Does the transfer of energy take place when you push a huge rock with all your might and fail to move it? Where is the energy you spend going?

(N/A) In physics,work is defined as the product of force and displacement $(W = F \times s)$. Since the rock does not move,the displacement $(s)$ is $0$,meaning no mechanical work is done on the rock.
However,energy is still being expended by your body. When you push the rock,your muscles contract and perform internal work. This energy is primarily dissipated as heat into the environment and the contact surface between your hands and the rock. $A$ negligible amount may be stored as elastic potential energy due to the slight deformation of the rock's surface.