Thermal diffusion equation with heat per unit length?

Let us say we have a metal rod. Along that rod there is a rate of heat generation of H per unit length. If we assume we are in the steady state then I would expect us (from the thermal diffusion equation) to have the following expression:
$$kappa frac{partial^2 T}{partial x^2}=-frac{H}{A}$$
Where $A$ is the cross sectional area of the rod. I have however seen this written* instead as:
$$kappa frac{partial^2 T}{partial x^2}=-H$$

Which of these is right and why?

*Blundell, S. and Blundell, K., Concepts in thermal physics, 2nd ed, page 101