What is the process of main way the energy is transfered through the copper wall of the water tank?

You need to study the material more carefully, paying special attention to what the words mean. Energy is not a physical unit. It is a philosophical concept and an accounting technique used to analyze mechanical and chemical exchanges. In nuclear physics it is defined as a wavelength of light, in biology it is a synonym for metabolism, and in public utilities they say energy when they mean connectivity. Anybody who uses the word in any other context either does not know what he is talking about, or is peddling something you don't need.

What you are talking about is heat, and the word you are looking for is 'conduction'. Now get a dictionary or go to dictionary.com and study what 'conduction' really means.

*Some people will tell you that energy is capacity to do work. But work is capacity to do disordering of energy. So then energy is capacity to do disordering of energy. That is called a circular definition, using a word to define itself.