Duty of indirect fired heat

[MortenA]

This question is about the duty of a gas heater of the "water" bath type (indirect fired heater).

Its regarding the actual duty when moving away from the gas design flow rate but requiring the same duty (e.i. increased dT(gas).

E.g:

Design:

Gas flow rate=1000000 kg/hr
Tin=-10 deg C
Tout=-5 deg C

Upset condition:
Tin=-20 dec C
Tout=-5 deg C =>

decreased gas flow rate since no additional heat exchangers is available

For a "normal" heat exchanger this will mean that the actual duty decreases if the hot side inlet temp is kept constant because of the reduced inside (gas side) heat transfer coefficient. You then have to itterate to find the actual gas flow rate and corresponding heating medium outlet temperature.

But for an indirect heater i would assume that the temperature of the heat transfer medium would increase until the driving temperature difference was sufficiently high to "get rid of the fired heat". This is off course disregarding increased loss to surronding through exhaust, vessel sides etc.

Is this correct and is the increase in loss small when flow decrease is large?