Consider a hydrodynamically fully developed laminar flow through a circular pipe with the flow along the axis (i.e., $z$ direction). In the following statements, $T$ is the temperature of the fluid, $T_{w}$ is the wall temperature and $T_{m}$ is the bulk mean temperature of the fluid. Which one of the following statements is TRUE?
- For a thermally fully developed flow, $\frac{\partial T}{\partial z}=0$, always.
- For constant wall temperature of the duct, $\frac{d T_{m}}{d z}=$ constant.
- Nusselt number varies linearly along the $z$ direction for a thermally fully developed flow.
- For constant wall temperature ( $T_{w}>T_{m}$ ) of the duct, $\frac{d T_{m}}{d z}$ increases exponentially with distance along $z$ direction.