I am studying the non dimensional heat equation for a finite rod, and have the quantity $$Q=-\frac{\partial \theta}{\partial x}$$ where $\theta$ and $x$ are non dimensional temperature and distance respectively. I was wondering what this quantity means.
Question 1: Is it heat flow in the positive x direction? Does it depend on direction at all?
Question 2: Since it is non-dimensional, does that make it heat flow relative to heat flow everywhere else, and so if say one end of a rod has a lot of heat loss and the other end doesn't lose as much, then $Q$ is quite small (like $0.1$) at the end where a lot of heat is not lost, and high at the other end ($2$)? And if heat loss everywhere is very low, but the same, then $Q=1$ everywhere?
Question 3: I also believe there to be some significance to the cases $Q=0$, $0<Q<1$, $Q=1$ and $Q>1$, so if someone could explain what these cases mean too, that would be very much appreciated. :)
EDIT
What do I think about these questions?
Q1) I think it represents heat flow in the positive x-direction, but I am not sure what this means at the end of a finite rod.
Q2) I think what I wrote is true (about what different values of $Q$ mean), and just wanted to check if I am right in thinking this.
Q3) I think $Q=0$ means heat stays constant at that point and doesn't flow, $0<Q<1$ means less heat flowing in the x-direction that other parts of the system, $Q=1$ means heat flow which is equal to the average heat flow over the whole system, $Q>1$ means more heat flowing the the x-direction that other parts of the system.
Are my beliefs correct?