I need a solution to the heat equation that shows temp increase in an object, e.g. a cube or sphere, in sunlight. The object is assumed to be exposed on all sides except one. It is a solid object with a certain surface emissivity and heat capacity. In other words, I don't care what is inside the object. It absorbs some light from the sun and heats up, and heat is radiated and convected in air so that it reaches an equilibrium temperature. The solution presumably uses the parabolic PDE and the Neumann boundary condition. A Matlab formulation would be great!
To the extent that convection is important, LOL. Temperature differences drive the fluid flows, which drive the heat loss. It would be a lot easier with a sphere than a cube, but the real problem is relating surface temperature with heat loss. If you put it in a vacuum, so you only had radiative losses, it would be easily tractable.