# Thermodynamics of a Stone Patio

1. Feb 6, 2009

### sbe

1. The problem statement, all variables and given/known data

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?

2. Relevant equations

Black body radiation, Conduction and convection heat loss.

3. 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.