How to formulate surface temperature of a material exposed to sunlight and wind? I am currently searching for a model or an approach (reference, course, demonstration) to formulate and estimate surface temperature of a known material (for example, concrete, metal), exposed to sunlight/wind, over a given period of time (day, week). The objective would be to be able to give an estimated time serie of the surface temperature based on local weather data.
The hypothesis I want to start with: 


*

*I consider the material homogenous, and the surface whose temperature I want to estiamte is flat ;

*I consider only one face (the studied face) to be exposed to sunlight/wind/other weather conditions (others faces are exposed to air temperature) ;

*I suppose I do not know the exact thickness or shape of my material (let's say a block of concrete)

*However, I know that my block of material is thick enough to not be considered as an infinitely small sheet. For example, I consider 2meters thick concrete. Semi-infinite thickness hypothesis can be assumed, if practical.

*I consider there isn't any rain/snow/ice


The data/parameters I have :


*

*Any thermodynamic properties of the material itself

*Time series of ambient air temperature, sunlight intensity (therefore if sunny or cloudy), windspeed.

*Position of the sun, and incidence angle of sunlight on my surface at any given time. 


I have started researching papers/courses about estimation of the surface temperature with similar inputs, finding some papers presenting specific applications and hypothesis valid in only certain scenarios or with specific materials, or only valid for maximum temperature. I am still searching for a more generic expression of the surface temperature (or if possible, temperature model in the first centimeters below the surface), considering I have access to properties of the material and significant weather data.
 A: The semi-infinite approximation will hold as long as the Fourier number
$$ Fo = \frac{\alpha t}{L^2} < 0.05$$
where $\alpha$ is the slab thermal diffusivity, $L$ is the slab thickness, and $t$ is time. So, for times $t <\frac{0.05L^2}{\alpha} $, we can make the semi-infinite approximation. 
You said you consider 2 m of concrete. I estimate $\alpha = \frac{k}{\rho c_p} = 5 \times 10^{-7} m^2/s$, thus the semi-infinite approximation will only be valid for $ t = \frac{0.05\times2^2}{5\times10^{-7}}=400,000$ seconds or ~ 4.5 days. You said you wanted to track the time for days/weeks, so I don't think we can apply the semi-infinite approximation for your purpose. 
If you still want to use the semi-infinite approximation, I suggest using the form derived in Carslaw and Jaeger, Chapter 2:
$$ \frac{T(x,t)-T_\infty}{T_0-T_\infty} = erf(\frac{\zeta}{2})+exp(\beta \zeta + \beta^2) \times erfc(\frac{\zeta}{2} + \beta)$$
where $\zeta = \frac{x}{\sqrt{\alpha t}} $, $\beta = \frac{\bar{h}\sqrt{\alpha t}}{k}$. If you want the surface temperature, simply set $x=0$ and then you have it as a function of time. 
You can use the effective heat transfer coefficient $\bar{h} = \bar{h}_{conv} + \bar{h}_{rad}$ which combines both convection and radiation heat transfer coefficients (which can change with time). 
Given that this solution is only valid for a 2 meter slab of concrete for 2 hours, however, I'm not sure if it's what you really want.
A 2 meter concrete slab will reach steady state in about $t = \frac{1.5*2^2}{5 \times 10^{-7}} = 12,000,000$ seconds or 138 days, so I also don't think steady-state solutions are useful to you.
In the regime that you're interested in (days/weeks) I suggest using series solutions or one-term approximations found in any heat transfer text. The series solutions are valid for all times. You can use an effective $\bar{h} = \bar{h}_{conv} + \bar{h}_{rad}$ in your boundary condition, which may change with time.
