Hey @LiamRuvio ,
Your script seems like a pretty reasonable steady state model if you are trying to understand the average temperature of the 0.2m thick asphalt layer over the course of a day. On that time scale, it makes sense to use the total daily radiation and I would expect the thermal diffusivity of asphalt to allow the heat to penetrate 0.2 meters deep into the material over that time. If you wanted to account for the convective and radiative losses to the air and surrounding environment, you could do a few iterations of re-computing the surface temperature using the Delta T and some standard heat transfer coefficients, like the ones you might find in the ASHRAE handbook of fundamentals. You can see that we use some of those methods in this part of honeybee when we estimate the U-Factor of constructions.
But I am sure that your surface is getting much hotter than what your script is showing during the peak condition where the sun is intensely focused on the top most layer of the asphalt and not much time has passed to enable the heat to conduct into the ground or convect/radiate off the surface. So you could probably adjust your script to better understand this condition by looking at the radiation over a very short period of time (eg. the length of time the material is in the focal point) and you can lower the thickness to a depth that you would expect the heat to conduct to in that time given the Thermal Diffusivity of asphalt. At that time scale, you can probably also ignore the convective and radiative component unless it’s more than an hour or so.
Simple steady state models like that can be really useful for adjusting things like the material solar absorptance or heat capacity and understanding how they will influence the temperature. And, assuming that you’ve estimated the input radiation correctly with a detailed Radiance simulation, the results probably won’t be that far from reality.
It’s also possible to build some more sophisticated transient models using similar methods but, at that point, I usually find it easier to “hack” EnergyPlus to get it to do what I want rather than scripting up a whole new model. For a case like this, I might simulate a single “ground zone” with an asphalt top over the course of a day and overwrite the diffuse EPW radiation values to be equal to the radiation results of the Radiance simulation (setting the direct sun to zero) since I know that EnergyPlus can’t model the radiation accurately on its own. EnergyPlus even has some methods for scheduling the solar radiation on design days if you really wanted to get into results at fine timesteps.
But these types of custom-built workflows are how most engineers and product designers build heat transfer models, whether they are testing the heat given off within an electrical appliance or they’re estimating the temperature of a sun shield for a space craft.