Trouble finding priming tube length (similar to boiler tube)

[DBrown89]

Hey guys. Been struggling with a problem for a bit and any help would be much appreciated. On a team designing a liquid fuel camp stove for an engineering class.

-Before fuel is combusted, it must be vaporized in priming tube.
-I am allowed to assume constant surface temperature on outer surface of tube. (Ts)
-Tube is divided into two regions.

-In region A, fuel is heated from tank temp (Tamb) to its boiling point (Tb). I think I have this section done, but I would not mind hearing alternate methods or confirming my own if it's convenient.​

-More importantly, in region B, fuel is vaporized as Ts and Tf (fuel temp = Tb) remain constant.​

I think everything will be known but length, which i am trying to find for each region

Given:
fuel properties (kerosene)
Ri and Ro (radii), if it helps Ri=~Ro
mdot

Assumptions:
constant Ts
frictionless
laminar flow


If values are needed to determine method
mdot=.000385
Ts=~1000K (Seems to high to me but thats what the teacher said so dont worry about it)
Ti=298K
Tb=~523K
Ri=.004m
Ro=.005m

Some of these values are undetermined, but should be within the ballpark

 

[DBrown89]

Oh and laminar flow is an assumption i asked my teacher if i could make. He said yes, but this does not necessarily mean it is a practical thing to do.