Constant heat flux vs temperature

I'm trying to understand when to use MERM Eqn 36.28 vs Eqn 36.31.   It states that the former is used for constant heat flux and the latter for constant wall temp but what does this mean exactlly?  Just want to know if there is a rule of thumb for knowing when each is applicable based on problem statement parameters. Thanks. 

Your question seems to be what is the difference between constant temperature and constant heat flux?  That should be fairly obvious, but in case it is not: say you have a water flow rate through a pipe AND a burner applying heat to the pipe wall.  Wall temperature can be held constant for a given heat flux by controlling the temperature of the supply water and the rate of the supply water : if the rate and temperature of the water is enough to balance out the input heat, you get a constant wall temperature. If the water is too cold or the flow rate too high, it will cool the wall.  If the water temperature is too high or the flow rate too slow, you will heat the wall... for a given heat flux. Or, you could vary the input heat and maintain the wall temperature that way for a given water flow and temperature.

Of course, that is not always the case, because if you have a phase change in the system, the change of phase is able to absorb more heat.  So even for the same flow rate, if you add more heat, the wall temperature will stay the same (over a certain region).  But those Nusselt numbers aren't dealing with 2 phase heat exchange.