What are the specific units of the function f with respect to the posson's heat equation?

General
1

So far I have to go by:

$$ -\kappa \nabla u = heat flux $$

$$ - \kappa \bigtriangleup u = f in \Omega $$

According to Mark S. Gockenbach says “From this equation the units of f can be determined.”

So at this point I know that heat flux is a known quantity with known SI and imperial units to go by for a heat flux quantity.

So supposing a heat problem with a mesh being measured in mm how might I determine it what the units of f are? (and or its classification of stuff that is being assigned to f what are they?)

2

See, for example Dimensional analysis - Wikipedia. The units of f for the heat equation are power per unit volume, \mathrm{M L}^{-1} \mathrm{T}^{-3}. SI units would be \mathrm{Wm}^{-3}.