Strange units of measurement of heat transfer coefficient in Newton's cooling law

In my finite element software there is the following equation:

in the original Newton's cooling law h has the units $W/(m^2 K)$. Why here it has the units $W/(m^3 K)$?

Thank you so much.

• It must be a typo. – Chet Miller May 2 '18 at 11:49
• Hello @ChesterMiller the units are right. Also in other windows and in other releases of the software there are the same units. – Gennaro Arguzzi May 2 '18 at 14:37
• Oh. I didn't notice the equation at the top of the window. Sorry. – Chet Miller May 2 '18 at 14:48
• $h_ext$ is not convective heat transfer coefficient. Your memory is correct and the terminology in the software is not. $h_ext$ is volumetric heat coefficient. $h_ext = h_c * a$ where $h_c$ is convective heat transfer coefficient and $a$ is the surface area per unit volume. – user115350 May 5 '18 at 22:26
• Hello @user115350 htrans and hc are different, in fact in software I can set hc=/=0 and htrans=0. – Gennaro Arguzzi May 6 '18 at 8:26

It looks like the heat source $Q$ is given in $W/m^3$.
Since $h=\frac{Q}{\Delta T}$ the units must be $W/(m^3 K)$.