Is this equation of in and output of a material right? 
$\rm Q_{absorb} =ΔU+Q_{thermal \ radiation} +Q_{heat \ conduction}$

(Suggesting no heat expansion)
Should I consider Fourier's law of conduction and the Stefan-Boltzmann law to specify it?
 A: Change in internal energy comes from

*

*Heat power being transferred into it (times time)


*Plus total work energy done on it, such as compression/expansion.


*Maybe chemical/nuclear depending


*Not phase transition as this is internal.
Heat goes in via

*

*Net radiation (yes by Stefan-Boltzman),


*Convection, which I don’t think you have included. This requires estimating a coefficient of convection. (If you are not assuming that youve reached steady state where the whole object is at around the same temperature, then you’ll need to determine internal thermal gradients, or use some estimating based on thermal diffusivity, because instantaneous convection depends on the object’s surface temperature not average temperature.)


*Plus contact conduction, in which case you need to estimate the thermal contact resistance and estimate the thermal gradients from the surface being contacted (or use some estimating based on thermal diffusivity). Technically needs to be done even if steady state - because the object could have temperature gradients that continue. If the contacting object(s) is transferring heat symmetrically/uniformly then this last step won’t be needed after all.
Steady state:
$$\Delta U= 0=~ \dot{q}_{conduct}~ t+  \dot{q}_{convect} ~t+  \dot{q}_{radiate} ~t + work$$
For varying
$$dU= \dot{q}_{conduct} ~dt+  \dot{q}_{convect} ~dt+  \dot{q}_{radiate}~ dt + dw$$
Which you could integrate for $\Delta U$
