We use "h" for "Convection heat transfer coefficient" in heat transfer, "h" for enthalpy in thermodynamics. please don't confuse those things because that are just a alphabet to mention some quantity.
In matlab pdetool uses "h" alphabet like h*u=r for Dirichlet b.c. This is to generalize the b.c that can be applied for complex problem where we are uncertain about exact boundary condition, where we can try partial weight to different boundary locations (especially in script file) and we can do different different simulations. In well-pose problem if we want to use b.c u=0; then we should give h=1; and r=0.
In Neumann b.c "q" acts similar to "h" in Dirichlet b.c.
In heat transfer, source(Q) is heat generated in the process and unit is joule. If u r doing some steady state analysis using numerical methods then we mostly define "Q" is heat produced per unit volume (J/m^3). If u r doing transient analysis (Q) is heat produced per unit volume per time (that is watt/m^3)
heat flux is denoted by (q): This is heat transferred per unit area. Here the heat may in joule or watt so unit of heat flux may be J/m^2 or W/m^2.
