How Much Heat Needs to be Removed to Cool a Stone Patio Below 105F?

In summary, the person is trying to determine how much heat needs to be removed from a flat surface made of either slate or bluestone in order to reduce the surface temperature to below 105F in full sunlight. They make assumptions about the materials and the environment, and mention the heat loss and heat gain components. They have calculated the heat loss and are now trying to calculate the surface temperature in order to determine the heat that needs to be removed.
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Homework Statement



I am trying to determine approximately how much heat I have to remove from a flat surface made of either 1) Slate or 2) Bluestone to reduce the surface temperature to below 105F in full sunlight. Assumptions are that that the stone is mortar set on top of a 4" concrete slab which is on top of a gravel base. The gravel and ground are dry.

I know from measurement that Slate in full sunlight, siting on the ground reaches a surface temperature of approximately 143F with no wind. Bluestone is approximately 8 F cooler.

What I'm assuming this means is that this is the temperature for which heat loss (black body radiation, conduction, convection) are in balance with heat gain which I assume is about 100 w/sf (please excuse all the mixing of units). So I guess my question is how much heat must I remove so the stone is in balance at 105F?


Homework Equations



Black body radiation, Conduction and convection heat loss.


The Attempt at a Solution



I calculated each of the components of the heat loss for the stone but I don't know how to calculate what the surface temperature should be (to see if it jives with my measurements) . Perhaps if I did I would see how to run the calculations the other way around ie start with a target temperature, calculate the heat losses. I'm thinking if I did then the difference between the two would be the heat I need to remove.
 
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  • #2
I calculated the total heat loss of the stone for both materials to be about 73.7 W/m2. Assuming I have an ambient temperature of 25C (77F) and a target temperature of 40C (104F) I then calculated the net heat gain to be 26.3 W/m2. So what I'm not sure is if this is the actual answer to my question or if I am missing something.
 

Related to How Much Heat Needs to be Removed to Cool a Stone Patio Below 105F?

1. What is the purpose of understanding the thermodynamics of a stone patio?

The purpose of understanding the thermodynamics of a stone patio is to better understand the heat transfer and energy flow within the patio. This can help with choosing appropriate materials and designing the patio for maximum comfort and efficiency.

2. How does the material of the stone patio affect its thermodynamics?

The material of the stone patio can greatly affect its thermodynamics. Different materials have different thermal conductivity and heat absorption properties, which can impact the temperature of the patio and its surroundings. For example, darker stones will absorb more heat from the sun compared to lighter stones.

3. What factors influence the thermodynamics of a stone patio?

Some of the main factors that influence the thermodynamics of a stone patio include the material and color of the stones, the amount of sunlight it receives, the type of foundation and base beneath the patio, and the surrounding environment and climate.

4. How can I improve the thermodynamics of my stone patio?

There are a few ways to improve the thermodynamics of a stone patio. One way is to choose lighter colored stones that will reflect more sunlight and reduce heat absorption. Another way is to incorporate shade elements, such as trees or umbrellas, to reduce the amount of direct sunlight on the patio. Additionally, proper insulation and ventilation can also help regulate the temperature of the patio.

5. Is it important to consider the thermodynamics of a stone patio in colder climates?

Yes, it is important to consider the thermodynamics of a stone patio in colder climates. Stone patios can retain heat and transfer it to the surrounding area, which can help keep the patio and adjacent spaces warmer during colder months. However, it's also important to consider proper drainage and moisture control to prevent the patio from becoming too cold and potentially causing damage.

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