Consider flow in a circular tube. Within the test section length $($between $1$ and $2)$ a constant heat

flux q$\_($s$)^(\text{'}\text{'})$ is maintained.

$7\mathrm{.}1.$ For the following two cases, sketch the surface temperature T$\_($s$)($x$)$ and the fluid mean

temperature T$\_($m$)($x$)$ as a function of distance along the test section x $.$

Case A: flow is hydrodynamically and thermally fully developed.

Case B: flow is not developed.

$7\mathrm{.}2.$ Assuming that the surface flux q$\_($s$)^(\text{'}\text{'})$ and the inlet mean temperature T$\_($m$,1)$ are identical for both

cases, will the exit mean temperature T$\_($m$,2)$ for case A be greater than, equal to$,$ or less than

T$\_($m$,2)$ for case B $?$

Briefly explain why.