I need some thermodynamic physics anons to help me out here. Im trying to calculate temp 2 in pic related. it is assumed temp 1 is just the average year round temperature for a given solar flux, albedo and emissivity or in maths terms.
Ks(1-albedo)=4(sigma)T^4
where Ks is the solar constant and T= temperature.
Albedo 2 is a result of a bunch of sand spread over a 1km square area. i can easily calculated temperature 2 just using the above equation but how do i account for thermal transition along the perimeter and how do i calculate the minimum distance where the MAJORITY of the area under the sand is just temp ( because the smaller the sand covered area is the easier conduction will make the temperature uniform with the ground beside it)