What is Log Mean Temperature difference? Should it be considered as average temperature difference or not & why?

LMTD is not the Average temperature difference. It is used to determine the temperature driving force for heat transfer in flow systems most notably in the design of Heat Exchangers. LMTD is temperature difference between the hot and cold feeds/fluids at each end of the double pipe exchanger. The more the LMTD the more good Heat Transfer takes place. But its Calculation varies based on the flow properties and conditions. 

LMTD is not an  average temperature difference. It is used in sizing and designing of a heat exchanger. LMTD covers the effect of temperature variation by both fluids , cold and hot.It includes the effect of inlet and outlet temperatures of cold and hot fluids and gives more accurate results.