Heat transfer coefficient is used for heat transfer between fluid and the wall surface, not conduction through the wall. For a steady state, you would need 2 heat transfer coefficients $h_i$, $h_e$ and also wall conductivity $\lambda$. $$\dot{Q} = \left(T_{fi}-T_{wi}\right)\cdot A_i\cdot h_i = \left(T_{wi}-T_{we}\right)\cdot \frac{2\pi \lambda L}{\ln\left(\frac{r_e}{r_i}\right)} = \left(T_{we}-T_{fe}\right)\cdot A_e\cdot h_e$$ Increasing length is a little bit different than increasing radius, because fluid temperature will probably change along the length (in some situations this can be negligible). For inlet and outlet fluid temperatures $T_{fi0}$ and $T_{fi1}$ and thermal capacity $cp$: $$\dot{Q} = \left(T_{fi0}-T_{fi1}\right)\cdot \dot{m}\cdot cp$$

I am not sure what the question is, but differences in sensitivities to $r$ and $L$ are easily explained by $r$ influencing heat transfer area $\propto r$ but also cross-section area $\propto r^2$, so the net effect for $q\propto \frac{1}{r}$. On the other hand, $L$ influences just the heat transfer area, so $q\propto L$.

Heat transfer coefficient is used for heat transfer between fluid and the wall surface, not conduction through the wall. For a steady state, you would need 2 heat transfer coefficients $h_i$, $h_e$ and also wall conductivity $\lambda$. $$\dot{Q} = \left(T_{fi}-T_{wi}\right)\cdot A_i\cdot h_i = \left(T_{wi}-T_{we}\right)\cdot \frac{2\pi \lambda L}{\ln\left(\frac{r_e}{r_i}\right)} = \left(T_{we}-T_{fe}\right)\cdot A_e\cdot h_e$$ Increasing length is a little bit different than increasing radius, because fluid temperature will probably change along the length (in some situations this can be negligible). For inlet and outlet fluid temperatures $T_{fi0}$ and $T_{fi1}$ and thermal capacity $cp$: $$\dot{Q} = \left(T_{fi0}-T_{fi1}\right)\cdot \dot{m}\cdot cp$$

I am not sure what the question is, but differences in sensitivities to $r$ and $L$ are easily explained by $r$ influencing heat transfer area $\propto r$ but also cross-section area $\propto r^2$, so the net effect for $q\propto \frac{1}{r}$. On the other hand, $L$ influences just the heat transfer area, so $q\propto L$.

If you are interested in dependence on pipe length, it is better to use a more precise model, where a very short section of pipe with length $dx$ transfers small amount of heat $d\dot{Q}$ into the environment with constant temperature $T_e$ ($U$ is overall heat transfer coefficient per unit length of the pipe), which also changes temperature of the fluid in a pipe by $dT$:

$$d\dot{Q} = \left(T(x)-T_e\right)\cdot U = -dT\cdot \dot{m}\cdot cp$$

This is a simple differential equation, which you can directly integrate:

$$\int\limits_{T_{i0}}^{T(x)}\frac{1}{T(x)-T_e} dx = -\frac{U}{\dot{m}\cdot cp}\cdot \int\limits_0^x dx$$

This leads to a internal fluid temperature profile along the pipe $T(x)$:

$$T(x) = T_e+\left(T_{i0}-T_e\right)\cdot \exp\left(-\frac{U}{\dot{m}\cdot cp}\cdot x\right)$$

Here is an example: