Describing the cooling of a room without any electrical or mechanical devices

[Fabioonier]

TL;DR Summary

Hoy is it possible to cool the air of a room just using ice?

Hello. I ask nothing here from a long time ago.
One of my students is doing research on how to cool the air in a room without using any electrical or mechanical devices. For example: using just ice.
What we need is how to solve/describe the process using math. For example: how to use/solve the Newton's cooling law in this case? Is this a convection case? What could be a good toy model to solve the math of this problem?
Thanks for your answers

 

[Chestermiller]

Are you able to say in words the physical mechanisms involved? Do you need only the final temperature, or do you need the average air temperature vs time?

 

[russ_watters]

In HVAC we don't typically bother with time to heat/cool calculations, we just need to know the load, which is a function of weather, envelope construction, ventilation and internal heat generation. But sure, stick a big block of ice in a room and it will cool. That's how we used to do refrigeration and why the Imperial unit of refrigeration is a big block of ice.

 

[Fabioonier]

Thanks, @Chestermiller for your question. I need to be more specific.
In general, let's suppose we have a room with air at a temperature T and we want to cool it to T' but we don't want to use air conditioner nor fans: just ice in a bucket, for example.
I think the process could be heat transfer by convection and I could use the Newton's Cooling Law, but I would want to know what "toy model" I could use to solve the equation: can I model the system like a ice rod surrounded by air?
The first problem that I found is that convection is defined as the transfer mechanism between a surface of a solid body and the surrouning fluid. The second problem that I found is that, typically, in those systems heat trasfers from the solid surface to the fluid and the fluid heats.
What we want to describe is how the air is cooled because of the ice... or if it would be possible to cool the air in a room usibg just ice in a bucket.
Thanks.

 

[Fabioonier]

In HVAC we don't typically bother with time to heat/cool calculations, we just need to know the load, which is a function of weather, envelope construction, ventilation and internal heat generation. But sure, stick a big block of ice in a room and it will cool. That's how we used to do refrigeration and why the Imperial unit of refrigeration is a big block of ice.

Hi, @russ_watters. Thanks for your answer.
What I want to know is the heat transfer process when you cool a room with a big block of ice. In your experience and research, is it a convection process? How could you use and solve an equation like the Newton's Cooling Law or heat tranfer by convection to describe it?
Thanks.

 

[russ_watters]

This thread is homework-style. Please repost in the appropriate homework help forum and provide your attempt at a solution. Thread locked.

 

[berkeman]

Thread is reopened at the request of @Chestermiller

 

[Chestermiller]

This is for the OP.

A basic principle of good modeling practice is to start with the simplest model you can think of and build complexity in later versions until you arrive at the version you desire. Why? If you can't solve a simpler model, you will never be able to solve the full model in all its complexity. Plus, with simpler models, you can get results in short order (which describe quantitatively much of what you are interested), and these earlier results can then be compared with results for more complex versions to get a quantitative picture of the effects of each model improvement.

OP, I would like you to look over the following excerpts from Transport Phenomena by Bird, Stewart, and Lightfoot to see if you can follow what they are doing in these two analyses: Section 10.9 Free Convection Heat Transfer and Problem 11.4-5 Free Convection Heat Transfer From a Vertical Plate. If you can follow these, we can proceed further.

 

[Lnewqban]

What I want to know is the heat transfer process when you cool a room with a big block of ice.

This specific case tends to keep both temperatures, the surface of the air and the air in the room close to have constant values.
That happens because the air in the room is normally cooled, but simultaneously heated by other sources of heat and humidity, such as persons, light fixtures, Sun radiation through glassing, roof and walls, etc.

Therefore, the difference in temperature mentioned by Newton may become more or less constant in a steady state of balanced heat fluxes.
The rate of heat loss of the air in the room to the ice, then will be also constant (untill all the ice is melted).

The room could even increase its internal air temperature, in a case in which the heat gain from those hot sources is greater than the cooling effect of our block of ice.

Please, see:
https://en.m.wikipedia.org/wiki/Heat_transfer_coefficient

https://en.m.wikipedia.org/wiki/Cooling_load

https://en.m.wikipedia.org/wiki/Ton_of_refrigeration

In the event of your students start contemplating the idea of free cooling via ice, please, mention to them that the water forming the block of ice was cooled by electricity and a machine, located far from that room.