And is there a term called local average heat transfer coefficient?
All heat transfer coefficients are local in the sense that they are based on conditions at one location. All heat transfer coefficients are instantaneous since heat is moving at any instant in time. There are tables of heat transfer coefficients for certain average conditions. As an example: there are coefficients for heat transfer between steam and cooling water in a shell and tube exchanger based on typical designs. These are useful for initial sizing of heat exchangers but are not used for the final design. Those coefficients are calculated for the specific conditions.
