boundary condition for temperature

ane

The boundary condition for temperature in the problem of unsteady boundary layer problem is

T = Tw at y = 0 and T = Te as y goes to infinity

when considering the following non-dimensional variables where the first one is theta = (T - Tw)/(Te - Tw)

and the second one is theta = (T - Te)/(Tw - Te),

we have for the first one T = 0 at y = 0, T = 1 at y infinity

and for the second one T = 1 at y = 0, T = 0 at y infinity

Note: Tw wall temperature, Te temperature far from the wall, theta dimensionless variable for temperature

can you explain what is the meaning of differences between these two cases and when we should apply the first one and the second one?