What is the difference between convection and conduction?
Convection is a mechanism that enhances conductive heat transport, rather than being a separate physical phenomenon.  It operates by bringing hotter parcels of fluid and colder parcels of fluid into closer physical proximity with one another so that conduction can take place more easily and rapidly.  One way this is accomplished is by shearing the fluid near a heated wall in such a way that the colder faster-moving layers further from the wall flow over the hotter slower-moving layers closer to the wall to physically cause the temperature gradient normal to the wall to increase.  This enhances the rate of conductive heat transfer.  Another situation is where the fluid is being mixed by a stirrer to create thin striations of hotter fluid and colder fluid throughout the fluid.  Conduction between these hotter and colder striations increases, again because of the much larger temperature gradients that have been created.  This is typical of how convection works.

What I'm saying is that the deformations experienced by the fluid while flowing are such that they cause the temperature gradients in the fluid to get higher, and this increases the rate of heat transfer.

Imagine a deck of cards split in half, with all the red cards (hot) in one half and all the black cards (cold) in the other half. If you bring these two slabs of hot and cold material together and wait, heat transfer will occur very slowly between the hot and cold regions. However, if you shuffle the deck so that there is a hot (red) card sandwiched in between every pair of cold (black) cards, and a cold (black) card sandwiched in between every pair of hot (red) cards, the heat transfer between the hot and cold layers will be much more rapid. This shuffling effect is what convection does.