I am studying the non-dimensional heat equation, and was wondering what the quantity $$-\frac{\partial\theta}{\partial x}$$ represents. $\theta$ and $x$ are non-dimensional versions of temperature and distance respectively, e.g. $x=X/L$ where $X$ is normal distance, and $L$ is the length of the rod.
What does this quantity bein $0$ or $1$ or some other number actually mean?
EDIT: I asked this question on physics stack exchange in search for a more in depth answer. It is linked here.
$-\partial \theta/\partial x = 0$ means that if you go along on the rod there is no change in temperature or, in other words, that the temperature is constant w.r.t. to your position on the rod, indicated by $x$.
The number being nonzero you would have a linear decrease in temperature along the rod since
$$-\frac{\partial \theta}{\partial x} = k$$
where $k>0$ implies that
$$\theta = -kx$$
EDIT: In the case $k<0$ you would of course have a linear increase.