# Method to solve solar heat transfer equation

Solar radiation heat transfer between two surfaces is a fairly common problem for solar physics. The equations vary; but usually include the solar energy flux and thermal radiation from a surface described with the Stefan-Boltzmann equation. This is : phi= sigmaT^4. For two surfaces and a source, you get an equation like this: Total flux (watts/meter^2) (time,Temp_surface1, Temp_surface2)= solar flux+ sigma(temp_surface1)^4 + sigma*(temp_surface2)^4. This is a quartic equation with three variables. The examples I have seen hold time constant over an hour (e.g. Noon-1p.m.) and find solar flux from a table. That leaves the two surface temperatures (e.g. a metal absorbing plate and cover in a solar water heater) as unknowns. The Total flux becomes a function of the temperature of the two surfaces and the resultant IR radiation from the two surfaces. What is the best approach to analyze a system like this? I want to find a relation or relations between the two temperatures and then verify it by experiment using an IR meter (Extech).

• A good text is Solar Engineering of Thermal Processes by Duffie and Beckman
– user207455
Jun 8, 2019 at 18:33
• Thanks Mike. I have the 1973 edition and the 2013 edition. I'm trying to find a workable formula. Tried the ones on p.129 which suggest ~ an educated guess on the cover temperature and then refine the figures. That's sort of what I've been doing. I may be getting to something. I'm studying plastic covers and have some formulas from an article on solar air heaters. Link is ...citeseerx.ist.psu.edu/viewdoc/… Jun 9, 2019 at 19:26