is commonly used in situations where the temperature gradient within the system is small and the thermal properties are constant. Some examples include electronic devices, food processing, and chemical reactors.

What are the limitations of the lumped capacitance model?

The lumped capacitance model is a simplified approach and may not accurately predict the temperature in systems with large temperature gradients or varying thermal properties. It also assumes that the system is at steady-state, which may not always be the case. Additionally, it may not be suitable for systems with complex geometries or transient heat transfer processes.

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